From 44c646565df991c25c676a9e43be42b50fa71c2c Mon Sep 17 00:00:00 2001 From: Camille Date: Wed, 28 Dec 2022 16:21:50 +0100 Subject: [PATCH 01/39] Testing the pymapdl.convert_script by adding vm12 --- doc/source/verif-manual/vm-012/vm12.py | 130 +++++++++++++++++++++++++ 1 file changed, 130 insertions(+) create mode 100644 doc/source/verif-manual/vm-012/vm12.py diff --git a/doc/source/verif-manual/vm-012/vm12.py b/doc/source/verif-manual/vm-012/vm12.py new file mode 100644 index 000000000..cd4729dac --- /dev/null +++ b/doc/source/verif-manual/vm-012/vm12.py @@ -0,0 +1,130 @@ +"""VM12 COMBINED BENDING AND TORSION""" + +""" +Problem Description: + - +Reference: + - C*** USING PIPE16 STR. OF MATL., TIMOSHENKO, + PART 1, 3RD ED., PAGE 299, PROB. 2 +""" + +from ansys.mapdl.core import launch_mapdl + +# start mapdl and clear it +mapdl = launch_mapdl(loglevel="WARNING", print_com=True) +mapdl.clear() # optional as MAPDL just started + +# enter verification example mode and the pre-processing routine +mapdl.verify("vm12") +mapdl.prep7() + +mapdl.antype("STATIC") +mapdl.et(1, "PIPE16") +mapdl.r(1, 4.67017, 2.33508) # REAL CONSTANTS FOR SOLID CROSS SECTION +mapdl.mp("EX", 1, 30e6) +mapdl.mp("NUXY", 1, 0.3) +mapdl.n(1) +mapdl.n(2, "", "", 300) +mapdl.e(1, 2) +mapdl.d(1, "ALL") +mapdl.f(2, "MZ", 9000) +mapdl.f(2, "FX", -250) +mapdl.finish() +mapdl.slashsolu() +mapdl.outpr("BASIC", 1) +with mapdl.non_interactive: + mapdl.run("/OUT,SCRATCH") + mapdl.solve() + mapdl.finish() + mapdl.post1() + mapdl.etable("P_STRS", "NMISC", 86) + mapdl.etable("SHR", "NMISC", 88) + mapdl.run("/OUT") + mapdl.run("/GOPR") +mapdl.last_response +mapdl.get("P_STRESS", "ELEM", 1, "ETAB", "P_STRS") +mapdl.get("SHEAR", "ELEM", 1, "ETAB", "SHR") +mapdl.dim("LABEL", "CHAR", 2, 2) +mapdl.dim("VALUE", "", 2, 3) +mapdl.run("LABEL(1,1) = 'MAX PRIN','MAX SH S'") +mapdl.run("LABEL(1,2) = 'STRS psi','TRS psi '") +mapdl.vfill("VALUE(1", "1)", "DATA", 7527, 3777) +mapdl.vfill("VALUE(1", "2)", "DATA", "P_STRESS", "(SHEAR/2)") +mapdl.vfill("VALUE(1", "3)", "DATA", "ABS(P_STRESS/7527 )", "ABS((SHEAR/2)/3777 )") +mapdl.save("TABLE_1") +mapdl.run("FINI") +mapdl.run("/CLEAR,NOSTART") + +mapdl.prep7() +mapdl.run("C*** USING PIPE288") +mapdl.run("ANTYPE,STATIC") +mapdl.et(1, "PIPE288", "", "", "", 2) +mapdl.sectype(1, "PIPE") +mapdl.secdata(4.67017, 2.33508) +mapdl.keyopt(1, 3, 3) # CUBIC SHAPE FUNCTION +mapdl.mp("EX", 1, 30e6) +mapdl.mp("NUXY", 1, 0.3) +mapdl.n(1) +mapdl.n(2, "", "", 300) +mapdl.e(1, 2) +mapdl.d(1, "ALL") +mapdl.f(2, "MZ", 9000) +mapdl.f(2, "FX", -250) +mapdl.finish() + +mapdl.slashsolu() +mapdl.outpr("BASIC", 1) +with mapdl.non_interactive: + mapdl.run("/OUT,SCRATCH") + mapdl.solve() + mapdl.finish() + mapdl.post1() + mapdl.set("LAST") + mapdl.graphics("POWER") + mapdl.eshape(1) + mapdl.view(1, 1, 1, 1) + mapdl.plesol("S", 1) + mapdl.run("/OUT") + mapdl.run("/GOPR") +mapdl.get("P_STRESS", "PLNSOL", 0, "MAX") +mapdl.plesol("S", "INT") +mapdl.get("SHEAR", "PLNSOL", 0, "MAX") +mapdl.dim("LABEL", "CHAR", 2, 2) +mapdl.dim("VALUE", "", 2, 3) +mapdl.run("LABEL(1,1) = 'MAX PRIN','MAX SH S'") +mapdl.run("LABEL(1,2) = 'STRS psi','TRS psi '") +mapdl.vfill("VALUE(1", "1)", "DATA", 7527, 3777) +mapdl.vfill("VALUE(1", "2)", "DATA", "P_STRESS", "(SHEAR/2)") +mapdl.vfill("VALUE(1", "3)", "DATA", "ABS(P_STRESS/7527 )", "ABS((SHEAR/2)/3777 )") +mapdl.save("TABLE_2") +mapdl.run("FINI") +mapdl.run("/CLEAR,NOSTART") +mapdl._run("/NOPR") # It is not recommended to use '/NOPR' in a normal PyMAPDL session. +mapdl.com("") + +with mapdl.non_interactive: + mapdl.run("/OUT,vm12,vrt") + mapdl.com("------------------- VM12 RESULTS COMPARISON ---------------------") + mapdl.com("") + mapdl.com("| TARGET | Mechanical APDL | RATIO") + mapdl.com("") + mapdl.resume("TABLE_1") + mapdl.com("USING PIPE16") + mapdl.com("") + mapdl.run("*VWRITE,LABEL(1,1),LABEL(1,2),VALUE(1,1),VALUE(1,2),VALUE(1,3)") + mapdl.run("(1X,A8,A8,' ',F10.0,' ',F12.0,' ',1F15.3)") + mapdl.com("") + mapdl.resume("TABLE_2") + mapdl.com("USING PIPE288") + mapdl.com("") + mapdl.run("*VWRITE,LABEL(1,1),LABEL(1,2),VALUE(1,1),VALUE(1,2),VALUE(1,3)") + mapdl.run("(1X,A8,A8,' ',F10.0,' ',F12.0,' ',1F15.3)") + mapdl.com("") + mapdl.com("-----------------------------------------------------------------") + mapdl.run("/OUT") + mapdl.run("/GOPR") + +mapdl.finish() +mapdl.starlist("vm12", "vrt") + +mapdl.exit() From a5edbfa67a2f12105ad5282856fd66e2c732b51b Mon Sep 17 00:00:00 2001 From: Camille Date: Thu, 29 Dec 2022 12:31:05 +0100 Subject: [PATCH 02/39] Trying to change a doc dependency --- requirements/requirements_doc.txt | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/requirements/requirements_doc.txt b/requirements/requirements_doc.txt index 580d8247e..3d55d213b 100644 --- a/requirements/requirements_doc.txt +++ b/requirements/requirements_doc.txt @@ -8,7 +8,7 @@ pyvista==0.37.0 vtk==9.1.0 # Documentation dependencies -Sphinx==5.3.0 +Sphinx==5.2.3 numpydoc==1.5.0 ansys-sphinx-theme==0.8.0 sphinx-copybutton==0.5.1 From ec93aa45acb917ac8b44d6dd8b7d1f41b1a37840 Mon Sep 17 00:00:00 2001 From: Camille Date: Mon, 16 Jan 2023 12:20:16 +0100 Subject: [PATCH 03/39] Using Sphinx Gallery with VM files --- .gitignore | 1 + doc/source/_static/README.md | 1 - doc/source/_static/vm10_setup.png | Bin 0 -> 19771 bytes doc/source/_static/vm10_setup_1.png | Bin 0 -> 48079 bytes doc/source/_static/vm1_setup.png | Bin 0 -> 64584 bytes doc/source/_static/vm2_setup.png | Bin 0 -> 19064 bytes doc/source/_static/vm3_setup.png | Bin 0 -> 13541 bytes doc/source/_static/vm4_setup.png | Bin 0 -> 21913 bytes doc/source/_static/vm5_setup.png | Bin 0 -> 11501 bytes doc/source/_static/vm6_setup.png | Bin 0 -> 36859 bytes doc/source/_static/vm7_setup.png | Bin 0 -> 8814 bytes doc/source/_static/vm7_setup_1.png | Bin 0 -> 7864 bytes doc/source/_static/vm7_setup_2.png | Bin 0 -> 33578 bytes doc/source/_static/vm8_setup.png | Bin 0 -> 7688 bytes doc/source/_static/vm9_setup.png | Bin 0 -> 18432 bytes doc/source/_static/vm9_setup_2.png | Bin 0 -> 75708 bytes doc/source/conf.py | 23 +- doc/source/index.rst | 1 + examples/verif-manual/README.txt | 3 + ...y_indeterminate_reaction_force_analysis.py | 146 +++++ .../vm-002-beam_stresses_and_deflections.py | 242 +++++++ ...-003-thermally_loaded_support_structure.py | 189 ++++++ .../vm-004-deflection_of_a_hinged_support.py | 204 ++++++ ...erally_loaded_tapered_support_structure.py | 223 +++++++ .../verif-manual/vm-006-pinched_cylinder.py | 445 +++++++++++++ ...-plastic_compression_of_a_pipe_assembly.py | 616 ++++++++++++++++++ .../vm-008-parametric_calculation.py | 237 +++++++ ...deflection_of_unequal_stiffness_springs.py | 375 +++++++++++ .../vm-010-bending_of_a_t-shaped_beam.py | 285 ++++++++ .../vm-012-combined-bending-and-torsion.py | 134 ++++ requirements/requirements_doc.txt | 2 +- 31 files changed, 3123 insertions(+), 4 deletions(-) delete mode 100644 doc/source/_static/README.md create mode 100644 doc/source/_static/vm10_setup.png create mode 100644 doc/source/_static/vm10_setup_1.png create mode 100644 doc/source/_static/vm1_setup.png create mode 100644 doc/source/_static/vm2_setup.png create mode 100644 doc/source/_static/vm3_setup.png create mode 100644 doc/source/_static/vm4_setup.png create mode 100644 doc/source/_static/vm5_setup.png create mode 100644 doc/source/_static/vm6_setup.png create mode 100644 doc/source/_static/vm7_setup.png create mode 100644 doc/source/_static/vm7_setup_1.png create mode 100644 doc/source/_static/vm7_setup_2.png create mode 100644 doc/source/_static/vm8_setup.png create mode 100644 doc/source/_static/vm9_setup.png create mode 100644 doc/source/_static/vm9_setup_2.png create mode 100644 examples/verif-manual/README.txt create mode 100644 examples/verif-manual/vm-001-statically_indeterminate_reaction_force_analysis.py create mode 100644 examples/verif-manual/vm-002-beam_stresses_and_deflections.py create mode 100644 examples/verif-manual/vm-003-thermally_loaded_support_structure.py create mode 100644 examples/verif-manual/vm-004-deflection_of_a_hinged_support.py create mode 100644 examples/verif-manual/vm-005-laterally_loaded_tapered_support_structure.py create mode 100644 examples/verif-manual/vm-006-pinched_cylinder.py create mode 100644 examples/verif-manual/vm-007-plastic_compression_of_a_pipe_assembly.py create mode 100644 examples/verif-manual/vm-008-parametric_calculation.py create mode 100644 examples/verif-manual/vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py create mode 100644 examples/verif-manual/vm-010-bending_of_a_t-shaped_beam.py create mode 100644 examples/verif-manual/vm-012-combined-bending-and-torsion.py diff --git a/.gitignore b/.gitignore index 97a53435a..3aa3d06e8 100644 --- a/.gitignore +++ b/.gitignore @@ -74,6 +74,7 @@ instance/ # Sphinx documentation doc/_build/ +doc/source/verif-manual-2/ # PyBuilder .pybuilder/ diff --git a/doc/source/_static/README.md b/doc/source/_static/README.md deleted file mode 100644 index ff7796e46..000000000 --- a/doc/source/_static/README.md +++ /dev/null @@ -1 +0,0 @@ -Static files will be found here (like images and other assets). diff --git a/doc/source/_static/vm10_setup.png b/doc/source/_static/vm10_setup.png new file mode 100644 index 0000000000000000000000000000000000000000..3bafea3401860e4594c60746af1c7c49647a20b9 GIT binary patch literal 19771 zcmdqJWmuGJ*FS8_(A|O{-6crt01^@-jX1Dr*a%2Bs0>4=gQVclNC_w%(lT^NcdB&9 z5brsA-}m!>{>SltdOyA&IP{u1W1VZQYpvgkbHZSn%0&3|_}8voBT`jS)V_A@ItKjp z;@ttCq$f*Tf`6{NYAZvpmGm+G1`oGvo@hL|cC9Ri;N0vsc!s=IF><|jjoc0QcYW5H 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zfX|liFK(qn56|&d&GZVTeRyEM`Ejs)eX0WQ*f_2jQ05+busQYROZk$^P}-|m@63sR z)pn3Lm$z4w<5oiZ3Vd*=(A{t39LtEY@m=BX>ZY=0%L>8B1E17x)w`)0T6|}w-0U15 z^W(-xZ{=j9$!Wa{k)SCZ_;92ac)1PbEjWxvdpX|`ec~}A-S3_>i$-hxT(XEs2v!grgQ86h<0&ZaQjj)^ zpKZI&Wc_0N1Me_U4uNr^FZOep^PT&SFtp=`40zW6-3wMS|6A^epZ)Jz)iHxfBy8+y T?hA|g1zg64D1&l+bo9RgVV-3a literal 0 HcmV?d00001 diff --git a/doc/source/conf.py b/doc/source/conf.py index 4124e342c..ae38cbd57 100644 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -1,7 +1,10 @@ """Sphinx documentation configuration file.""" from datetime import datetime +import os from ansys_sphinx_theme import pyansys_logo_black as logo +import numpy as np +import pyvista # Project information project = "pymapdl-examples" @@ -54,9 +57,9 @@ # convert rst to md for ipynb "pypandoc": True, # path to your examples scripts - "examples_dirs": [], + "examples_dirs": ["../../examples/verif-manual"], # path where to save gallery generated examples - "gallery_dirs": ["verif-manual", "technology_showcase_examples"], + "gallery_dirs": ["verif-manual-2"], # Pattern to search for example files "filename_pattern": r"\.py", # Remove the "Download all examples" button from the top level gallery @@ -104,6 +107,22 @@ # type, unless multiple values are being returned" } +# Manage errors +pyvista.set_error_output_file("errors.txt") + +# Ensure that offscreen rendering is used for docs generation +pyvista.OFF_SCREEN = True + +# must be less than or equal to the XVFB window size +pyvista.rcParams["window_size"] = np.array([1024, 768]) + +# Save figures in specified directory +pyvista.FIGURE_PATH = os.path.join(os.path.abspath("./images/"), "auto-generated/") +if not os.path.exists(pyvista.FIGURE_PATH): + os.makedirs(pyvista.FIGURE_PATH) + + +pyvista.BUILDING_GALLERY = True # static path html_static_path = ["_static"] diff --git a/doc/source/index.rst b/doc/source/index.rst index a270581fc..39952416e 100644 --- a/doc/source/index.rst +++ b/doc/source/index.rst @@ -291,4 +291,5 @@ which necesitate more resources. :maxdepth: 3 verif-manual/index + verif-manual-2/index technology_showcase_examples/index diff --git a/examples/verif-manual/README.txt b/examples/verif-manual/README.txt new file mode 100644 index 000000000..bd81a3826 --- /dev/null +++ b/examples/verif-manual/README.txt @@ -0,0 +1,3 @@ +Examples +======== +These examples demonstrate using the PyMAPDL library. \ No newline at end of file diff --git a/examples/verif-manual/vm-001-statically_indeterminate_reaction_force_analysis.py b/examples/verif-manual/vm-001-statically_indeterminate_reaction_force_analysis.py new file mode 100644 index 000000000..6f67334f7 --- /dev/null +++ b/examples/verif-manual/vm-001-statically_indeterminate_reaction_force_analysis.py @@ -0,0 +1,146 @@ +r""" +.. _ref_statically_indeterminate_example: + +Statically Indeterminate Reaction Force Analysis +------------------------------------------------ +Problem Description: + - A prismatical bar with built-in ends is loaded axially at two + intermediate cross sections. Determine the reactions :math:`R_1` + and :math:`R_2`. + +Reference: + - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and + Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, + pg. 26, problem 10. + +Analysis Type(s): + - Static Analysis ``ANTYPE=0`` + +Element Type(s): + - 3-D Spar (or Truss) Elements (LINK180) + +.. image:: _static/vm1_setup.png + :width: 400 + :alt: VM1 Problem Sketch + +Material Properties + - :math:`E = 30 \cdot 10^6 psi` + +Geometric Properties: + - :math:`a = b = 0.3` + - :math:`l = 10 in` + +Loading: + - :math:`F_1 = 2*F_2 = 1000 lb` + +Analytical Equations: + - :math:`P = R_1 + R_2` where :math:`P` is load. + - :math:`\frac{R_2}{R_1} = \frac{a}{b}` + Where :math:`a` and :math:`b` are the ratios of distances between + the load and the wall. + +""" +# sphinx_gallery_thumbnail_path = '_static/vm1_setup.png' + +from ansys.mapdl.core import launch_mapdl + +# start mapdl and clear it +mapdl = launch_mapdl() +mapdl.clear() # optional as MAPDL just started + +# enter verification example mode and the pre-processing routine +mapdl.verify() +mapdl.prep7() + +############################################################################### +# Define Material +# ~~~~~~~~~~~~~~~ +# Set up the material and its type (a single material, with a linking-type +# section and a Young's modulus of 30e6). + +mapdl.antype("STATIC") +mapdl.et(1, "LINK180") +mapdl.sectype(1, "LINK") +mapdl.secdata(1) +mapdl.mp("EX", 1, 30e6) + +############################################################################### +# Define Geometry +# ~~~~~~~~~~~~~~~ +# Set up the nodes and elements. This creates a mesh just like in the +# problem setup. + +mapdl.n(1, 0, 0) +mapdl.n(2, 0, 4) +mapdl.n(3, 0, 7) +mapdl.n(4, 0, 10) +mapdl.e(1, 2) +mapdl.egen(3, 1, 1) + + +############################################################################### +# Define Boundary Conditions +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Full constrain nodes 1 and 4, by incrementing from node 1 to node 4 +# in steps of 3. Apply y-direction forces to nodes 2 and 3, with +# values of -500 lb and -1000 lb respectively. Then exit prep7. +# +# Effectiely, this sets: +# - :math:`F_1 = 2*F_2 = 1000 lb` + +mapdl.d(1, "ALL", "", "", 4, 3) +mapdl.f(2, "FY", -500) +mapdl.f(3, "FY", -1000) +mapdl.finish() + + +############################################################################### +# Solve +# ~~~~~ +# Enter solution mode and solve the system. + +mapdl.run("/SOLU") +out = mapdl.solve() +mapdl.finish() + +############################################################################### +# Post-processing +# ~~~~~~~~~~~~~~~ +# Enter post-processing. Select the nodes at ``y=10`` and ``y=0``, and +# sum the forces there. Then store the y-components in two variables: +# ``reaction_1`` and ``reaction_2``. + +mapdl.post1() +mapdl.nsel("S", "LOC", "Y", 10) +mapdl.fsum() +reaction_1 = mapdl.get("REAC_1", "FSUM", "", "ITEM", "FY") +mapdl.nsel("S", "LOC", "Y", 0) +mapdl.fsum() +reaction_2 = mapdl.get("REAC_2", "FSUM", "", "ITEM", "FY") + + +############################################################################### +# Check Results +# ~~~~~~~~~~~~~ +# Now that we have the reaction forces we can compare them to the +# expected values of 900 lbs and 600 lbs for reactions 1 and 2 respectively. +# +# Analytical results obtained from: +# - :math:`P = R_1 + R_2` where :math:`P` is load of 1500 lbs +# - :math:`\frac{R_2}{R_1} = \frac{a}{b}` +# +# Hint: Solve for each reaction force independently. +# +results = f""" + --------------------- RESULTS COMPARISON --------------------- + | TARGET | Mechanical APDL | RATIO + /INPUT FILE= LINE= 0 + R1, lb 900.0 {abs(reaction_1)} {abs(reaction_1) / 900} + R2, lb 600.0 {abs(reaction_2)} {abs(reaction_2) / 600} + ---------------------------------------------------------------- + """ +print(results) + +############################################################################### +# stop mapdl +mapdl.exit() diff --git a/examples/verif-manual/vm-002-beam_stresses_and_deflections.py b/examples/verif-manual/vm-002-beam_stresses_and_deflections.py new file mode 100644 index 000000000..b43fcbbae --- /dev/null +++ b/examples/verif-manual/vm-002-beam_stresses_and_deflections.py @@ -0,0 +1,242 @@ +r""" +.. _ref_vm2_example: + +Beam Stresses and Deflections +----------------------------- +**Problem Description** + +A standard 30 inch WF beam, with a cross-sectional area :math:`A`, +is supported as shown below and loaded on the overhangs by a +uniformly distributed load :math:`w`. Determine the maximum bending +stress, :math:`\sigma_max`, in the middle portion of the beam and +the deflection, :math:`\delta`, at the middle of the beam. + +**Reference** + +S. Timoshenko, Strength of Material, Part I, Elementary Theory and +Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, +pg. 98, problem 4. + +**Analysis Type(s)** + +Static Analysis ``ANTYPE=0`` + +**Element Type(s):** + +3-D 2 Node Beam (BEAM188) + +.. image:: _static/vm2_setup.png + :width: 400 + :alt: VM2 Problem Sketch + +**Material Properties** + +:math:`E = 30 \cdot 10^6 psi` + +**Geometric Properties** + +:math:`a = 120 in` +:math:`l = 240 in` +:math:`h = 30 in` +:math:`A = 50.65 in^2` +:math:`I_z = 7892 in^4` + +**Loading** + +:math:`w = (10000/12) lb/in` + +**Analytical Equations** + +- :math:`M` is the bending moment for the middle portion of the beam: + :math:`M = 10000 \cdot 10 \cdot 60 = 6 \cdot 10^6 lb \cdot in` +- Determination of the maximum stress in the middle portion of the beam is + :math:`\sigma_max = \frac{M h}{2 I_z}` +- The deflection, :math:`\delta`, at the middle of the beam can be defined + by the formulas of the transversally loaded beam: + :math:`\delta = 0.182 in` + +""" + +############################################################################### +# Start MAPDL +# ~~~~~~~~~~~ + +# sphinx_gallery_thumbnail_path = '_static/vm2_setup.png' + +from ansys.mapdl.core import launch_mapdl + +# Start mapdl and clear it. +mapdl = launch_mapdl() +mapdl.clear() + +# Enter verification example mode and the pre-processing routine. +mapdl.verify() +mapdl.prep7() + + +############################################################################### +# Define Element Type +# ~~~~~~~~~~~~~~~~~~~ +# Set up the element type (a beam-type). + +# Type of analysis: Static. +mapdl.antype("STATIC") + +# Element type: BEAM188. +mapdl.et(1, "BEAM188") + +# Special Features are defined by keyoptions of beam element: + +# KEYOPT(3) +# Shape functions along the length: +# Cubic +mapdl.keyopt(1, 3, 3) # Cubic shape function + +# KEYOPT(9) +# Output control for values extrapolated to the element +# and section nodes: +# Same as KEYOPT(9) = 1 plus stresses and strains at all section nodes +mapdl.keyopt(1, 9, 3, mute=True) + + +############################################################################### +# Define Material +# ~~~~~~~~~~~~~~~ +# Set up the material. + +mapdl.mp("EX", 1, 30e6) +mapdl.mp("PRXY", 1, 0.3) +print(mapdl.mplist()) + + +############################################################################### +# Define Section +# ~~~~~~~~~~~~~~ +# Set up the cross-section properties for a beam element. + +w_f = 1.048394965 +w_w = 0.6856481 +sec_num = 1 +mapdl.sectype(sec_num, "BEAM", "I", "ISection") +mapdl.secdata(15, 15, 28 + (2 * w_f), w_f, w_f, w_w) + + +############################################################################### +# Define Geometry +# ~~~~~~~~~~~~~~~ +# Set up the nodes and elements. Create nodes then create elements +# between nodes. + +# Define nodes +for node_num in range(1, 6): + mapdl.n(node_num, (node_num - 1) * 120, 0, 0) + +# Define one node for the orientation of the beam cross-section. +orient_node = mapdl.n(6, 60, 1) + +# Print the list of the created nodes. +print(mapdl.nlist()) + +############################################################################### +# Define elements + +for elem_num in range(1, 5): + mapdl.e(elem_num, elem_num + 1, orient_node) + +# Print the list of the created elements. +print(mapdl.elist()) + +# Display elements with their nodes numbers. +mapdl.eplot(show_node_numbering=True, line_width=5, cpos="xy", font_size=40) + + +############################################################################### +# Define Boundary Conditions +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Application of boundary conditions (BC). + +# BC for the beams seats +mapdl.d(2, "UX", lab2="UY") +mapdl.d(4, "UY") + +# BC for all nodes of the beam +mapdl.nsel("S", "LOC", "Y", 0) +mapdl.d("ALL", "UZ") +mapdl.d("ALL", "ROTX") +mapdl.d("ALL", "ROTY") +mapdl.nsel("ALL") + +############################################################################### +# Define Distributed Loads +# ~~~~~~~~~~~~~~~~~~~~~~~~ +# Apply a distributed force of :math:`w = (10000/12) lb/in` +# in the y-direction. + +# Parametrization of the distributed load. +w = 10000 / 12 + +# Application of the surface load to the beam element. +mapdl.sfbeam(1, 1, "PRES", w) +mapdl.sfbeam(4, 1, "PRES", w) +mapdl.finish() + + +############################################################################### +# Solve +# ~~~~~ +# Enter solution mode and solve the system. Print the solver output. + +mapdl.run("/SOLU") +out = mapdl.solve() +mapdl.finish() +print(out) + + +############################################################################### +# Post-processing +# ~~~~~~~~~~~~~~~ +# Enter post-processing. To get the stress and deflection results +# from the middle node and cross-section of the beam we can use +# :meth:`Mapdl.get_value `. + +# Enter the post-processing routine and select the first load step. +mapdl.post1() +mapdl.set(1) + +# Get the maximum stress at the middle of the beam. +s_eqv_max = mapdl.get_value("secr", 2, "s", "eqv", "max") + +# Get the deflection at the middle of the beam. +mid_node_uy = mapdl.get_value(entity="NODE", entnum=3, item1="u", it1num="y") + + +############################################################################### +# Check Results +# ~~~~~~~~~~~~~ +# Now that we have the results we can compare the nodal displacement and stress +# experienced by middle node of the beam to the known stresses -11,400 psi and +# 0.182 inches of the deflection. + +# Results obtained by hand-calculations. +stress_target = 11400.0 +deflection_target = 0.182 + +# Calculate the deviation. +stress_ratio = s_eqv_max / stress_target +deflection_ratio = mid_node_uy / deflection_target + +# Print output results. +output = f""" +----------------------------- VM3 RESULTS COMPARISON ----------------------------- + | TARGET | Mechanical APDL | RATIO | +---------------------------------------------------------------------------------- + Stress{stress_target:18.3f} {s_eqv_max:16.3f} {stress_ratio:14.3f} + Deflection{deflection_target:14.3f} {mid_node_uy:16.3f} {deflection_ratio:14.3f} +---------------------------------------------------------------------------------- +""" +print(output) + + +############################################################################### +# stop mapdl +mapdl.exit() diff --git a/examples/verif-manual/vm-003-thermally_loaded_support_structure.py b/examples/verif-manual/vm-003-thermally_loaded_support_structure.py new file mode 100644 index 000000000..5fd706dc2 --- /dev/null +++ b/examples/verif-manual/vm-003-thermally_loaded_support_structure.py @@ -0,0 +1,189 @@ +r""" +.. _ref_thermally_loaded_support_structure: + +Thermally Loaded Support Structure +---------------------------------- +Problem Description: + - Find the stresses in the copper and steel wire structure shown below. + The wires have a cross-sectional area of math:`A`. The structure is + subjected to a load math:`Q` and a temperature rise of math:`\Delta T` after + assembly. + +Reference: + - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and + Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, + pg. 30, problem 9. + +Analysis Type(s): + - Static Analysis ``ANTYPE=0`` + +Element Type(s): + - 3-D Spar (or Truss) Elements (LINK180) + +.. image:: _static/vm3_setup.png + :width: 400 + :alt: VM3 Problem Sketch + +Material Properties + - :math:`E_c = 16 \cdot 10^6 psi` + - :math:`E_s = 30 \cdot 10^6 psi` + - :math:`\alpha_c = 70 \cdot 10^{-7} in/in-^\circ F` + - :math:`\alpha_s = 92 \cdot 10^{-7} in/in-^\circ F` + +Geometric Properties: + - :math:`A = 0.1 in^2` + +Loading: + - :math:`Q = 4000 lb` + - :math:`\Delta T = 10 ^\circ F` + +Analytical Equations: + - The compressive force :math:`X` is given by the following equation + - :math:`X = \frac{\Delta T (\alpha_c - \alpha_s) (A_s - E_s) }{1 + \frac{1 E_s A_s}{2 E_c A_c}} + + \frac{Q}{1 + \frac{2 E_c A_c}{E_s A_s}}` + +Notes: + - Length of wires (20 in.), spacing between wires (10 in.), and the reference + temperature (70°F) are arbitrarily selected. The rigid lower beam is modeled + by nodal coupling. + +""" +# sphinx_gallery_thumbnail_path = '_static/vm3_setup.png' + +from ansys.mapdl.core import launch_mapdl + +# start mapdl and clear it +mapdl = launch_mapdl() +mapdl.clear() # optional as MAPDL just started + +# enter verification example mode and the pre-processing routine +mapdl.verify() +mapdl.prep7() + +############################################################################### +# Define Material +# ~~~~~~~~~~~~~~~ +# Set up the materials and their properties. We are using copper and +# steel here. +# - `EX` - X-direction elastic modulus +# - `ALPX` - Secant x - coefficient of thermal expansion +# + +mapdl.antype("STATIC") +mapdl.et(1, "LINK180") +mapdl.sectype(1, "LINK") +mapdl.secdata(0.1) +mapdl.mp("EX", 1, 16e6) +mapdl.mp("ALPX", 1, 92e-7) +mapdl.mp("EX", 2, 30e6) +mapdl.mp("ALPX", 2, 70e-7) +# Define the reference temperature for the thermal strain calculations. +mapdl.tref(70) + +############################################################################### +# Define Geometry: Nodes +# ~~~~~~~~~~~~~~~~~~~~~~ +# Set up the nodes and elements. This creates a mesh just like in the +# problem setup. We create a square of nodes and use `fill` to add +# mid-point nodes to two opposite sides. + +mapdl.n(1, -10) +mapdl.n(3, 10) +mapdl.fill() +mapdl.n(4, -10, -20) +mapdl.n(6, 10, -20) +mapdl.fill() +mapdl.nplot(nnum=True, cpos="xy") + +############################################################################### +# Define Geometry: Elements +# ~~~~~~~~~~~~~~~~~~~~~~~~~ +# Create two elements (using material #1) that are two sides of our +# square, as links. Then create a single element using material #2 +# between the first 2 that is parallel to them. + +mapdl.e(1, 4) +mapdl.e(3, 6) +mapdl.mat(2) +mapdl.e(2, 5) +mapdl.eplot(show_node_numbering=True, cpos="xy") + +############################################################################### +# Define Boundary Conditions +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# - Couple the degrees of freedom in y-displacement across nodes 5, 4, +# and 6. +# - Fix nodes 1, 2, and 3 in place. +# - Apply a force of -4000 in the y-direction to node 5 +# - Apply a uniform temperature of 80 to the whole body +# - Finally, exit the post-processor. + +mapdl.cp(1, "UY", 5, 4, 6) +mapdl.d(1, "ALL", "", "", 3) +mapdl.f(5, "FY", -4000) +mapdl.bfunif("TEMP", 80) +mapdl.finish() + + +############################################################################### +# Solve +# ~~~~~ +# - Enter solution mode +# - Specify a timestep of 1 to be used for this load step +# - Solve the system. +# + +mapdl.run("/SOLU") +mapdl.nsubst(1) +mapdl.solve() + +############################################################################### +# Post-processing +# ~~~~~~~~~~~~~~~ +# - Access the queries functions +# - Find a steel node and a copper node +# - Then use these to get the steel and copper elements +# - Finally extract the stress experienced by each element +# + +mapdl.post1() +q = mapdl.queries +steel_n = q.node(0, 0, 0) +copper_n = q.node(10, 0, 0) +steel_e = q.enearn(steel_n) +copper_e = q.enearn(copper_n) +mapdl.etable("STRS_ST", "LS", 1) +mapdl.etable("STRS_CO", "LS", 1) + +stress_steel = mapdl.get("_", "ELEM", steel_e, "ETAB", "STRS_ST") +stress_copper = mapdl.get("_", "ELEM", copper_e, "ETAB", "STRS_CO") + +############################################################################### +# Check Results +# ~~~~~~~~~~~~~ +# Now that we have the response we can compare the values to the +# expected stresses of 19695 and 10152 respectively. +# + +steel_target = 19695 +steel_ratio = stress_steel / steel_target +copper_target = 10152 +copper_ratio = stress_copper / copper_target + +message = f""" +------------------- VM3 RESULTS COMPARISON --------------------- + + | TARGET | Mechanical APDL | RATIO +---------------------------------------------------------------- + Steel {steel_target} {stress_steel} {steel_ratio:.6f} + Copper {copper_target} {stress_copper} {copper_ratio:.6f} + +---------------------------------------------------------------- + +""" +print(message) + + +############################################################################### +# stop mapdl +mapdl.exit() diff --git a/examples/verif-manual/vm-004-deflection_of_a_hinged_support.py b/examples/verif-manual/vm-004-deflection_of_a_hinged_support.py new file mode 100644 index 000000000..bc3b79fa1 --- /dev/null +++ b/examples/verif-manual/vm-004-deflection_of_a_hinged_support.py @@ -0,0 +1,204 @@ +r""" +.. _ref_deflection_of_a_hinged_support: + +Deflection of a Hinged Support +------------------------------ +Problem Description: + - A structure consisting of two equal steel bars, each of length :math:`l` + and cross-sectional area :math:`A`, with hinged ends is subjected to + the action of a load :math:`F`. Determine the stress, :math:`\sigma`, + in the bars and the deflection, :math:`\delta`, of point 2. Neglect + the weight of the bars as a small quantity in comparison with the load + :math:`F`. + +Reference: + - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and + Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, + pg. 10, problem 2. + +Analysis Type(s): + - Static Analysis ``ANTYPE=0`` + +Element Type(s): + - 3-D Spar (or Truss) Elements (LINK180) + +.. image:: _static/vm4_setup.png + :width: 400 + :alt: VM4 Problem Sketch + +Material Properties + - :math:`E = 30 \cdot 10^6 psi` + +Geometric Properties: + - :math:`l = 15 ft` + - :math:`A = 0.5 in^2` + - :math:`\Theta = 30 ^\circ` + +Loading: + - :math:`F = 5000 lb` + +Analytical Equations: + - The tensile force in the bars is :math:`S` + - :math:`S = \frac{P}{2 sin \Theta}` + - The necessary cross-sectional area :math:`A` is + - :math:`A = \frac{S}{\sigma}` + - The elongation of the bar :math:`AB` is + - :math:`B_1 D = \frac{\sigma l}{E}` + - The deflection :math:`BB_1` is + - :math:`BB_1 = \frac{B_1 D}{sin \Theta}` + +Notes: + - Consistent length units are used. The dimensions :math:`a` and :math:`b` are + calculated parametrically in the input as follows: + - :math:`a = 2 l cos \Theta`, + - :math:`b = l sin \Theta`. + +""" +# sphinx_gallery_thumbnail_path = '_static/vm4_setup.png' + +############################################################################### +# Start MAPDL +# ~~~~~~~~~~~ + +from math import cos, pi, sin + +from ansys.mapdl.core import launch_mapdl + +# start mapdl and clear it +mapdl = launch_mapdl() +mapdl.clear() # optional as MAPDL just started + +# enter verification example mode and the pre-processing routine +mapdl.verify() +mapdl.prep7() + +############################################################################### +# Define Material +# ~~~~~~~~~~~~~~~ +# Create a simple hinge geometry. +# We use the `LINK180` element type to model this and an elastic modulus +# of 30e6. +# We store the x-coordinate of node 3 and the y-coordinate of node 2 for +# ease of use later on. + +length_bar = 15 * 12 +theta = 30 +theta_rad = theta * pi / 180.0 +node3_x = 2 * length_bar * cos(theta_rad) +node2_y = length_bar * sin(theta_rad) + +mapdl.et(1, "LINK180") +mapdl.sectype(1, "LINK") +mapdl.secdata(0.5) +mapdl.mp("EX", 1, 30e6) + +############################################################################### +# Define Geometry +# ~~~~~~~~~~~~~~~ +# We create three nodes in an isosceles triangle shape, with elements +# along the equal sides, forming a hinge. + +n1 = mapdl.n(1, 0, 0, 0) +n2 = mapdl.n(2, node3_x * 0.5, -node2_y, 0) +n3 = mapdl.n(3, node3_x, 0, 0) + +mapdl.e(n1, n2) +mapdl.e(n2, n3) +mapdl.eplot(show_node_numbering=True, line_width=5, cpos="xy") + +############################################################################### +# Define Boundary Conditions +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# - Fix nodes 1 and 3 in place +# - Apply a force of -5000 in the negative y-direction to node 2 +# - Then finish the prep7 section + +mapdl.d(1, "ALL", "", "", 3, 2) +mapdl.f(2, "FY", -5000) +mapdl.finish() + + +############################################################################### +# Solve +# ~~~~~ +# Enter solution mode and solve the system. + +mapdl.run("/SOLU") +out = mapdl.solve() +mapdl.finish() + +############################################################################### +# Post-processing +# ~~~~~~~~~~~~~~~ +# Enter post-processing, get the results and view the nodal displacement +# as well as the equivalent stress on the nodes. +# +# We make the line width larger for ease of visualization as well as +# using two perceptually linear colormaps to enhance display of the +# data. + +mapdl.post1() +mapdl.post_processing.plot_nodal_displacement( + "Y", + cmap="magma", + line_width=5, + cpos="xy", + scalar_bar_args={"title": "Displacement", "vertical": False}, +) + +############################################################################### +# Principal nodal stress +# ~~~~~~~~~~~~~~~~~~~~~~ +# Use the ``post_processing`` attribute to get the principal nodal +# stress as an array. +# +# .. note:: +# This returns the same data as :func:`prnsol +# `, except instead of returning +# text, it returns a numpy array. + + +seqv = mapdl.post_processing.nodal_eqv_stress() + +# print out the nodes +for i, nnum in enumerate(mapdl.mesh.nnum): + print(f"Node {nnum} : {seqv[i]} psi") + +# Which is identical to: +# print(mapdl.prnsol('S', 'PRIN')) + +############################################################################### +# Check Results +# ~~~~~~~~~~~~~ +# Now that we have the results we can compare the nodal displacement and +# stress experienced by node 2 to the known quantities 10000 psi and +# -0.12 inches. To do this we: +# +# - Find the mid-node from the coordinates using the :class:`Query +# ` class +# - Get the y-displacement from node 2 +# - Get the element nearest to node 2 +# - Get the stress on this element +# - Compare + +q = mapdl.queries +mid_node = q.node(node3_x * 0.5, -node2_y, 0) +displacement = mapdl.get_value("NODE", mid_node, "U", "Y") +left_element = q.enearn(mid_node) +mapdl.etable("STRS", "LS", 1) +stress = mapdl.get_value("ELEM", left_element, "ETAB", "STRS") + +results = f""" +--------------------- RESULTS COMPARISON ----------------------- +| TARGET | TARGET | Mechanical APDL | RATIO +------------------------------------------------------------------ +Stress [psi] 10000 {stress} {stress/10000:.2f} +Displacement [in] -0.12 {displacement:.2f} {abs(displacement) / 0.12:.2f} +------------------------------------------------------------------ +""" + +print(results) + +############################################################################### +# stop mapdl +mapdl.exit() diff --git a/examples/verif-manual/vm-005-laterally_loaded_tapered_support_structure.py b/examples/verif-manual/vm-005-laterally_loaded_tapered_support_structure.py new file mode 100644 index 000000000..c4011d3f2 --- /dev/null +++ b/examples/verif-manual/vm-005-laterally_loaded_tapered_support_structure.py @@ -0,0 +1,223 @@ +r""" +.. _ref_vm5_example: + +Statically Indeterminate Reaction Force Analysis +------------------------------------------------ +Problem Description: + - A cantilever beam of thickness :math:`t` and length :math:`l` + has a depth which tapers uniformly from :math:`d` at the tip + to :math:`3d` at the wall. It is loaded by a force :math:`F` + at the tip, as shown. Find the maximum bending stress at the + mid-length (:math:`X = l`) and the fixed end of the beam. + +Reference: + - S. H. Crandall, N. C. Dahl, An Introduction to the Mechanics + of Solids, McGraw-Hill Book Co., Inc., New York, NY, 1959, + pg. 342, problem 7.18. + +Analysis Type(s): + - Static Analysis ``ANTYPE=0`` + +Element Type(s): + - 2-D 4-Node Sructural Solid Elements (PLANE182) + - 2-D 8-Node Structural Solid Elements (PLANE183) + +.. image:: _static/vm5_setup.png + :width: 400 + :alt: VM5 Problem Sketch + +Material Properties + - :math:`E = 30 \cdot 10^6 psi` + - :math:`\nu = 0.0` + - :math:`d = 3in` + - :math:`t = 2in` + +Geometric Properties: + - :math:`l = 50 in` + - :math:`d = 3 in` + - :math:`t = 2 in` + +Loading: + - :math:`F = 4000 lb` + +Notes: + - Two different solutions are obtained. The first solution uses + lower order PLANE182 elements and the second solution uses higher + order PLANE82 elements. The 2 inch thickness is incorporated + by using the plane stress with thickness option. Poisson's + ratio is set to 0.0 to agree with beam theory. + +""" +# sphinx_gallery_thumbnail_path = '_static/vm5_setup.png' + +############################################################################### +# Start MAPDL +# ~~~~~~~~~~~ + +from ansys.mapdl.core import launch_mapdl + +# start mapdl and clear it +mapdl = launch_mapdl() +mapdl.clear() # optional as MAPDL just started + +# enter verification example mode and the pre-processing routine +mapdl.verify() +mapdl.prep7() + +############################################################################### +# Define Material +# ~~~~~~~~~~~~~~~ +# Set up the material using PLANE182 with a thickness of 2 (using real +# constants), and create a material with a Young's modulus of 30e6, +# and a poisson's ratio of 0.0 to agree with beam theory. + +mapdl.antype("STATIC") +mapdl.et(1, "PLANE182", kop1=2, kop3=3) +mapdl.r(1, 2) +mapdl.mp("EX", 1, 30e6) +mapdl.mp("NUXY", 1, 0.0) + + +############################################################################### +# Define Geometry +# ~~~~~~~~~~~~~~~ +# Set up the nodes and elements. This creates a mesh just like in the +# problem setup. + +mapdl.n(1, 25) +mapdl.n(7, 75) +mapdl.fill() +mapdl.n(8, 25, -3) +mapdl.n(14, 75, -9) +mapdl.fill() +mapdl.e(2, 1, 8, 9) +mapdl.egen(6, 1, 1) +mapdl.eplot(show_node_numbering=True, cpos="xy") + + +############################################################################### +# Define Boundary Conditions +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Fix the nodes at the larger end (the "wall" end) and apply a vertical force +# to the whole structure. + +# constrain nodes at fixed end +mapdl.nsel("S", "LOC", "X", 75) +mapdl.d("ALL", "ALL") +mapdl.nsel("ALL") +mapdl.f(1, "FY", -4000) +mapdl.finish() + + +############################################################################### +# Solve +# ~~~~~ +# Enter solution mode and solve the system. + +mapdl.run("/SOLU") +mapdl.solve() +mapdl.finish() + +############################################################################### +# Post-processing +# ~~~~~~~~~~~~~~~ +# Enter post-processing. Get the stress at the fixed end and the mid point +# of the structure by querying the stress at nodes closest to these locations. +# We've gathered the code into a function because we'll have use for it later. + + +def fetch_mid_and_end_stress(m): + q = m.queries + m.post1() + end = q.node(75.0, 0.0, 0.0) + fixed_end_stress = m.get_value("NODE", end, "S", "X") + mid = q.node(50.0, 0.0, 0.0) + mid_stress = m.get_value("NODE", mid, "S", "EQV") + return fixed_end_stress, mid_stress + + +fixed_end_stress_182, mid_stress_182 = fetch_mid_and_end_stress(mapdl) + +############################################################################### +# Plotting +# ~~~~~~~~ +# View the equivalent stress, and displacement, of the cantilever with a +# ``displacement_factor`` of 26 to scale up the deformation to a visible +# amount. + +result = mapdl.result +result.plot_principal_nodal_stress( + 0, + "SEQV", + show_edges=True, + show_displacement=True, + displacement_factor=26.0, + cmap="Oranges", + cpos="xy", +) + +############################################################################### +# Redo with Plane 183 +# ~~~~~~~~~~~~~~~~~~~ +# Now we need to perform the simulation again but this time using the PLANE183 +# element type. We additionally remove midside nodes with ``emid``. + +mapdl.prep7() +mapdl.et(1, "PLANE183", kop3=3) +mapdl.emid() +mapdl.nsel("R", "LOC", "X", 75) +mapdl.nsel("R", "LOC", "Y", -4.5) + +mapdl.d("ALL", "ALL") +mapdl.nsel("ALL") +mapdl.finish() +mapdl.run("/SOLU") +mapdl.solve() +mapdl.finish() + +mapdl.post1() +# reuse our function from earlier +fixed_end_stress_183, mid_stress_183 = fetch_mid_and_end_stress(mapdl) +mapdl.finish() + +result = mapdl.result +result.plot_principal_nodal_stress( + 0, + "SEQV", + show_edges=True, + show_displacement=True, + displacement_factor=26.0, + cmap="Blues", + cpos="xy", +) + +############################################################################### +# Check Results +# ~~~~~~~~~~~~~ +# Now that we have the stresses we can compare them to the expected values +# of stress at the midpoint (8333) and the fixed end (7407) for both +# simulations. + + +results_182 = f""" +----------------- PLANE 182 RESULTS COMPARISON ---------------- +| LABEL | TARGET | Mechanical APDL | RATIO + mid stress 8333 {mid_stress_182:.2f} {mid_stress_182 / 8333:.2f} + end stress 7407 {fixed_end_stress_182:.2f} {fixed_end_stress_182 / 7407:.2f} +---------------------------------------------------------------- +""" + +results_183 = f""" +----------------- PLANE 183 RESULTS COMPARISON ---------------- +| LABEL | TARGET | Mechanical APDL | RATIO + mid stress 8333 {mid_stress_183:.2f} {mid_stress_183 / 8333:.2f} + end stress 7407 {fixed_end_stress_183:.2f} {fixed_end_stress_183 / 7407:.2f} +---------------------------------------------------------------- +""" +print(results_182) +print(results_183) + + +############################################################################### +# stop mapdl +mapdl.exit() diff --git a/examples/verif-manual/vm-006-pinched_cylinder.py b/examples/verif-manual/vm-006-pinched_cylinder.py new file mode 100644 index 000000000..1f469ecb6 --- /dev/null +++ b/examples/verif-manual/vm-006-pinched_cylinder.py @@ -0,0 +1,445 @@ +r""" +.. _ref_vm6_example: + +Pinched Cylinder +---------------- +Problem Description: + - A thin-walled cylinder is pinched by a force :math:`F` at the middle + of the cylinder length. Determine the radial displacement :math:`\delta` + at the point where the force :math:`F` is applied. + The ends of the cylinder are free edges. + +Reference: + - R. D. Cook, Concepts and Applications of Finite Element Analysis, 2nd Edition, + John Wiley and Sons, Inc., New York, NY, 1981, pp. 284-287. + H. Takemoto, R. D. Cook, "Some Modifications of an Isoparametric Shell + Element", International Journal for Numerical Methods in Engineering, Vol.7 + No. 3, 1973. + +Analysis Type(s): + - Static Analysis ``ANTYPE=0`` + +Element Type(s): + - 4-Node Finite Strain Shell Elements (SHELL181) + - 8-Node Finite Strain Shell Elements (SHELL281) + +.. image:: _static/vm6_setup.png + :width: 400 + :alt: VM6 Pinched Cylinder Problem Sketch + +Material Properties + - :math:`E = 10.5 \cdot 10^6 psi` + - :math:`\nu = 0.3125` + +Geometric Properties: + - :math:`l = 10.35 in` + - :math:`r = 4.953 in` + - :math:`t = 0.094 in` + +Loading: + - :math:`F = 100 lb` + +Analysis Assumptions and Modeling Notes: + - A one-eighth symmetry model is used. One-fourth of the load is applied + due to symmetry. + +""" +# sphinx_gallery_thumbnail_path = '_static/vm6_setup.png' + +############################################################################### +# Start MAPDL +# ~~~~~~~~~~~ + +from ansys.mapdl.core import launch_mapdl + +# Start mapdl. +mapdl = launch_mapdl() + + +############################################################################### +# Initiate Pre-Processing +# ~~~~~~~~~~~~~~~~~~~~~~~ +# Enter verification example mode and the pre-processing routine. + + +def start_prep7(): + mapdl.clear() + mapdl.verify() + mapdl.prep7() + + +start_prep7() + + +############################################################################### +# Define Element Type +# ~~~~~~~~~~~~~~~~~~~ +# Set up the element type (a shell-type). + +# Define the element type number. +def define_element(elem_type): + # Type of analysis: Static. + mapdl.antype("STATIC") + + # Define the element type number. + elem_num = 1 + + if elem_type == "SHELL181": + + # Element type: SHELL181. + mapdl.et(elem_num, elem_type) + + # Special Features are defined by keyoptions of shell element: + + # KEYOPT(3) + # Integration option: + # Full integration with incompatible modes. + mapdl.keyopt(elem_num, 3, 2) # Cubic shape function + + elif elem_type == "SHELL281": + + # Element type: SHELL181. + mapdl.et(elem_num, "SHELL281") + + return elem_type, mapdl.etlist() + + +# Return the number of the element type. +elem_type, elem_type_list = define_element(elem_type="SHELL181") +print( + f"Selected element type is: {elem_type},\n" + f"Printout the element list with its own properties:\n {elem_type_list}" +) + + +############################################################################### +# Define Material +# ~~~~~~~~~~~~~~~ +# Set up the material properties, where: +# Young Modulus is :math:`E = 10.5 \cdot 10^6 psi`, +# Poisson's ratio is :math:`\nu = 0.3125`. + +# Define material number. +mat_num = 1 + +# Define material properties. +def define_material(): + # Define material properties. + mapdl.mp("EX", mat_num, 10.5e6) + mapdl.mp("NUXY", mat_num, 0.3125) + return mapdl.mplist() + + +material_list = define_material() +print(material_list) + + +############################################################################### +# Define Section +# ~~~~~~~~~~~~~~ +# Set up the cross-section properties for a shell element. + +# Define cross-section number and thickness of the shell element. +sec_num = 1 +t = 0.094 + +# Define shell cross-section. +def define_section(): + # Define shell cross-section. + mapdl.sectype(secid=sec_num, type_="SHELL", name="shell181") + mapdl.secdata(t, mat_num, 0, 5) + return mapdl.slist() + + +section_list = define_section() +print(section_list) + + +############################################################################### +# Define Geometry +# ~~~~~~~~~~~~~~~ +# Set up the keypoints and create the area through the keypoints. + +# Define geometry of the simplified mathematical model. +def define_geometry(): + # Change active coordinate system + # to the global cylindrical coordinate system. + mapdl.csys(1) + + # Define keypoints by coordinates. + mapdl.k(1, 4.953) + mapdl.k(2, 4.953, "", 5.175) + + # Generate additional keypoints from a pattern of keypoints. + mapdl.kgen(2, 1, 2, 1, "", 90) + + # Create an area through keypoints. + mapdl.a(1, 2, 4, 3) + + if elem_type == "SHELL181": + # Plot the lines. + mapdl.lplot(color_lines=True, cpos="iso") + + # Plot the area using PyVista parameters. + mapdl.aplot( + title="Display the selected area", + cpos="iso", + vtk=True, + color="#06C2AC", + show_line_numbering=True, + show_area_numbering=True, + show_lines=True, + ) + + +define_geometry() + + +# Define the number of the keypoint where F is applied using inline function. +def keypoint_number(mapdl): + keypoint_num = mapdl.queries.kp(4.953, 90, 0) + return keypoint_num + + +# Call the function to get the number of keypoint. +top_keypoint = keypoint_number(mapdl) +print(f"The number of the keypoint where F is applied: {top_keypoint}") + + +############################################################################### +# Meshing +# ~~~~~~~ +# Define line division of the lines, then mesh the area with shell elements. + +# Define mesh properties and create the mesh with shell elements. +def meshing(): + # Specify the default number of line divisions. + mapdl.esize(size="", ndiv=8) + + # Mesh the area. + mapdl.amesh(1) + + # Define global cartesian coordinate system. + mapdl.csys(0) + + if elem_type == "SHELL181": + # Plot the mesh. + mapdl.eplot( + title="Plot of the currently selected elements", + vtk=True, + cpos="iso", + show_edges=True, + edge_color="white", + show_node_numbering=True, + color="purple", + ) + + # Print the list of elements. + print(mapdl.elist()) + + # Plot the nodes using VTK. + mapdl.nplot( + vtk=True, nnum=True, background="", cpos="iso", show_bounds=True, point_size=10 + ) + + # Print the list of nodes. + print(mapdl.nlist()) + + +meshing() + + +############################################################################### +# Define Boundary Conditions +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Application of symmetric boundary conditions for simplified model. + +# Select nodes by location and apply BC. +def define_bc(): + # Select nodes by location and apply BC. + mapdl.nsel("S", "LOC", "X", 0) + mapdl.dsym("SYMM", "X", 0) + mapdl.nsel("S", "LOC", "Y", 0) + mapdl.dsym("SYMM", "Y", 0) + mapdl.nsel("S", "LOC", "Z", 0) + mapdl.dsym("SYMM", "Z", 0) + mapdl.nsel("ALL") + + +define_bc() + + +############################################################################### +# Define Distributed Loads +# ~~~~~~~~~~~~~~~~~~~~~~~~ +# Apply the force of :math:`F = (100/4) lb` in the y-direction. + +# Define loads. +def define_loads(): + # Parametrization of the :math:`F` load for the quarter of the model. + force = 100 / 4 + + # Application of the load to the model. + mapdl.fk(top_keypoint, "FY", -force) + mapdl.finish() + + +define_loads() + + +############################################################################### +# Solve +# ~~~~~ +# Enter solution mode and solve the system. Print the solver output. + + +def solve_procedure(): + mapdl.run("/solu") + out = mapdl.solve() + mapdl.finish() + return out + + +simulation_info = solve_procedure() +print(simulation_info) + +############################################################################### +# Post-processing +# ~~~~~~~~~~~~~~~ +# Enter post-processing for the model with elements ``shell181``. +# Plotting nodal displacement. +# Get the the radial displacement at the node where force F is applied. + +# Start post-processing mode. +def post_processing(): + mapdl.post1() + mapdl.set(1) + + +post_processing() + + +############################################################################### +# Plotting +# ~~~~~~~~ +# Plot nodal displacement using PyVista. + + +def plot_nodal_disp(): + mapdl.post_processing.plot_nodal_displacement( + title="Nodal Displacements", + component="Y", + cpos="zx", + scalar_bar_args={"title": "Nodal Displacements", "vertical": True}, + show_node_numbering=True, + show_axes=True, + show_edges=True, + ) + + +plot_nodal_disp() + + +############################################################################### +# Getting the radial displacements +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# To determine the radial displacement :math:`\delta` at the point +# where F is applied, we can use :meth:`Mapdl.get_value `. + + +def get_displacements(): + # Select keypoint by its number ``top_keypoint``. + mapdl.ksel("S", vmin="top_keypoint") + + # Select the node associated with the selected keypoint. + mapdl.nslk() + + # Get the number of the selected node by :meth:`Mapdl.get ` + top_node = int(mapdl.get("_", "node", 0, "num", "max")) + + # Define radial displacement at the node where F is applied. + deflect_shell = mapdl.get_value( + entity="node", entnum=top_node, item1="u", it1num="y" + ) + + return top_node, deflect_shell + + +# Call the function and get the value of the deflection. +top_node_181, deflect_shell_181 = get_displacements() +print( + f"Number of the node attached to the top keypoint: {top_node_181},\n" + f"Radial displacement: {(round(deflect_shell_181, 4))}" +) + + +############################################################################### +# Rerun Model with SHELL281 +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Perform the simulation again using the element type SHELL281. + +# Restart pre-processing routine. +start_prep7() +elem_type = define_element(elem_type="SHELL281") +define_material() +define_section() +define_geometry() +meshing() +define_bc() +define_loads() + + +############################################################################### +# Solve +# ~~~~~ +# Enter solution mode and solve the system. Print the solver output. + +solve_procedure() + + +############################################################################### +# Post-processing +# ~~~~~~~~~~~~~~~ +# Enter post-processing for the model with elements ``shell281``. +# Plotting nodal displacement. +# Get the the radial displacement at the node where force F is applied. + +post_processing() +plot_nodal_disp() +top_node_281, deflect_shell_281 = get_displacements() + + +############################################################################### +# Check Results +# ~~~~~~~~~~~~~ +# Now we have the deflections, we can compare them to the expected values +# of radial deflection at the node where force :math:`F` was applied +# for both simulations. The expected value for :math:`\delta_{\mathrm{shell181}}` is 0.1139, +# and :math:`\delta_{\mathrm{shell281}}` is 0.1139. + +# Results obtained by hand-calculations. +deflect_target_181 = 0.1139 +deflect_target_281 = 0.1139 + +# Calculate the deviation. +deflect_ratio_shell_181 = abs(deflect_shell_181) / deflect_target_181 +deflect_ratio_shell_281 = abs(deflect_shell_281) / deflect_target_281 + +# Print output results. +output = f""" +---------------------------------------------------------------------------- +------------------------- VM3 RESULTS COMPARISON --------------------------- +---------------------------------------------------------------------------- + | TARGET | Mechanical APDL | RATIO | +---------------------------------------------------------------------------- + Deflection, in SHELL181{deflect_target_181:11.4f} {abs(deflect_shell_181):17.4f} + {deflect_ratio_shell_181:15.3f} + Deflection, in SHELL281{deflect_target_281:11.4f} {abs(deflect_shell_281):17.4f} + {deflect_ratio_shell_281:15.3f} +---------------------------------------------------------------------------- +""" +print(output) + +############################################################################### +# stop mapdl +mapdl.exit() diff --git a/examples/verif-manual/vm-007-plastic_compression_of_a_pipe_assembly.py b/examples/verif-manual/vm-007-plastic_compression_of_a_pipe_assembly.py new file mode 100644 index 000000000..cf8b632eb --- /dev/null +++ b/examples/verif-manual/vm-007-plastic_compression_of_a_pipe_assembly.py @@ -0,0 +1,616 @@ +r""" +.. _ref_vm7_example: + +Plastic Compression of a Pipe Assembly +-------------------------------------- +Problem Description: + - Two coaxial tubes, the inner one of 1020 CR steel and cross-sectional + area :math:`A_{\mathrm{s}}`, and the outer one of 2024-T4 aluminum alloy + and of area :math:`A_{\mathrm{a}}`, are compressed between heavy, flat end plates, + as shown below. Determine the load-deflection curve of the assembly + as it is compressed into the plastic region by an axial displacement. + Assume that the end plates are so stiff that both tubes are shortened by + exactly the same amount. + +Reference: + - S. H. Crandall, N. C. Dahl, An Introduction to the Mechanics of Solids, + McGraw-Hill Book Co., Inc., New York, NY, 1959, pg. 180, ex. 5.1. + +Analysis Type(s): + - Static, Plastic Analysis (``ANTYPE=0``) + +Element Type(s): + - Plastic Straight Pipe Element (PIPE288) + - 4-Node Finite Strain Shell (SHELL181) + - 3-D Structural Solid Elements (SOLID185) + +.. image:: _static/vm7_setup_2.png + :width: 400 + :alt: VM7 Finite Element Models + +Material Properties + - :math:`E_{\mathrm{s}} = 26875000\,psi` + - :math:`\sigma_{\mathrm{(yp)s}} = 86000\,psi` + - :math:`E_{\mathrm{a}} = 11000000\,psi` + - :math:`\sigma_{\mathrm{(yp)a}} = 55000\,psi` + - :math:`\nu = 0.3` + +.. image:: _static/vm7_setup_1.png + :width: 300 + :alt: VM7 Material Model + +Geometric Properties: + - :math:`l = 10\,in` + - :math:`A_{\mathrm{s}} = 7\,in^2` + - :math:`A_{\mathrm{a}} = 12\,in^2` + +Loading: + - 1st Load Step: :math:`\delta = 0.032\,in` + - 2nd Load Step: :math:`\delta = 0.050\,in` + - 3rd Load Step: :math:`\delta = 0.100\,in` + +.. image:: _static/vm7_setup.png + :width: 300 + :alt: VM7 Problem Sketch + +Analysis Assumptions and Modeling Notes: + - The following tube dimensions, which provide the desired cross-sectional + areas, are arbitrarily chosen: + + * Inner (steel) tube: inside radius = 1.9781692 in., wall thickness = 0.5 in. + * Outer (aluminum) tube: inside radius = 3.5697185 in., wall thickness = 0.5 in. + + - The problem can be solved in three ways: + + * using ``PIPE288`` - the plastic straight pipe element + * using ``SOLID185`` - the 3-D structural solid element + * using ``SHELL181`` - the 4-Node Finite Strain Shell + + - In the SOLID185 and SHELL181 cases, since the problem is axisymmetric, + only a one element :math:`\theta` -sector is modeled. A small angle :math:`\theta = 6°` + is arbitrarily chosen to reasonably approximate the circular boundary + with straight sided elements. + The nodes at the boundaries have the ``UX`` (radial) degree of freedom coupled. + In the SHELL181 model, the nodes at the boundaries additionally have + the ``ROTY`` degree of freedom coupled. + +""" + +############################################################################### +# Start MAPDL +# ~~~~~~~~~~~ +# Start MAPDL and import Numpy and Pandas libraries. + +# sphinx_gallery_thumbnail_path = '_static/vm7_setup.png' + +from ansys.mapdl.core import launch_mapdl +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd + +# Start MAPDL. +mapdl = launch_mapdl() + + +############################################################################### +# Pre-Processing +# ~~~~~~~~~~~~~~ +# Enter verification example mode and the pre-processing routine. + +mapdl.clear() +mapdl.verify() +mapdl.prep7(mute=True) + + +############################################################################### +# Parameterization +# ~~~~~~~~~~~~~~~~ + +# Angle of the model sector. +theta = 6 + +# Deflection load steps. +defl_ls1 = -0.032 +defl_ls2 = -0.05 +defl_ls3 = -0.1 + + +############################################################################### +# Define Element Type +# ~~~~~~~~~~~~~~~~~~~ +# Set up the element types . + +# Element type PIPE288. +mapdl.et(1, "PIPE288") + +# Special Features are defined by keyoptions of pipe element. +# KEYOPT(4)(2) +# Hoop strain treatment: +# Thick pipe theory. +mapdl.keyopt(1, 4, 2) # Cubic shape function + +# Element type SOLID185. +mapdl.et(2, "SOLID185") + +# Element type SHELL181. +mapdl.et(3, "SHELL181") # FULL INTEGRATION + +# Special Features are defined by keyoptions of shell element. +# KEYOPT(3)(2) +# Integration option: +# Full integration with incompatible modes. +mapdl.keyopt(3, 3, 2) + +# Print +print(mapdl.etlist()) + + +############################################################################### +# Define Material +# ~~~~~~~~~~~~~~~ +# Set up the material properties. +# +# * Young Modulus of steel is: :math:`E_{\mathrm{s}} = 26875000\,psi`, +# * Yield strength of steel is: :math:`\sigma_{\mathrm{(yp)s}} = 86000\, psi`, +# * Young Modulus of aluminum is: :math:`E_{\mathrm{a}} = 11000000\,psi`, +# * Yield strength of aluminum is: :math:`\sigma_{\mathrm{(yp)a}} = 55000\,psi`, +# * Poisson's ratio is: :math:`\nu = 0.3` + +# Steel material model. +# Define Young's moulus and Poisson ratio for Steel. +mapdl.mp("EX", 1, 26.875e6) +mapdl.mp("PRXY", 1, 0.3) + +# Define non-linear material properties for Steel. +mapdl.tb("BKIN", 1, 1) +mapdl.tbtemp(0) +mapdl.tbdata(1, 86000, 0) + +# Aluminum material model. +# Define Young's moulus and Poisson ratio for Aluminum. +mapdl.mp("EX", 2, 11e6) +mapdl.mp("PRXY", 2, 0.3) + +# Define non-linear material properties for Aluminum. +mapdl.tb("BKIN", 2, 1) +mapdl.tbtemp(0) +mapdl.tbdata(1, 55000, 0) + +# Print +print(mapdl.mplist()) + + +############################################################################### +# Plot Stress - Strain Curve +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Use Matplotlib library to plot material model curves of steel and aluminum. + +# Define stress - strain properties of the steel. +steel = {"stress_s": [0, 86000, 86000, 86000], "strain_s": [0, 0.032, 0.1, 0.2]} + +# Define yielding strength point of the steel on the curve. +xp = steel["strain_s"][1] +yp = steel["stress_s"][1] + +# Set up the settings of the steel curve. +plt.plot( + steel["strain_s"], + steel["stress_s"], + label="1020 CR STEEL", + linewidth=2, + color="steelblue", + linestyle="-", + marker="o", +) +plt.plot(xp, yp, marker="o") + +# Annotation settings +plt.annotate( + r"${(\sigma_{yp})_s}$", + xy=(xp, yp), + xytext=(0.05, 75000), + arrowprops=dict(facecolor="steelblue", shrink=0.05), + bbox=dict(facecolor="steelblue", edgecolor="black", boxstyle="round, pad=1"), +) + +# Define stress - strain properties of the aluminum. +aluminum = {"stress_a": [0, 55000, 55000, 55000], "strain_a": [0, 0.05, 0.1, 0.2]} + +# Define yielding strength point of the Aluminum on the curve. +xp = aluminum["strain_a"][1] +yp = aluminum["stress_a"][1] + +# Set up the settings of the aluminum curve. +plt.plot( + aluminum["strain_a"], + aluminum["stress_a"], + label="2024-T4 Aluminum", + linewidth=2, + color="sandybrown", + linestyle="-", + marker="o", +) +plt.plot(xp, yp, marker="o") + +# Annotation settings +plt.annotate( + r"${(\sigma_{yp})_a}$", + xy=(xp, yp), + xytext=(0.07, 45000), + arrowprops=dict(facecolor="sandybrown", shrink=0.05), + bbox=dict(facecolor="sandybrown", edgecolor="black", boxstyle="round, pad=1"), +) + +plt.grid(True) +plt.legend() +plt.title("Stress - Strain Curve", fontsize=18) +plt.show() + + +############################################################################### +# Define Section +# ~~~~~~~~~~~~~~ +# Set up the cross-section properties for a shell and pipe elements. + +# Shell cross-section for inside tube(steel). +mapdl.sectype(1, "SHELL") + +# Thickness (SHELL181) +mapdl.secdata(0.5, 1, 0, 5) + +# Shell cross-section for outside tube(aluminum). +mapdl.sectype(2, "SHELL") + +# Thickness (SHELL181) +mapdl.secdata(0.5, 2, 0, 5) + +# Define Pipe cross-section for inside tube(steel). +mapdl.sectype(3, "PIPE") + +# Outside diameter and wall thickness settings for inside tube(PIPE288). +mapdl.secdata(4.9563384, 0.5) + +# Pipe cross-section for outside tube(aluminum) . +mapdl.sectype(4, "PIPE") + +# Outside diameter and wall thickness settings for outside tube (PIPE288). +mapdl.secdata(8.139437, 0.5) + +# Print the section properties for all sections. +print(mapdl.slist()) + + +############################################################################### +# Define Geometry +# ~~~~~~~~~~~~~~~ +# Set up the nodes and create the elements through the nodes. + +# Generate nodes and elements for PIPE288. +mapdl.n(1, x=0, y=0, z=0) +mapdl.n(2, x=0, y=0, z=10) + +# Create element for steel(inside) tube cross-section. +mapdl.mat(1) +mapdl.secnum(3) +mapdl.e(1, 2) + +# Create element for aluminum(outside) tube cross-section. +mapdl.mat(2) +mapdl.secnum(4) +mapdl.e(1, 2) + +# Activate the global cylindrical coordinate system. +mapdl.csys(1) + +# Generate nodes and elements for SOLID185. +mapdl.n(node=101, x=1.9781692) +mapdl.n(node=101, x=1.9781692) +mapdl.n(node=102, x=2.4781692) +mapdl.n(node=103, x=3.5697185) +mapdl.n(node=104, x=4.0697185) +mapdl.n(node=105, x=1.9781692, z=10) +mapdl.n(node=106, x=2.4781692, z=10) +mapdl.n(node=107, x=3.5697185, z=10) +mapdl.n(node=108, x=4.0697185, z=10) + +# Generate 2nd set of nodes to form a theta degree slice. +mapdl.ngen(itime=2, inc=10, node1=101, node2=108, dy=theta) + +# Rotate nodal coordinate systems into the active system. +mapdl.nrotat(node1=101, node2=118, ninc=1) + +# Create elements for Inside (Steel) tube. +mapdl.type(2) +mapdl.mat(1) +mapdl.e(101, 102, 112, 111, 105, 106, 116, 115) + +# Create elements for Outside (Aluminum) tube +mapdl.mat(2) +mapdl.e(103, 104, 114, 113, 107, 108, 118, 117) + +# Generate nodes. +mapdl.n(node=201, x=2.2281692) +mapdl.n(node=203, x=2.2281692, z=10) +mapdl.n(node=202, x=3.8197185) +mapdl.n(node=204, x=3.8197185, z=10) + +# Generate nodes to form a theta degree slice +mapdl.ngen(itime=2, inc=4, node1=201, node2=204, dy=theta) + +# Create element for Steel(Inside) tube cross-section. +mapdl.type(3) +mapdl.secnum(1) +mapdl.e(203, 201, 205, 207) + +# Create element for Aluminum(Outside) tube cross-section. +mapdl.secnum(2) +mapdl.e(204, 202, 206, 208) + +# Plot element model to demonstrate the axisymmetric element model. +cpos = [ + (19.67899462804619, 17.856836088414664, 22.644135378046194), + (2.03485925, 0.21270071036846988, 5.0), + (0.0, 0.0, 1.0), +] +mapdl.eplot(cpos=cpos) + + +############################################################################### +# Define Boundary Conditions +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Application of boundary conditions (BC) for simplified axisymmetric model. + +# Apply constraints to the PIPE288 model. +# Fix all DOFs for bottom end of PIPE288. +mapdl.d(node=1, lab="ALL") + +# Allow only UZ DOF at top end of the PIPE288. +mapdl.d(node=2, lab="UX", lab2="UY", lab3="ROTX", lab4="ROTY", lab5="ROTZ") + +# Apply constraints to SOLID185 and SHELL181 models" +# Couple nodes at boundary in RADIAL direction for SOLID185. +mapdl.cp(nset=1, lab="UX", node1=101, node2=111, node3=105, node4=115) +mapdl.cpsgen(itime=4, nset1=1) + +# Couple nodes at boundary in RADIAL direction for the SHELL181. +mapdl.cp(5, lab="UX", node1=201, node2=205, node3=203, node4=20) +mapdl.cpsgen(itime=2, nset1=5) + +# Couple nodes at boundary in ROTY dir for SHELL181. +mapdl.cp(7, lab="ROTY", node1=201, node2=205) +mapdl.cpsgen(itime=4, nset1=7) + +# Select only nodes in SOLID185 and SHELL181 models. +mapdl.nsel(type_="S", item="NODE", vmin=101, vmax=212) + +# Select only nodes at theta = 0 from the selected set. +mapdl.nsel("R", "LOC", "Y", 0) + +# Apply symmetry boundary conditions. +mapdl.dsym("SYMM", "Y", 1) + +# Select only nodes in SOLID185 and SHELL181 models. +mapdl.nsel(type_="S", item="NODE", vmin=101, vmax=212) + +# elect nodes at theta from the selected set. +mapdl.nsel("R", "LOC", "Y", theta) + +# Apply symmetry boundary conditions. +mapdl.dsym("SYMM", "Y", 1) + +# Select all nodes and RESELECT only nodes at Z = 0. +mapdl.nsel("ALL") +mapdl.nsel("R", "LOC", "Z", 0) + +# Constrain bottom nodes in Z direction. +mapdl.d("ALL", "UZ", 0) + +# Select all nodes. +mapdl.nsel("ALL") +mapdl.finish(mute=True) + + +############################################################################### +# Solve +# ~~~~~ +# Enter solution mode and solve the system. + +# Start solution procedure. +mapdl.slashsolu() + +# Define solution function. +def solution(deflect): + mapdl.nsel("R", "LOC", "Z", 10) + mapdl.d(node="ALL", lab="UZ", value=deflect) + mapdl.nsel("ALL") + mapdl.solve() + + +# Run each load step to reproduce needed deflection subsequently. +# Load Step 1 +solution(deflect=defl_ls1) + +# Load Step 2 +solution(deflect=defl_ls2) + +# Load Step 3 +solution(deflect=defl_ls3) +mapdl.finish(mute=True) + + +############################################################################### +# Post-processing +# ~~~~~~~~~~~~~~~ +# Enter post-processing. + +# Enter the post-processing routine. +mapdl.post1(mute=True) + + +############################################################################### +# Getting loads +# ~~~~~~~~~~~~~ +# Set up the function to get load values of each load step of the simplified +# axisymmetric model and convert it to the full model. + + +def getload(): + + # Select the nodes in the PIPE288 element model. + mapdl.nsel(type_="S", item="NODE", vmin=1, vmax=2) + mapdl.nsel("R", "LOC", "Z", 0) + + # Sum the nodal force contributions of elements. + mapdl.fsum() + + # Extrapolation of the force results in the full 360 (deg) model. + load_288 = mapdl.get_value("FSUM", 0, "ITEM", "FZ") + + # Select the nodes in the SOLID185 element model. + mapdl.nsel(type_="S", item="NODE", vmin=101, vmax=118) + mapdl.nsel("R", "LOC", "Z", 0) + mapdl.fsum() + + # Get the force value of the simplified model. + load_185_theta = mapdl.get_value("FSUM", 0, "ITEM", "FZ") + + # Extrapolation of the force results in the full 360 (deg) model. + load_185 = load_185_theta * 360 / theta + + # Select the nodes in the SHELL181 element model. + mapdl.nsel("S", "NODE", "", 201, 212) + mapdl.nsel("R", "LOC", "Z", 0) + + # Sum the nodal force contributions of elements. + mapdl.fsum() + + # Get the force value of the simplified model. + load_181_theta = mapdl.get_value("FSUM", 0, "ITEM", "FZ") + + # Extrapolation of the force results in the full 360 (deg) model. + load_181 = load_181_theta * 360 / theta + + # Return load results of each element model. + return abs(round(load_288, 0)), abs(round(load_185, 0)), abs(round(load_181, 0)) + + +############################################################################### +# Getting Loads For Each Load Step +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Obtain the loads of the model using :func:`getload()` function. + +# Activate Load Step 1 and extract load data. +mapdl.set(1, 1) +pipe288_ls1, solid185_ls1, shell181_ls1 = getload() + +# Activate Load Step 2 and extract load data. +mapdl.set(2, 1) +pipe288_ls2, solid185_ls2, shell181_ls2 = getload() + +# Activate Load Step 3 and extract load data. +mapdl.set(3, 1) +pipe288_ls3, solid185_ls3, shell181_ls3 = getload() + + +############################################################################### +# Check Results +# ~~~~~~~~~~~~~ +# Finally we have the results of the loads for the simplified axisymmetric model, +# which can be compared with expected target values for models with ``PIPE288``, +# ``SOLID185``, and ``SHELL181`` elements. Loads expected for each load step are: +# +# - 1st Load Step with deflection :math:`\delta = 0.032 (in)` has :math:`load_1 = 1024400\,(lb)`. +# - 2nd Load Step with deflection :math:`\delta = 0.05 (in)` has :math:`load_2 = 1262000\,(lb)`. +# - 3rd Load Step with deflection :math:`\delta = 0.1 (in)` has :math:`load_3 = 1262000\,(lb)`. + +target_res = np.asarray( + [1024400, 1262000, 1262000, 1024400, 1262000, 1262000, 1024400, 1262000, 1262000] +) + +simulation_res = np.asarray( + [ + pipe288_ls1, + pipe288_ls2, + pipe288_ls2, + solid185_ls1, + solid185_ls2, + solid185_ls3, + shell181_ls1, + shell181_ls2, + shell181_ls3, + ] +) + +main_columns = { + "Target": target_res, + "Mechanical APDL": simulation_res, + "Ratio": list(np.divide(simulation_res, target_res)), +} + +row_tuple = [ + ("PIPE288", "Load, lb for Deflection = 0.032 in"), + ("PIPE288", "Load, lb for Deflection = 0.05 in"), + ("PIPE288", "Load, lb for Deflection = 0.1 in"), + ("SOLID185", "Load, lb for Deflection = 0.032 in"), + ("SOLID185", "Load, lb for Deflection = 0.05 in"), + ("SOLID185", "Load, lb for Deflection = 0.1 in"), + ("SHELL181", "Load, lb for Deflection = 0.032 in"), + ("SHELL181", "Load, lb for Deflection = 0.05 in"), + ("SHELL181", "Load, lb for Deflection = 0.1 in"), +] + +index_names = ["Element Type", "Load Step"] +row_indexing = pd.MultiIndex.from_tuples(row_tuple) +df = pd.DataFrame(main_columns, index=row_indexing) + +df.style.set_caption("Results Comparison",).set_table_styles( + [ + { + "selector": "th.col_heading", + "props": [ + ("background-color", "#FFEFD5"), + ("color", "black"), + ("border", "0.5px solid black"), + ("font-style", "italic"), + ("text-align", "center"), + ], + }, + { + "selector": "th.row_heading", + "props": [ + ("background-color", "#FFEFD5"), + ("color", "black"), + ("border", "0.5px solid black"), + ("font-style", "italic"), + ("text-align", "center"), + ], + }, + {"selector": "td:hover", "props": [("background-color", "#FFF8DC")]}, + {"selector": "th", "props": [("max-width", "120px")]}, + {"selector": "", "props": [("border", "0.5px solid black")]}, + { + "selector": "caption", + "props": [ + ("color", "black"), + ("font-style", "italic"), + ("font-size", "24px"), + ("text-align", "center"), + ], + }, + ], +).set_properties( + **{ + "background-color": "#FFFAFA", + "color": "black", + "border-color": "black", + "border-width": "0.5px", + "border-style": "solid", + "text-align": "center", + } +).format( + "{:.3f}" +) + +############################################################################### +# stop mapdl +mapdl.exit() diff --git a/examples/verif-manual/vm-008-parametric_calculation.py b/examples/verif-manual/vm-008-parametric_calculation.py new file mode 100644 index 000000000..1021ee8de --- /dev/null +++ b/examples/verif-manual/vm-008-parametric_calculation.py @@ -0,0 +1,237 @@ +r""" +.. _ref_vm8_example: + +Parametric Calculation +---------------------- +Problem Description: + - Write a user file macro to calculate the distance ``d`` between either nodes + or keypoints in ``PREP7``. Define abbreviations for calling the macro and + verify the parametric expressions by using the macro to calculate + the distance between nodes :math:`N_1` and :math:`N_2` and + between keypoints :math:`K_3` and :math:`K_4`. + +Reference: + - None. + +Analysis Type(s): + - Parametric Arithmetic. + +Element Type: + - None. + +Geometric Properties(Coordinates): + - :math:`N_{\mathrm{1(x,y,z)}} = 1.5, 2.5, 3.5` + - :math:`N_{\mathrm{2(x,y,z)}} = -3.7, 4.6, -3` + - :math:`K_{\mathrm{3(x,y,z)}} = 100, 0, 30` + - :math:`K_{\mathrm{4(x,y,z)}} = -200,25,80` + +.. image:: _static/vm8_setup.png + :width: 300 + :alt: VM8 Problem Sketch + +Analysis Assumptions and Modeling Notes: + - Instead of ``*CREATE``, ``*USE``, etc., we have created a class + ``Create`` with methods that correspond to each type of simulation. + This class gives a possibility to change coordinates and reuse it. + The simulation can be checked not just by target values, but also + with the simple distances' formula between keypoints as: + + * Calculate distance between two keypoints in the Cartesian coordinate system: + :math:`D = \sqrt[2]{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}` + * Python representation of the distance formula: + .. doctest:: + + import math + # Define coordinates for keypoints K3 and K4. + x1, y1, z1 = 100, 0, 30 + x2, y2, z2 = -200, 25, 80 + dist_kp = math.sqrt((x2 - x1)**2 + (y2 - y1)**2 + (z2 - z1)**2) + print(dist_kp) + +""" + +############################################################################### +# Start MAPDL +# ~~~~~~~~~~~ +# Start MAPDL and import Numpy and Pandas libraries. + +# sphinx_gallery_thumbnail_path = '_static/vm8_setup.png' + +from ansys.mapdl.core import launch_mapdl +import numpy as np +import pandas as pd + +# Start MAPDL. +mapdl = launch_mapdl() + + +############################################################################### +# Pre-Processing +# ~~~~~~~~~~~~~~ +# Enter verification example mode and the pre-processing routine. + +mapdl.clear() +mapdl.verify() +mapdl.prep7(mute=True) + + +############################################################################### +# Define Class +# ~~~~~~~~~~~~ +# Identifying the class ``create`` with methods ``create_kp_method`` and +# ``create_node_method`` to calculate and plot the distances between keypoints +# and nodes. + + +class Create: + def __init__(self, p1, p2): + # Points Attributes. + self.p1 = p1 + self.p2 = p2 + + def kp_distances(self): + + # Define keypoints by coordinates. + kp1 = mapdl.k(npt=3, x=self.p1[0], y=self.p1[1], z=self.p1[2]) + kp2 = mapdl.k(npt=4, x=self.p2[0], y=self.p2[1], z=self.p2[2]) + + # Get the distance between keypoints. + dist_kp, kx, ky, kz = mapdl.kdist(kp1, kp2) + + # Plot keypoints. + mapdl.kplot( + show_keypoint_numbering=True, + vtk=True, + background="grey", + show_bounds=True, + font_size=26, + ) + return dist_kp + + def node_distances(self): + + # Define nodes by coordinates. + node1 = mapdl.n(node=1, x=self.p1[0], y=self.p1[1], z=self.p1[2]) + node2 = mapdl.n(node=2, x=self.p2[0], y=self.p2[1], z=self.p2[2]) + + # Get the distance between nodes. + dist_node, node_x, node_y, node_z = mapdl.ndist(node1, node2) + + # Plot nodes. + mapdl.nplot(nnum=True, vtk=True, color="grey", show_bounds=True, font_size=26) + return dist_node + + @property + def p1(self): + # Getting value + return self._p1 + + @p1.setter + def p1(self, new_value): + # Check the data type: + if not isinstance(new_value, list): + raise ValueError("The coordinates should be implemented by the list!") + # Check the quantity of items: + if len(new_value) != 3: + raise ValueError( + "The coordinates should have three items in the list as [X, Y, Z]" + ) + self._p1 = new_value + + @property + def p2(self): + return self._p2 + + @p2.setter + def p2(self, new_value): + # Check the data type: + if not isinstance(new_value, list): + raise ValueError("The coordinates should be implemented by the list!") + # Check the quantity of items: + if len(new_value) != 3: + raise ValueError( + "The coordinates should have three items in the list as [X, Y, Z]" + ) + self._p2 = new_value + + +############################################################################### +# Distance between keypoints +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Using already created method for keypoints to get the distance between them +# and print out an output. The keypoints have got next coordinates: +# +# * :math:`K_{\mathrm{3(x,y,z)}} = 100, 0, 30` +# * :math:`K_{\mathrm{4(x,y,z)}} = -200, 25,80` + +kp1 = [100, 0, 30] +kp2 = [-200, 25, 80] +kp = Create(kp1, kp2) +kp_dist = kp.kp_distances() +print(f"Distance between keypoint is: {kp_dist:.2f}\n\n") + +# Print the list of keypoints. +print(mapdl.klist()) + + +############################################################################### +# Distance between nodes. +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Using already created method for nodes to get the distance between them and +# print out an output. The nodes have got next coordinates: +# +# * :math:`N_{\mathrm{1(x,y,z)}} = 1.5, 2.5, 3.5` +# * :math:`N_{\mathrm{2(x,y,z)}} = -3.7, 4.6, -3` + +node1 = [1.5, 2.5, 3.5] +node2 = [-3.7, 4.6, -3] +nodes = Create(node1, node2) +node_dist = nodes.node_distances() +print(f"Distance between nodes is: {node_dist:.2f}\n\n") + +# Print the list of nodes. +print(mapdl.nlist()) + + +############################################################################### +# Check Results +# ~~~~~~~~~~~~~ +# Finally we have the results of the distances for both simulations, +# which can be compared with expected target values: +# +# - 1st simulation to get the distance between keypoints :math:`K_3` and :math:`K_4`, +# where :math:`LEN_1 = 305.16\,(in)` +# - 2nd simulation to get the distance between nodes :math:`N_1` and :math:`N_2`, +# where :math:`LEN_2 = 8.58\,(in)` +# +# For better representation of the results we can use ``pandas`` dataframe +# with following settings below: + +# Define the names of the rows. +row_names = ["N1 - N2 distance (LEN2)", "K3 - K4 distance (LEN1)"] + +# Define the names of the columns. +col_names = ["Target", "Mechanical APDL", "RATIO"] + +# Define the values of the target results. +target_res = np.asarray([8.5849, 305.16]) + +# Create an array with outputs of the simulations. +simulation_res = np.asarray([node_dist, kp_dist]) + +# Identifying and filling corresponding columns. +main_columns = { + "Target": target_res, + "Mechanical APDL": simulation_res, + "Ratio": list(np.divide(simulation_res, target_res)), +} + +# Create and fill the output dataframe with pandas. +df2 = pd.DataFrame(main_columns, index=row_names).round(2) + +# Apply settings for the dataframe. +df2.head() + +############################################################################### +# stop mapdl +mapdl.exit() diff --git a/examples/verif-manual/vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py b/examples/verif-manual/vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py new file mode 100644 index 000000000..925433be0 --- /dev/null +++ b/examples/verif-manual/vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py @@ -0,0 +1,375 @@ +r""" +.. _ref_vm9_example: + +Large Lateral Deflection of Unequal Stiffness Springs +----------------------------------------------------- +Problem Description: + - A two-spring system is subjected to a force :math:`F` as shown below. + Determine the strain energy of the system and + the displacements :math:`\delta_x` and :math:`\delta_y`. + +Reference: + - G. N. Vanderplaats, *Numerical Optimization Techniques for Engineering + Design with Applications*, McGraw-Hill Book Co., Inc., New York, + NY,1984, pp. 72-73, ex. 3-1. + +Analysis Type(s): + - Nonlinear Transient Dynamic Analysis (``ANTYPE = 4``) + +Element Type(s): + - Spring-Damper Elements (COMBIN14) + - Spring-Damper Elements (COMBIN40) + +.. image:: _static/vm9_setup_2.png + :width: 400 + :alt: Geometry of COMBIN14 and COMBIN40 + +Material Properties + - :math:`k_1 = 8\,N/cm` + - :math:`k_2 = 1\,N/cm` + - :math:`m = 1` + +Geometric Properties: + - :math:`l = 10\,cm` + +Loading: + - :math:`F = 5{\sqrt[2]{2}}\,N` + - :math:`\alpha = 45\,º` + +.. image:: _static/vm9_setup.png + :width: 400 + :alt: VM9 Problem Sketch + +Analysis Assumptions and Modeling Notes: + - The solution to this problem is best obtained by adding mass and using + the "slow dynamics" technique with approximately critical damping. + Combination elements ``COMBIN40`` are used to provide damping + in the :math:`X` and :math:`Y` directions. Approximate damping coefficients + :math:`c_x` and :math:`c_y`, in the :math:`X` and :math:`Y` directions respectively, + are determined from: + + * :math:`c_x = \sqrt[2]{k_xm}` + * :math:`c_y = \sqrt[2]{k_ym}` + + where m is arbitrarily assumed to be unity. + + - :math:`k_x` and :math:`k_y` cannot be known before solving so are approximated + by :math:`k_y = k_2 = 1\,N/cm` and :math:`k_x = k_y/2 = 0.5\,N/cm`, + hence :math:`c_x = 1.41` and :math:`c_y = 2.0`. Large deflection analysis is + performed due to the fact that the resistance to the load is a function of + the deformed position. ``POST1`` is used to extract results from + the solution phase. + +""" + +############################################################################### +# Start MAPDL +# ~~~~~~~~~~~ +# Start MAPDL and import Numpy and Pandas libraries. + +# sphinx_gallery_thumbnail_path = '_static/vm9_setup.png' + +from ansys.mapdl.core import launch_mapdl +import numpy as np +import pandas as pd + +# Start MAPDL. +mapdl = launch_mapdl() + + +############################################################################### +# Pre-Processing +# ~~~~~~~~~~~~~~ +# Enter verification example mode and the pre-processing routine. + +mapdl.clear() +mapdl.verify() +mapdl.prep7(mute=True) + + +############################################################################### +# Parameterization +# ~~~~~~~~~~~~~~~~ +# Parameterization block includes main variables as : +# +# * :math:`l = 10\,cm` - spring length. +# * :math:`k_1 = 8\,N/cm` - stiffness of the 1st spring. +# * :math:`k_2 = 1\,N/cm` - stiffness of the 2nd spring. +# * :math:`m = 1` - mass. +# * :math:`F = 5\sqrt[2]{2}\,N` - main load +# * :math:`\alpha = 45\,º` - force angle +# * :math:`c_x = \sqrt[2]{k_xm} = 1,41` - damping coefficient, x-direction. +# * :math:`c_y = \sqrt[2]{k_ym} = 2.0` - damping coefficient, y-direction. + +# Main variables: +length = 10 +k_spring1 = 8 +k_spring2 = 1 +c_damp_x = 1.41 +c_damp_y = 2.0 +mass = 1 + +# Fx and Fy has been obtained by the projection F on the X and Y axes. +f_x = 5 +f_y = 5 + + +############################################################################### +# Define Element Type +# ~~~~~~~~~~~~~~~~~~~ +# Set up the element types. + +# Element type COMBIN14. +mapdl.et(1, "COMBIN14") + +# Special Features are defined by keyoptions of the element COMBIN14. +# KEYOPT(3)(2) +# Degree-of-freedom selection for 2-D and 3-D behavior: +# 2-D longitudinal spring-damper (2-D elements must lie in an X-Y plane) +mapdl.keyopt(1, 3, 2) + +# Element type COMBIN40. +mapdl.et(3, "COMBIN40") + +# Special Features are defined by keyoptions of the element COMBIN40. +# KEYOPT(3)(1) +# Element degrees of freedom: +# UX (Displacement along nodal X axes) +mapdl.keyopt(3, 3, 1) + +# KEYOPT(6)(2) +# Mass location: +# Mass at node J +mapdl.keyopt(3, 6, 2) + +# Element type COMBIN40. +mapdl.et(4, "COMBIN40") + +# Special Features are defined by keyoptions of the element COMBIN40. +# KEYOPT(3)(2) +# Element degrees of freedom: +# UX (Displacement along nodal X axes) +mapdl.keyopt(4, 3, 2) + +# KEYOPT(6)(2) +# Mass location: +# Mass at node J +mapdl.keyopt(4, 6, 2) + +# Print the list of the elements and their attributes. +print(mapdl.etlist()) + + +############################################################################### +# Define Real Constants +# ~~~~~~~~~~~~~~~~~~~~~ +# Define damping coefficients :math:`c_x = 1.41`, :math:`c_y = 2.0` and +# stiffness values :math:`k_1 = 8\,N/cm`, :math:`k_2 = 1\,N/cm` for the +# spring elements. + +# Define real constant 1 with stiffness k2. +mapdl.r(nset=1, r1=k_spring2) # SPRING STIFFNESS = 1 + +# Define real constant 2 with stiffness k1. +mapdl.r(nset=2, r1=k_spring1) # SPRING STIFFNESS = 8 + +# Define real constant 3 with damping coef. in X-direction and mass. +mapdl.r(nset=3, r2=c_damp_x, r3=mass) + +# Define real constant 4 with damping coef. in y-direction and mass. +mapdl.r(nset=4, r2=c_damp_y, r3=mass) + +# Print the real constant list. +print(mapdl.rlist()) + + +############################################################################### +# Define Nodes +# ~~~~~~~~~~~~ +# Set up the nodes coordinates using python ``for`` loop. + +# Lists with nodes coordinates. +node_x_coord = [0, 0, 0, -1, 0] +node_y_coord = [0, 10, 20, 10, 9] + +# Create nodes. +for i in range(0, 5): + mapdl.n(node=i + 1, x=node_x_coord[i], y=node_y_coord[i]) + +# Print the list of the created nodes. +print(mapdl.nlist()) + + +############################################################################### +# Create Elements +# ~~~~~~~~~~~~~~~ +# Create the elements through the nodes. + +# Create spring element COMBIN14 between nodes 1 nad 2 +# with stiffness k_2 = 1 N/cm. +mapdl.type(1) +mapdl.real(1) +mapdl.e(1, 2) + +# Create spring element COMBIN14 between nodes 2 nad 3 +# with stiffness k_1 = 8 N/cm. +mapdl.type(1) +mapdl.real(2) +mapdl.e(2, 3) + +# Create spring element COMBIN40 between nodes 4 nad 2 +# with damping coefficient c_x = 1.41. +mapdl.type(3) +mapdl.real(3) +mapdl.e(4, 2) + +# Create spring element COMBIN40 between nodes 5 nad 2 +# with damping coefficient c_y = 2.0. +mapdl.type(4) +mapdl.real(4) +mapdl.e(5, 2) + +# Print the list of the created elements. +print(mapdl.elist()) + + +############################################################################### +# Define Boundary Conditions +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Application of boundary conditions (BC) for the spring model. + +# Unselect the node where the force is applied. +mapdl.nsel("U", "NODE", vmin=2) + +# Apply BC to the selected set of the nodes. +mapdl.d("ALL", "ALL") +mapdl.nsel("ALL") + +# Finish pre-processing mode. +mapdl.finish(mute=True) + + +############################################################################### +# Solution settings +# ~~~~~~~~~~~~~~~~~ +# Enter solution mode and apply settings for *Transient Dynamic Analysis*. + +# Starts solution (/solu) mode. +mapdl.slashsolu() + +# Define transient analysis with large deflection setting. +mapdl.antype("TRANS") +mapdl.nlgeom("ON") + +# Specifies the stepped loading condition within a load step. +mapdl.kbc(1) + +# Apply forces to the node 2. +mapdl.f(2, "FX", f_x) +mapdl.f(2, "FY", f_y) + +# Uses automatic time stepping. +mapdl.autots("ON") + +# Specifies the number of substeps to be taken this load step. +mapdl.nsubst(30) + +# Controls the solution printout. +mapdl.outpr("", "LAST") +mapdl.outpr("VENG", "LAST") + +# Sets the time for a load step. +mapdl.time(15, mute=True) + + +############################################################################### +# Solve +# ~~~~~ +# Solve the system , avoiding the printing output. + +# Run the simulation. +mapdl.solve() +mapdl.finish(mute=True) + + +############################################################################### +# Post-processing +# ~~~~~~~~~~~~~~~ +# Enter post-processing, avoiding the printing output. + +# Enter the post-processing mode. +mapdl.post1(mute=True) + + +############################################################################### +# Getting Displacements +# ~~~~~~~~~~~~~~~~~~~~~ +# Enter post-processing. To get results of the strain energy and displacements +# in X and Y directions from the node where the force is applied using +# :meth:`Mapdl.get_value `. + +# Defines the data set to be read from the results file by the time-point. +mapdl.set(time=15) + +# Fills a table of element values for further processing for strain energy. +mapdl.etable("SENE", "SENE") + +# Sum all active entries in element stress table. +mapdl.ssum() + +# Get the value of the stain energy of the spring elements. +strain_energy = mapdl.get_value(entity="SSUM", entnum=0, item1="ITEM", it1num="SENE") + +# Prints nodal solution results of the X, Y, and Z structural displacements +# and vector sum. +print(mapdl.prnsol("U", "COMP")) + +# Get the value of the displacements in X-direction. +disp_x = mapdl.get_value(entity="NODE", entnum=2, item1="U", it1num="X") + +# Get the value of the displacements in Y-direction. +disp_y = mapdl.get_value(entity="NODE", entnum=2, item1="U", it1num="Y") + + +############################################################################### +# Check Results +# ~~~~~~~~~~~~~ +# Finally we have the results of the strain energy and +# displacements in :math:`X` and :math:`Y` directions, which can be compared with +# expected target values: +# +# - Strain energy of the system :math:`U_{\mathrm{(energy)}} = 24.01\;N\,cm`. +# - Displacement in X-direction :math:`U_x = 8.631\,cm`. +# - Displacement in Y-direction :math:`U_y = 4.533\,cm`. +# +# For better representation of the results we can use ``pandas`` dataframe +# with following settings below: + +# Define the names of the rows. +row_names = ["Strain Energy, N-cm", "Deflection-x , cm", "Deflection-y , cm"] + +# Define the names of the columns. +col_names = ["Target", "Mechanical APDL", "RATIO"] + +# Define the values of the target results. +target_res = np.asarray([24.01, 8.631, 4.533]) + +# Create an array with outputs of the simulations. +simulation_res = np.asarray([strain_energy, disp_x, disp_y]) + +# Identifying and filling corresponding columns. +main_columns = { + "Target": target_res, + "Mechanical APDL": simulation_res, + "Ratio": list(np.divide(simulation_res, target_res)), +} + +# Create and fill the output dataframe with pandas. +df2 = pd.DataFrame(main_columns, index=row_names).round(2) + +# Apply settings for the dataframe. +df2.head() + +############################################################################### +# stop mapdl +mapdl.exit() diff --git a/examples/verif-manual/vm-010-bending_of_a_t-shaped_beam.py b/examples/verif-manual/vm-010-bending_of_a_t-shaped_beam.py new file mode 100644 index 000000000..f38997d88 --- /dev/null +++ b/examples/verif-manual/vm-010-bending_of_a_t-shaped_beam.py @@ -0,0 +1,285 @@ +r""" +.. _ref_vm10_example: + +Bending of a Tee-Shaped Beam +---------------------------- +Problem Description: + - Find the maximum tensile :math:`\sigma_{\mathrm{(B,Bot)}}` and compressive + :math:`\sigma_{\mathrm{(B,Top)}}` + bending stresses in an unsymmetrical `T-beam` subjected to uniform bending :math:`M_z`, + with dimensions and geometric properties as shown below. + +Reference: + - S. H. Crandall, N. C. Dahl, *An Introduction to the Mechanics of Solids*, + McGraw-Hill Book Co., Inc., New York, NY, 1959, pg. 294, ex. 7.2. + +Analysis Type(s): + - Static Analysis (``ANTYPE = 0``) + +Element Type(s): + - 3-D 2 Node Beam (``BEAM188``) + +.. figure:: _static/vm10_setup_1.png + :align: center + :width: 400 + :alt: VM10 Geometry of Beam188 and Element Model + :figclass: align-center + + **Figure 1: VM10 Geometry of Beam188 and Element Model** + +Material Properties + - :math:`E = 30 \cdot 10^6 psi` + - :math:`\nu = 0.3` + +Geometric Properties: + - :math:`l = 100\,in` + - :math:`h = 1.5\,in` + - :math:`b = 8\,in` + +Loading: + - :math:`M_z = 100,000\,in\,lb` + +.. image:: _static/vm10_setup.png + :width: 400 + :alt: VM10 Problem Sketch + +Analysis Assumptions and Modeling Notes: + - A length :math:`(l = 100 in)` is arbitrarily selected since the bending moment is constant. + A `T-section` beam is modeled using flange width :math:`(6b)`, + flange thickness :math:`(\frac{h}{2})`, overall depth :math:`(2h + \frac{h}{2})`, and + stem thickness :math:`(b)`, input using :meth:`Mapdl.secdata `. + +""" + +############################################################################### +# Start MAPDL +# ~~~~~~~~~~~ +# Start MAPDL and import Numpy and Pandas libraries. + +# sphinx_gallery_thumbnail_path = '_static/vm10_setup.png' + +from ansys.mapdl.core import launch_mapdl +import numpy as np +import pandas as pd + +# Start MAPDL. +mapdl = launch_mapdl() + + +############################################################################### +# Pre-Processing +# ~~~~~~~~~~~~~~ +# Enter verification example mode and the pre-processing routine. + +mapdl.clear() +mapdl.verify() +mapdl.prep7(mute=True) + + +############################################################################### +# Define Element Type +# ~~~~~~~~~~~~~~~~~~~ +# Set up the element type ``BEAM188``. + +# Type of analysis: Static. +mapdl.antype("STATIC") + +# Element type: BEAM188. +mapdl.et(1, "BEAM188") + +# Special Features are defined by keyoptions of BEAM188: + +# KEYOPT(3) +# Shape functions along the length: +# Cubic +mapdl.keyopt(1, 3, 3) # Cubic shape function + +# Print the list with currently defined element types. +print(mapdl.etlist()) + + +############################################################################### +# Define Material +# ~~~~~~~~~~~~~~~ +# Set up the material, where: +# +# * :math:`E = 30 \cdot 10^6 psi` - Young Modulus of steel. +# * :math:`\nu = 0.3` - Poisson's ratio. + +# Steel material model. +# Define Young's moulus and Poisson ratio for Steel. +mapdl.mp("EX", 1, 30e6) +mapdl.mp("PRXY", 1, 0.3) + +# Print the list of material properties. +print(mapdl.mplist()) + + +############################################################################### +# Define Section +# ~~~~~~~~~~~~~~ +# Set up the cross-section properties for a beam elements, where: +# +# * :math:`w_1 = 6b = 6 \cdot 1.5 = 9\,in` - flange width. +# * :math:`w_2 = 2h + h/2 = 2 \cdot 8 + 8/2 = 20\,in` - overall depth. +# * :math:`t_1 = h/2 = 8/2 = 4\,in` - flange thickness. +# * :math:`t_2 = b = 1.5\,in` - stem thickness. + +# Parameterization of the cross-section dimensions. +sec_num = 1 +w1 = 9 +w2 = 20 +t1 = 4 +t2 = 1.5 + +# Define the beam cross-section. +mapdl.sectype(sec_num, "BEAM", "T") +mapdl.secdata(w1, w2, t1, t2) + +# Print the section properties. +print(mapdl.slist()) + +############################################################################### +# Define Geometry +# ~~~~~~~~~~~~~~~ +# Set up the nodes and elements. Create nodes between elements. + +# Define nodes for the beam element. +mapdl.n(1, x=0, y=0) +mapdl.n(2, x=100, y=0) + +# Define one node for the orientation of the beam T-section. +mapdl.n(3, x=0, y=1) + +# Print the list of the created nodes. +print(mapdl.nlist()) + +############################################################################### +# Define elements +# ~~~~~~~~~~~~~~~ +# Create element between nodes 1 and 2 using node 3 as orientational node. + +# Create element. +mapdl.e(1, 2, 3) + +# Print the list of the elements and their attributes. +print(mapdl.elist()) + +# Display elements with their nodes numbers. +cpos = [ + (162.20508123980457, 109.41124535475498, 112.95887397446565), + (50.0, 0.0, 0.0), + (-0.4135015240403764, -0.4134577015789461, 0.8112146563156641), +] + +mapdl.eplot(show_node_numbering=True, line_width=5, cpos=cpos, font_size=40) + + +############################################################################### +# Define Boundary Conditions +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Application of boundary conditions (BC). + +mapdl.d(node=1, lab="ALL", mute=True) +mapdl.d(node="ALL", lab="UZ", lab2="ROTX", lab3="ROTY", mute=True) + + +############################################################################### +# Define Distributed Loads +# ~~~~~~~~~~~~~~~~~~~~~~~~ +# Apply a bending moment :math:`\mathrm{M_{z}}= 100000\,in\,lb`. + +# Parametrization of the bending moment. +bending_mz = 100000 + +# Application of the surface load to the beam element. +mapdl.f(node=2, lab="MZ", value=bending_mz) +mapdl.finish(mute=True) + + +############################################################################### +# Solve +# ~~~~~ +# Enter solution mode and run the simulation. + +# Start solution procedure. +mapdl.slashsolu() + +# Define the number of substeps to be taken this load step. +mapdl.nsubst(1) +mapdl.solve(mute=True) + + +############################################################################### +# Post-processing +# ~~~~~~~~~~~~~~~ +# Enter post-processing. + +# Enter the post-processing routine. +mapdl.post1(mute=True) + + +############################################################################### +# Getting Displacements +# ~~~~~~~~~~~~~~~~~~~~~ +# Using :meth:`Mapdl.etable ` get the results of +# the the maximum tensile and compressive bending stresses in +# an unsymmetric `T-beam` with :meth:`Mapdl.get_value `. + +# Create a table of element values for BEAM188. +mapdl.etable(lab="STRS_B", item="LS", comp=1) +mapdl.etable(lab="STRS_T", item="LS", comp=31) + +# Get the value of the maximum compressive stress. +strss_top_compr = mapdl.get_value( + entity="ELEM", entnum=1, item1="ETAB", it1num="STRS_T" +) + +# Get the value of the maximum tensile bending stress. +strss_bot_tens = mapdl.get_value(entity="ELEM", entnum=1, item1="ETAB", it1num="STRS_B") + + +############################################################################### +# Check Results +# ~~~~~~~~~~~~~ +# Finally we have the results of the the maximum tensile and +# compressive bending stresses, which can be compared with expected target +# values: +# +# - maximum tensile bending stress :math:`\sigma_{\mathrm{(B,Bot)}} = 300\,psi`. +# - maximum compressive bending stress :math:`\sigma_{\mathrm{(B,Top)}} = -700\,psi`. +# +# For better representation of the results we can use ``pandas`` dataframe +# with following settings below: + +# Define the names of the rows. +row_names = [ + "$$Stress - \sigma_{\mathrm{(B,Bot)}},\,psi$$", + "$$Stress - \sigma_{\mathrm{(B,Top)}},\,psi$$", +] + +# Define the names of the columns. +col_names = ["Target", "Mechanical APDL", "RATIO"] + +# Define the values of the target results. +target_res = np.asarray([300, -700]) + +# Create an array with outputs of the simulations. +simulation_res = np.asarray([strss_bot_tens, strss_top_compr]) + +# Identifying and filling corresponding columns. +main_columns = { + "Target": target_res, + "Mechanical APDL": simulation_res, + "Ratio": list(np.divide(simulation_res, target_res)), +} + +# Create and fill the output dataframe with pandas. +df2 = pd.DataFrame(main_columns, index=row_names).round(1) + +# Apply settings for the dataframe. +df2.head() + +############################################################################### +# stop mapdl +mapdl.exit() diff --git a/examples/verif-manual/vm-012-combined-bending-and-torsion.py b/examples/verif-manual/vm-012-combined-bending-and-torsion.py new file mode 100644 index 000000000..ea0930dfe --- /dev/null +++ b/examples/verif-manual/vm-012-combined-bending-and-torsion.py @@ -0,0 +1,134 @@ +r""" +.. _ref_vm12_example: + +Combined bending and torsion +---------------------------- + +Problem Description: + - TO DO + +Reference: + - C*** USING PIPE16 STR. OF MATL., TIMOSHENKO, + PART 1, 3RD ED., PAGE 299, PROB. 2 +""" + +from ansys.mapdl.core import launch_mapdl + +# start mapdl and clear it +mapdl = launch_mapdl(loglevel="WARNING", print_com=True) +mapdl.clear() # optional as MAPDL just started + +# enter verification example mode and the pre-processing routine +mapdl.verify("vm12") +mapdl.prep7() + +mapdl.antype("STATIC") +mapdl.et(1, "PIPE16") +mapdl.r(1, 4.67017, 2.33508) # REAL CONSTANTS FOR SOLID CROSS SECTION +mapdl.mp("EX", 1, 30e6) +mapdl.mp("NUXY", 1, 0.3) +mapdl.n(1) +mapdl.n(2, "", "", 300) +mapdl.e(1, 2) +mapdl.d(1, "ALL") +mapdl.f(2, "MZ", 9000) +mapdl.f(2, "FX", -250) +mapdl.finish() +mapdl.slashsolu() +mapdl.outpr("BASIC", 1) +with mapdl.non_interactive: + mapdl.run("/OUT,SCRATCH") + mapdl.solve() + mapdl.finish() + mapdl.post1() + mapdl.etable("P_STRS", "NMISC", 86) + mapdl.etable("SHR", "NMISC", 88) + mapdl.run("/OUT") + mapdl.run("/GOPR") +mapdl.last_response +mapdl.get("P_STRESS", "ELEM", 1, "ETAB", "P_STRS") +mapdl.get("SHEAR", "ELEM", 1, "ETAB", "SHR") +mapdl.dim("LABEL", "CHAR", 2, 2) +mapdl.dim("VALUE", "", 2, 3) +mapdl.run("LABEL(1,1) = 'MAX PRIN','MAX SH S'") +mapdl.run("LABEL(1,2) = 'STRS psi','TRS psi '") +mapdl.vfill("VALUE(1", "1)", "DATA", 7527, 3777) +mapdl.vfill("VALUE(1", "2)", "DATA", "P_STRESS", "(SHEAR/2)") +mapdl.vfill("VALUE(1", "3)", "DATA", "ABS(P_STRESS/7527 )", "ABS((SHEAR/2)/3777 )") +mapdl.save("TABLE_1") +mapdl.run("FINI") +mapdl.run("/CLEAR,NOSTART") + +mapdl.prep7() +mapdl.run("C*** USING PIPE288") +mapdl.run("ANTYPE,STATIC") +mapdl.et(1, "PIPE288", "", "", "", 2) +mapdl.sectype(1, "PIPE") +mapdl.secdata(4.67017, 2.33508) +mapdl.keyopt(1, 3, 3) # CUBIC SHAPE FUNCTION +mapdl.mp("EX", 1, 30e6) +mapdl.mp("NUXY", 1, 0.3) +mapdl.n(1) +mapdl.n(2, "", "", 300) +mapdl.e(1, 2) +mapdl.d(1, "ALL") +mapdl.f(2, "MZ", 9000) +mapdl.f(2, "FX", -250) +mapdl.finish() + +mapdl.slashsolu() +mapdl.outpr("BASIC", 1) +with mapdl.non_interactive: + mapdl.run("/OUT,SCRATCH") + mapdl.solve() + mapdl.finish() + mapdl.post1() + mapdl.set("LAST") + mapdl.graphics("POWER") + mapdl.eshape(1) + mapdl.view(1, 1, 1, 1) + mapdl.plesol("S", 1) + mapdl.run("/OUT") + mapdl.run("/GOPR") +mapdl.get("P_STRESS", "PLNSOL", 0, "MAX") +mapdl.plesol("S", "INT") +mapdl.get("SHEAR", "PLNSOL", 0, "MAX") +mapdl.dim("LABEL", "CHAR", 2, 2) +mapdl.dim("VALUE", "", 2, 3) +mapdl.run("LABEL(1,1) = 'MAX PRIN','MAX SH S'") +mapdl.run("LABEL(1,2) = 'STRS psi','TRS psi '") +mapdl.vfill("VALUE(1", "1)", "DATA", 7527, 3777) +mapdl.vfill("VALUE(1", "2)", "DATA", "P_STRESS", "(SHEAR/2)") +mapdl.vfill("VALUE(1", "3)", "DATA", "ABS(P_STRESS/7527 )", "ABS((SHEAR/2)/3777 )") +mapdl.save("TABLE_2") +mapdl.run("FINI") +mapdl.run("/CLEAR,NOSTART") +mapdl._run("/NOPR") # It is not recommended to use '/NOPR' in a normal PyMAPDL session. +mapdl.com("") + +with mapdl.non_interactive: + mapdl.run("/OUT,vm12,vrt") + mapdl.com("------------------- VM12 RESULTS COMPARISON ---------------------") + mapdl.com("") + mapdl.com("| TARGET | Mechanical APDL | RATIO") + mapdl.com("") + mapdl.resume("TABLE_1") + mapdl.com("USING PIPE16") + mapdl.com("") + mapdl.run("*VWRITE,LABEL(1,1),LABEL(1,2),VALUE(1,1),VALUE(1,2),VALUE(1,3)") + mapdl.run("(1X,A8,A8,' ',F10.0,' ',F12.0,' ',1F15.3)") + mapdl.com("") + mapdl.resume("TABLE_2") + mapdl.com("USING PIPE288") + mapdl.com("") + mapdl.run("*VWRITE,LABEL(1,1),LABEL(1,2),VALUE(1,1),VALUE(1,2),VALUE(1,3)") + mapdl.run("(1X,A8,A8,' ',F10.0,' ',F12.0,' ',1F15.3)") + mapdl.com("") + mapdl.com("-----------------------------------------------------------------") + mapdl.run("/OUT") + mapdl.run("/GOPR") + +mapdl.finish() +mapdl.starlist("vm12", "vrt") + +mapdl.exit() diff --git a/requirements/requirements_doc.txt b/requirements/requirements_doc.txt index 3d55d213b..580d8247e 100644 --- a/requirements/requirements_doc.txt +++ b/requirements/requirements_doc.txt @@ -8,7 +8,7 @@ pyvista==0.37.0 vtk==9.1.0 # Documentation dependencies -Sphinx==5.2.3 +Sphinx==5.3.0 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mode 100644 doc/source/verif-manual/vm-010/vm-010-bending_of_a_t-shaped_beam.py delete mode 100644 doc/source/verif-manual/vm-010/vm-010-bending_of_a_t-shaped_beam.py.md5 delete mode 100644 doc/source/verif-manual/vm-010/vm-010-bending_of_a_t-shaped_beam.rst delete mode 100644 doc/source/verif-manual/vm-010/vm-010-bending_of_a_t-shaped_beam_codeobj.pickle delete mode 100644 doc/source/verif-manual/vm-012/vm12.py diff --git a/.gitignore b/.gitignore index 3aa3d06e8..a4b2dfb15 100644 --- a/.gitignore +++ b/.gitignore @@ -74,7 +74,7 @@ instance/ # Sphinx documentation doc/_build/ -doc/source/verif-manual-2/ +doc/source/verif-manual/ # PyBuilder .pybuilder/ diff --git a/doc/source/conf.py b/doc/source/conf.py index ae38cbd57..d7bac090d 100644 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -2,9 +2,11 @@ from datetime import datetime import os +from ansys.mapdl import core as pymapdl from ansys_sphinx_theme import pyansys_logo_black as logo import numpy as np import pyvista +from sphinx_gallery.sorting import FileNameSortKey # Project information project = "pymapdl-examples" @@ -59,11 +61,13 @@ # path to your examples scripts "examples_dirs": ["../../examples/verif-manual"], # path where to save gallery generated examples - "gallery_dirs": ["verif-manual-2"], + "gallery_dirs": ["verif-manual"], # Pattern to search for example files "filename_pattern": r"\.py", # Remove the "Download all examples" button from the top level gallery "download_all_examples": False, + # Sort gallery example by file name instead of number of lines (default) + "within_subsection_order": FileNameSortKey, # directory where function granular galleries are stored "backreferences_dir": None, # Modules for which function level galleries are created. In @@ -122,7 +126,9 @@ os.makedirs(pyvista.FIGURE_PATH) +# necessary when building the sphinx gallery pyvista.BUILDING_GALLERY = True +pymapdl.BUILDING_GALLERY = True # static path html_static_path = ["_static"] diff --git a/doc/source/index.rst b/doc/source/index.rst index 39952416e..a270581fc 100644 --- a/doc/source/index.rst +++ b/doc/source/index.rst @@ -291,5 +291,4 @@ which necesitate more resources. :maxdepth: 3 verif-manual/index - verif-manual-2/index technology_showcase_examples/index diff --git a/doc/source/verif-manual/_static/custom.css b/doc/source/verif-manual/_static/custom.css deleted file mode 100644 index 97bda40f4..000000000 --- a/doc/source/verif-manual/_static/custom.css +++ /dev/null @@ -1,17 +0,0 @@ -@import url("default.css"); - -.red-text { - color: red; -} - -.green-text { - color: green; -} - -.blue-text { - color: blue; -} - -.yellow-text { - color: yellow; -} \ No newline at end of file diff --git a/doc/source/verif-manual/_static/lathe_cutter_model.png 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-readily-obtainable theoretical solutions using PyMAPDL. - -These problems may then serve as the basis for additional validation -and qualification of Mechanical APDL capabilities for specific -applications that may be of interest. +:orphan: +Examples +======== +These examples demonstrate using the PyMAPDL library. .. raw:: html @@ -23,10 +16,10 @@ applications that may be of interest. .. only:: html - .. image:: images/thumb/sphx_glr_vm-001-statically_indeterminate_reaction_force_analysis_thumb.png + .. image:: /verif-manual/images/thumb/sphx_glr_vm-001-statically_indeterminate_reaction_force_analysis_thumb.png :alt: Statically Indeterminate Reaction Force Analysis - :ref:`sphx_glr_vm-001-statically_indeterminate_reaction_force_analysis.py` + :ref:`sphx_glr_verif-manual_vm-001-statically_indeterminate_reaction_force_analysis.py` .. raw:: html @@ -40,10 +33,10 @@ applications that may be of interest. .. only:: html - .. image:: images/thumb/sphx_glr_vm-002-beam_stresses_and_deflections_thumb.png + .. image:: /verif-manual/images/thumb/sphx_glr_vm-002-beam_stresses_and_deflections_thumb.png :alt: Beam Stresses and Deflections - :ref:`sphx_glr_vm-002-beam_stresses_and_deflections.py` + :ref:`sphx_glr_verif-manual_vm-002-beam_stresses_and_deflections.py` .. raw:: html @@ -57,10 +50,10 @@ applications that may be of interest. .. only:: html - .. image:: images/thumb/sphx_glr_vm-003-thermally_loaded_support_structure_thumb.png + .. image:: /verif-manual/images/thumb/sphx_glr_vm-003-thermally_loaded_support_structure_thumb.png :alt: Thermally Loaded Support Structure - :ref:`sphx_glr_vm-003-thermally_loaded_support_structure.py` + :ref:`sphx_glr_verif-manual_vm-003-thermally_loaded_support_structure.py` .. raw:: html @@ -74,10 +67,10 @@ applications that may be of interest. .. only:: html - .. image:: images/thumb/sphx_glr_vm-004-deflection_of_a_hinged_support_thumb.png + .. image:: /verif-manual/images/thumb/sphx_glr_vm-004-deflection_of_a_hinged_support_thumb.png :alt: Deflection of a Hinged Support - :ref:`sphx_glr_vm-004-deflection_of_a_hinged_support.py` + :ref:`sphx_glr_verif-manual_vm-004-deflection_of_a_hinged_support.py` .. raw:: html @@ -91,10 +84,10 @@ applications that may be of interest. .. only:: html - .. image:: images/thumb/sphx_glr_vm-005-laterally_loaded_tapered_support_structure_thumb.png + .. image:: /verif-manual/images/thumb/sphx_glr_vm-005-laterally_loaded_tapered_support_structure_thumb.png :alt: Statically Indeterminate Reaction Force Analysis - :ref:`sphx_glr_vm-005-laterally_loaded_tapered_support_structure.py` + :ref:`sphx_glr_verif-manual_vm-005-laterally_loaded_tapered_support_structure.py` .. raw:: html @@ -108,10 +101,10 @@ applications that may be of interest. .. only:: html - .. image:: images/thumb/sphx_glr_vm-006-pinched_cylinder_thumb.png + .. image:: /verif-manual/images/thumb/sphx_glr_vm-006-pinched_cylinder_thumb.png :alt: Pinched Cylinder - :ref:`sphx_glr_vm-006-pinched_cylinder.py` + :ref:`sphx_glr_verif-manual_vm-006-pinched_cylinder.py` .. raw:: html @@ -125,10 +118,10 @@ applications that may be of interest. .. only:: html - .. image:: images/thumb/sphx_glr_vm-007-plastic_compression_of_a_pipe_assembly_thumb.png + .. image:: /verif-manual/images/thumb/sphx_glr_vm-007-plastic_compression_of_a_pipe_assembly_thumb.png :alt: Plastic Compression of a Pipe Assembly - :ref:`sphx_glr_vm-007-plastic_compression_of_a_pipe_assembly.py` + :ref:`sphx_glr_verif-manual_vm-007-plastic_compression_of_a_pipe_assembly.py` .. raw:: html @@ -142,10 +135,10 @@ applications that may be of interest. .. only:: html - .. image:: images/thumb/sphx_glr_vm-008-parametric_calculation_thumb.png + .. image:: /verif-manual/images/thumb/sphx_glr_vm-008-parametric_calculation_thumb.png :alt: Parametric Calculation - :ref:`sphx_glr_vm-008-parametric_calculation.py` + :ref:`sphx_glr_verif-manual_vm-008-parametric_calculation.py` .. raw:: html @@ -159,10 +152,10 @@ applications that may be of interest. .. only:: html - .. image:: images/thumb/sphx_glr_vm-009-large_lateral_deflection_of_unequal_stiffness_springs_thumb.png + .. image:: /verif-manual/images/thumb/sphx_glr_vm-009-large_lateral_deflection_of_unequal_stiffness_springs_thumb.png :alt: Large Lateral Deflection of Unequal Stiffness Springs - :ref:`sphx_glr_vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py` + :ref:`sphx_glr_verif-manual_vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py` .. raw:: html @@ -176,10 +169,10 @@ applications that may be of interest. .. only:: html - .. image:: images/thumb/sphx_glr_vm-010-bending_of_a_t-shaped_beam_thumb.png + .. image:: /verif-manual/images/thumb/sphx_glr_vm-010-bending_of_a_t-shaped_beam_thumb.png :alt: Bending of a Tee-Shaped Beam - :ref:`sphx_glr_vm-010-bending_of_a_t-shaped_beam.py` + :ref:`sphx_glr_verif-manual_vm-010-bending_of_a_t-shaped_beam.py` .. raw:: html @@ -187,6 +180,23 @@ applications that may be of interest. +.. raw:: html + +
+ +.. only:: html + + .. image:: /verif-manual/images/thumb/sphx_glr_vm-012-combined-bending-and-torsion_thumb.png + :alt: Combined bending and torsion + + :ref:`sphx_glr_verif-manual_vm-012-combined-bending-and-torsion.py` + +.. raw:: html + +
Combined bending and torsion
+
+ + .. raw:: html @@ -194,18 +204,18 @@ applications that may be of interest. .. toctree:: :hidden: - :includehidden: - - vm-001/vm-001-statically_indeterminate_reaction_force_analysis - vm-002/vm-002-beam_stresses_and_deflections - vm-003/vm-003-thermally_loaded_support_structure - vm-004/vm-004-deflection_of_a_hinged_support - vm-005/vm-005-laterally_loaded_tapered_support_structure - vm-006/vm-006-pinched_cylinder - vm-007/vm-007-plastic_compression_of_a_pipe_assembly - vm-008/vm-008-parametric_calculation - vm-009/vm-009-large_lateral_deflection_of_unequal_stiffness_springs - vm-010/vm-010-bending_of_a_t-shaped_beam + + /verif-manual/vm-001-statically_indeterminate_reaction_force_analysis + /verif-manual/vm-002-beam_stresses_and_deflections + /verif-manual/vm-003-thermally_loaded_support_structure + /verif-manual/vm-004-deflection_of_a_hinged_support + /verif-manual/vm-005-laterally_loaded_tapered_support_structure + /verif-manual/vm-006-pinched_cylinder + /verif-manual/vm-007-plastic_compression_of_a_pipe_assembly + /verif-manual/vm-008-parametric_calculation + /verif-manual/vm-009-large_lateral_deflection_of_unequal_stiffness_springs + /verif-manual/vm-010-bending_of_a_t-shaped_beam + /verif-manual/vm-012-combined-bending-and-torsion diff --git a/doc/source/verif-manual/sg_execution_times.rst b/doc/source/verif-manual/sg_execution_times.rst index 8573f1a86..c0281a9de 100644 --- a/doc/source/verif-manual/sg_execution_times.rst +++ b/doc/source/verif-manual/sg_execution_times.rst @@ -1,31 +1,32 @@ :orphan: -.. _sphx_glr_sg_execution_times: +.. _sphx_glr_verif-manual_sg_execution_times: Computation times ================= +**00:21.824** total execution time for **verif-manual** files: -**00:15.747** total execution time for **verif-manual** files: - -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_vm-006-pinched_cylinder.py` (``vm-006-pinched_cylinder.py``) | 00:04.904 | 0.0 MB | -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_vm-005-laterally_loaded_tapered_support_structure.py` (``vm-005-laterally_loaded_tapered_support_structure.py``) | 00:02.092 | 0.0 MB | -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_vm-007-plastic_compression_of_a_pipe_assembly.py` (``vm-007-plastic_compression_of_a_pipe_assembly.py``) | 00:01.807 | 0.0 MB | -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_vm-004-deflection_of_a_hinged_support.py` (``vm-004-deflection_of_a_hinged_support.py``) | 00:01.316 | 0.0 MB | -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_vm-003-thermally_loaded_support_structure.py` (``vm-003-thermally_loaded_support_structure.py``) | 00:01.294 | 0.0 MB | -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_vm-008-parametric_calculation.py` (``vm-008-parametric_calculation.py``) | 00:01.098 | 0.0 MB | -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_vm-002-beam_stresses_and_deflections.py` (``vm-002-beam_stresses_and_deflections.py``) | 00:00.960 | 0.0 MB | -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_vm-010-bending_of_a_t-shaped_beam.py` (``vm-010-bending_of_a_t-shaped_beam.py``) | 00:00.939 | 0.0 MB | -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py` (``vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py``) | 00:00.909 | 0.0 MB | -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_vm-001-statically_indeterminate_reaction_force_analysis.py` (``vm-001-statically_indeterminate_reaction_force_analysis.py``) | 00:00.426 | 0.0 MB | -+-------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_verif-manual_vm-006-pinched_cylinder.py` (``vm-006-pinched_cylinder.py``) | 00:04.746 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_verif-manual_vm-001-statically_indeterminate_reaction_force_analysis.py` (``vm-001-statically_indeterminate_reaction_force_analysis.py``) | 00:02.878 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_verif-manual_vm-007-plastic_compression_of_a_pipe_assembly.py` (``vm-007-plastic_compression_of_a_pipe_assembly.py``) | 00:02.832 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_verif-manual_vm-005-laterally_loaded_tapered_support_structure.py` (``vm-005-laterally_loaded_tapered_support_structure.py``) | 00:02.239 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_verif-manual_vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py` (``vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py``) | 00:01.547 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_verif-manual_vm-003-thermally_loaded_support_structure.py` (``vm-003-thermally_loaded_support_structure.py``) | 00:01.492 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_verif-manual_vm-008-parametric_calculation.py` (``vm-008-parametric_calculation.py``) | 00:01.280 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_verif-manual_vm-004-deflection_of_a_hinged_support.py` (``vm-004-deflection_of_a_hinged_support.py``) | 00:01.257 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_verif-manual_vm-012-combined-bending-and-torsion.py` (``vm-012-combined-bending-and-torsion.py``) | 00:01.249 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_verif-manual_vm-002-beam_stresses_and_deflections.py` (``vm-002-beam_stresses_and_deflections.py``) | 00:01.193 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| 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zg1=rJ8xk5M9=dXArObIwEp>+7wcJw8N9*KlavCQ(zL=Qz=x#nw^NQ=z@?gR4^s1?Z zq$IzHh{iN;Fkw?(Zns)-_Vv5d=jXV%hA{EcMqM^?*rKBJj4X?P-~3inJ&5&8!;}8J z8@;hqP5TAUV93ocIfv~>XSyjKF5ZgAuEW~@QxNi2j+-PcKG=F4t ztX;+D@VMnC@{X;{{s93h;X;RAdN>Z5jqhc}kL*qV`6I*BY*HF`ySsw>`MY)IOZF*b zwM%vmIr77z1w^$=Aw29yu%5UL$^2UmMzZQY&XedE){mAEY9F}c?kBl?758nvaJkse{yFFns>HjCS&z3YN6xklgB}BzQbZr;@)d3IX18bP(wPrJ(Put^QI$=W_3XLgn&&R~6e>X0MjXc?}_(W!)?zoSG@| zk|VlR2b1#-hr>a}s<1L&{@{a01<&3;Blr=qGx7YN0w^#zbp?2&CQ47AJ)5K+E!=NV zV8w6OL=$OXn?1KD*@|H&(=7Wtqrgh;gg`&ZTMZGJBzzo~pnO)>k1$;\n", - "\n", - "Material Properties\n", - " - $E = 30 \\cdot 10^6 psi$\n", - "\n", - "Geometric Properties:\n", - " - $a = b = 0.3$\n", - " - $l = 10 in$\n", - "\n", - "Loading:\n", - " - $F_1 = 2*F_2 = 1000 lb$\n", - "\n", - "Analytical Equations:\n", - " - $P = R_1 + R_2$ where $P$ is load.\n", - " - $\\frac{R_2}{R_1} = \\frac{a}{b}$\n", - " Where $a$ and $b$ are the ratios of distances between\n", - " the load and the wall.\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# sphinx_gallery_thumbnail_path = '_static/vm1_setup.png'\n", - "\n", - "from ansys.mapdl.core import launch_mapdl\n", - "\n", - "# start mapdl and clear it\n", - "mapdl = launch_mapdl()\n", - "mapdl.clear() # optional as MAPDL just started\n", - "\n", - "# enter verification example mode and the pre-processing routine\n", - "mapdl.verify()\n", - "mapdl.prep7()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Define Material\n", - "Set up the material and its type (a single material, with a linking-type\n", - "section and a Young's modulus of 30e6).\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "mapdl.antype(\"STATIC\")\n", - "mapdl.et(1, \"LINK180\")\n", - "mapdl.sectype(1, \"LINK\")\n", - "mapdl.secdata(1)\n", - "mapdl.mp(\"EX\", 1, 30e6)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Define Geometry\n", - "Set up the nodes and elements. This creates a mesh just like in the\n", - "problem setup.\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "mapdl.n(1, 0, 0)\n", - "mapdl.n(2, 0, 4)\n", - "mapdl.n(3, 0, 7)\n", - "mapdl.n(4, 0, 10)\n", - "mapdl.e(1, 2)\n", - "mapdl.egen(3, 1, 1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Define Boundary Conditions\n", - "Full constrain nodes 1 and 4, by incrementing from node 1 to node 4\n", - "in steps of 3. Apply y-direction forces to nodes 2 and 3, with\n", - "values of -500 lb and -1000 lb respectively. Then exit prep7.\n", - "\n", - "Effectiely, this sets:\n", - "- $F_1 = 2*F_2 = 1000 lb$\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "mapdl.d(1, \"ALL\", \"\", \"\", 4, 3)\n", - "mapdl.f(2, \"FY\", -500)\n", - "mapdl.f(3, \"FY\", -1000)\n", - "mapdl.finish()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Solve\n", - "Enter solution mode and solve the system.\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "mapdl.run(\"/SOLU\")\n", - "out = mapdl.solve()\n", - "mapdl.finish()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Post-processing\n", - "Enter post-processing. Select the nodes at ``y=10`` and ``y=0``, and\n", - "sum the forces there. Then store the y-components in two variables:\n", - "``reaction_1`` and ``reaction_2``.\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "mapdl.post1()\n", - "mapdl.nsel(\"S\", \"LOC\", \"Y\", 10)\n", - "mapdl.fsum()\n", - "reaction_1 = mapdl.get(\"REAC_1\", \"FSUM\", \"\", \"ITEM\", \"FY\")\n", - "mapdl.nsel(\"S\", \"LOC\", \"Y\", 0)\n", - "mapdl.fsum()\n", - "reaction_2 = mapdl.get(\"REAC_2\", \"FSUM\", \"\", \"ITEM\", \"FY\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Check Results\n", - "Now that we have the reaction forces we can compare them to the\n", - "expected values of 900 lbs and 600 lbs for reactions 1 and 2 respectively.\n", - "\n", - "Analytical results obtained from:\n", - "- $P = R_1 + R_2$ where $P$ is load of 1500 lbs\n", - "- $\\frac{R_2}{R_1} = \\frac{a}{b}$\n", - "\n", - "Hint: Solve for each reaction force independently.\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "results = f\"\"\"\n", - " --------------------- RESULTS COMPARISON ---------------------\n", - " | TARGET | Mechanical APDL | RATIO\n", - " /INPUT FILE= LINE= 0\n", - " R1, lb 900.0 {abs(reaction_1)} {abs(reaction_1) / 900}\n", - " R2, lb 600.0 {abs(reaction_2)} {abs(reaction_2) / 600}\n", - " ----------------------------------------------------------------\n", - " \"\"\"\n", - "print(results)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "stop mapdl\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "mapdl.exit()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3.10.8 ('.venv': venv)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.8" - }, - "vscode": { - "interpreter": { - "hash": "269550a72b951409c73f23ea9b5a89d868b3d5a683e175acf6d5151541610ed6" - } - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/doc/source/verif-manual/vm-001/vm-001-statically_indeterminate_reaction_force_analysis.py b/doc/source/verif-manual/vm-001/vm-001-statically_indeterminate_reaction_force_analysis.py deleted file mode 100644 index 6f67334f7..000000000 --- a/doc/source/verif-manual/vm-001/vm-001-statically_indeterminate_reaction_force_analysis.py +++ /dev/null @@ -1,146 +0,0 @@ -r""" -.. _ref_statically_indeterminate_example: - -Statically Indeterminate Reaction Force Analysis ------------------------------------------------- -Problem Description: - - A prismatical bar with built-in ends is loaded axially at two - intermediate cross sections. Determine the reactions :math:`R_1` - and :math:`R_2`. - -Reference: - - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and - Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, - pg. 26, problem 10. - -Analysis Type(s): - - Static Analysis ``ANTYPE=0`` - -Element Type(s): - - 3-D Spar (or Truss) Elements (LINK180) - -.. image:: _static/vm1_setup.png - :width: 400 - :alt: VM1 Problem Sketch - -Material Properties - - :math:`E = 30 \cdot 10^6 psi` - -Geometric Properties: - - :math:`a = b = 0.3` - - :math:`l = 10 in` - -Loading: - - :math:`F_1 = 2*F_2 = 1000 lb` - -Analytical Equations: - - :math:`P = R_1 + R_2` where :math:`P` is load. - - :math:`\frac{R_2}{R_1} = \frac{a}{b}` - Where :math:`a` and :math:`b` are the ratios of distances between - the load and the wall. - -""" -# sphinx_gallery_thumbnail_path = '_static/vm1_setup.png' - -from ansys.mapdl.core import launch_mapdl - -# start mapdl and clear it -mapdl = launch_mapdl() -mapdl.clear() # optional as MAPDL just started - -# enter verification example mode and the pre-processing routine -mapdl.verify() -mapdl.prep7() - -############################################################################### -# Define Material -# ~~~~~~~~~~~~~~~ -# Set up the material and its type (a single material, with a linking-type -# section and a Young's modulus of 30e6). - -mapdl.antype("STATIC") -mapdl.et(1, "LINK180") -mapdl.sectype(1, "LINK") -mapdl.secdata(1) -mapdl.mp("EX", 1, 30e6) - -############################################################################### -# Define Geometry -# ~~~~~~~~~~~~~~~ -# Set up the nodes and elements. This creates a mesh just like in the -# problem setup. - -mapdl.n(1, 0, 0) -mapdl.n(2, 0, 4) -mapdl.n(3, 0, 7) -mapdl.n(4, 0, 10) -mapdl.e(1, 2) -mapdl.egen(3, 1, 1) - - -############################################################################### -# Define Boundary Conditions -# ~~~~~~~~~~~~~~~~~~~~~~~~~~ -# Full constrain nodes 1 and 4, by incrementing from node 1 to node 4 -# in steps of 3. Apply y-direction forces to nodes 2 and 3, with -# values of -500 lb and -1000 lb respectively. Then exit prep7. -# -# Effectiely, this sets: -# - :math:`F_1 = 2*F_2 = 1000 lb` - -mapdl.d(1, "ALL", "", "", 4, 3) -mapdl.f(2, "FY", -500) -mapdl.f(3, "FY", -1000) -mapdl.finish() - - -############################################################################### -# Solve -# ~~~~~ -# Enter solution mode and solve the system. - -mapdl.run("/SOLU") -out = mapdl.solve() -mapdl.finish() - -############################################################################### -# Post-processing -# ~~~~~~~~~~~~~~~ -# Enter post-processing. Select the nodes at ``y=10`` and ``y=0``, and -# sum the forces there. Then store the y-components in two variables: -# ``reaction_1`` and ``reaction_2``. - -mapdl.post1() -mapdl.nsel("S", "LOC", "Y", 10) -mapdl.fsum() -reaction_1 = mapdl.get("REAC_1", "FSUM", "", "ITEM", "FY") -mapdl.nsel("S", "LOC", "Y", 0) -mapdl.fsum() -reaction_2 = mapdl.get("REAC_2", "FSUM", "", "ITEM", "FY") - - -############################################################################### -# Check Results -# ~~~~~~~~~~~~~ -# Now that we have the reaction forces we can compare them to the -# expected values of 900 lbs and 600 lbs for reactions 1 and 2 respectively. -# -# Analytical results obtained from: -# - :math:`P = R_1 + R_2` where :math:`P` is load of 1500 lbs -# - :math:`\frac{R_2}{R_1} = \frac{a}{b}` -# -# Hint: Solve for each reaction force independently. -# -results = f""" - --------------------- RESULTS COMPARISON --------------------- - | TARGET | Mechanical APDL | RATIO - /INPUT FILE= LINE= 0 - R1, lb 900.0 {abs(reaction_1)} {abs(reaction_1) / 900} - R2, lb 600.0 {abs(reaction_2)} {abs(reaction_2) / 600} - ---------------------------------------------------------------- - """ -print(results) - -############################################################################### -# stop mapdl -mapdl.exit() diff --git a/doc/source/verif-manual/vm-001/vm-001-statically_indeterminate_reaction_force_analysis.py.md5 b/doc/source/verif-manual/vm-001/vm-001-statically_indeterminate_reaction_force_analysis.py.md5 deleted file mode 100644 index f1b77ea5d..000000000 --- a/doc/source/verif-manual/vm-001/vm-001-statically_indeterminate_reaction_force_analysis.py.md5 +++ /dev/null @@ -1 +0,0 @@ -90172b3683c5a48710ab734d2f973446 \ No newline at end of file diff --git a/doc/source/verif-manual/vm-001/vm-001-statically_indeterminate_reaction_force_analysis.rst b/doc/source/verif-manual/vm-001/vm-001-statically_indeterminate_reaction_force_analysis.rst deleted file mode 100644 index 49535c435..000000000 --- a/doc/source/verif-manual/vm-001/vm-001-statically_indeterminate_reaction_force_analysis.rst +++ /dev/null @@ -1,345 +0,0 @@ - -.. DO NOT EDIT. -.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. -.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: -.. "vm-001-statically_indeterminate_reaction_force_analysis.py" -.. LINE NUMBERS ARE GIVEN BELOW. - -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here ` - to download the full example code - -.. rst-class:: sphx-glr-example-title - -.. _sphx_glr_vm-001-statically_indeterminate_reaction_force_analysis.py: - - -.. _ref_statically_indeterminate_example: - -Statically Indeterminate Reaction Force Analysis ------------------------------------------------- -Problem Description: - - A prismatical bar with built-in ends is loaded axially at two - intermediate cross sections. Determine the reactions :math:`R_1` - and :math:`R_2`. - -Reference: - - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and - Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, - pg. 26, problem 10. - -Analysis Type(s): - - Static Analysis ``ANTYPE=0`` - -Element Type(s): - - 3-D Spar (or Truss) Elements (LINK180) - -.. image:: _static/vm1_setup.png - :width: 400 - :alt: VM1 Problem Sketch - -Material Properties - - :math:`E = 30 \cdot 10^6 psi` - -Geometric Properties: - - :math:`a = b = 0.3` - - :math:`l = 10 in` - -Loading: - - :math:`F_1 = 2*F_2 = 1000 lb` - -Analytical Equations: - - :math:`P = R_1 + R_2` where :math:`P` is load. - - :math:`\frac{R_2}{R_1} = \frac{a}{b}` - Where :math:`a` and :math:`b` are the ratios of distances between - the load and the wall. - -.. GENERATED FROM PYTHON SOURCE LINES 43-55 - -.. code-block:: default - - # sphinx_gallery_thumbnail_path = '_static/vm1_setup.png' - - from ansys.mapdl.core import launch_mapdl - - # start mapdl and clear it - mapdl = launch_mapdl() - mapdl.clear() # optional as MAPDL just started - - # enter verification example mode and the pre-processing routine - mapdl.verify() - mapdl.prep7() - - - - - -.. rst-class:: sphx-glr-script-out - - .. code-block:: none - - - *****MAPDL VERIFICATION RUN ONLY***** - DO NOT USE RESULTS FOR PRODUCTION - - ***** MAPDL ANALYSIS DEFINITION (PREP7) ***** - - - -.. GENERATED FROM PYTHON SOURCE LINES 56-60 - -Define Material -~~~~~~~~~~~~~~~ -Set up the material and its type (a single material, with a linking-type -section and a Young's modulus of 30e6). - -.. GENERATED FROM PYTHON SOURCE LINES 60-67 - -.. code-block:: default - - - mapdl.antype("STATIC") - mapdl.et(1, "LINK180") - mapdl.sectype(1, "LINK") - mapdl.secdata(1) - mapdl.mp("EX", 1, 30e6) - - - - - -.. rst-class:: sphx-glr-script-out - - .. code-block:: none - - - MATERIAL 1 EX = 0.3000000E+08 - - - -.. GENERATED FROM PYTHON SOURCE LINES 68-72 - -Define Geometry -~~~~~~~~~~~~~~~ -Set up the nodes and elements. This creates a mesh just like in the -problem setup. - -.. GENERATED FROM PYTHON SOURCE LINES 72-81 - -.. code-block:: default - - - mapdl.n(1, 0, 0) - mapdl.n(2, 0, 4) - mapdl.n(3, 0, 7) - mapdl.n(4, 0, 10) - mapdl.e(1, 2) - mapdl.egen(3, 1, 1) - - - - - - -.. rst-class:: sphx-glr-script-out - - .. code-block:: none - - - GENERATE 3 TOTAL SETS OF ELEMENTS WITH NODE INCREMENT OF 1 - SET IS SELECTED ELEMENTS IN RANGE 1 TO 1 IN STEPS OF 1 - - MAXIMUM ELEMENT NUMBER= 3 - - - -.. GENERATED FROM PYTHON SOURCE LINES 82-90 - -Define Boundary Conditions -~~~~~~~~~~~~~~~~~~~~~~~~~~ -Full constrain nodes 1 and 4, by incrementing from node 1 to node 4 -in steps of 3. Apply y-direction forces to nodes 2 and 3, with -values of -500 lb and -1000 lb respectively. Then exit prep7. - -Effectiely, this sets: -- :math:`F_1 = 2*F_2 = 1000 lb` - -.. GENERATED FROM PYTHON SOURCE LINES 90-97 - -.. code-block:: default - - - mapdl.d(1, "ALL", "", "", 4, 3) - mapdl.f(2, "FY", -500) - mapdl.f(3, "FY", -1000) - mapdl.finish() - - - - - - -.. rst-class:: sphx-glr-script-out - - .. code-block:: none - - - ***** ROUTINE COMPLETED ***** CP = 0.000 - - - -.. GENERATED FROM PYTHON SOURCE LINES 98-101 - -Solve -~~~~~ -Enter solution mode and solve the system. - -.. GENERATED FROM PYTHON SOURCE LINES 101-106 - -.. code-block:: default - - - mapdl.run("/SOLU") - out = mapdl.solve() - mapdl.finish() - - - - - -.. rst-class:: sphx-glr-script-out - - .. code-block:: none - - - FINISH SOLUTION PROCESSING - - - ***** ROUTINE COMPLETED ***** CP = 0.000 - - - -.. GENERATED FROM PYTHON SOURCE LINES 107-112 - -Post-processing -~~~~~~~~~~~~~~~ -Enter post-processing. Select the nodes at ``y=10`` and ``y=0``, and -sum the forces there. Then store the y-components in two variables: -``reaction_1`` and ``reaction_2``. - -.. GENERATED FROM PYTHON SOURCE LINES 112-122 - -.. code-block:: default - - - mapdl.post1() - mapdl.nsel("S", "LOC", "Y", 10) - mapdl.fsum() - reaction_1 = mapdl.get("REAC_1", "FSUM", "", "ITEM", "FY") - mapdl.nsel("S", "LOC", "Y", 0) - mapdl.fsum() - reaction_2 = mapdl.get("REAC_2", "FSUM", "", "ITEM", "FY") - - - - - - - - - -.. GENERATED FROM PYTHON SOURCE LINES 123-134 - -Check Results -~~~~~~~~~~~~~ -Now that we have the reaction forces we can compare them to the -expected values of 900 lbs and 600 lbs for reactions 1 and 2 respectively. - -Analytical results obtained from: -- :math:`P = R_1 + R_2` where :math:`P` is load of 1500 lbs -- :math:`\frac{R_2}{R_1} = \frac{a}{b}` - -Hint: Solve for each reaction force independently. - - -.. GENERATED FROM PYTHON SOURCE LINES 134-144 - -.. code-block:: default - - results = f""" - --------------------- RESULTS COMPARISON --------------------- - | TARGET | Mechanical APDL | RATIO - /INPUT FILE= LINE= 0 - R1, lb 900.0 {abs(reaction_1)} {abs(reaction_1) / 900} - R2, lb 600.0 {abs(reaction_2)} {abs(reaction_2) / 600} - ---------------------------------------------------------------- - """ - print(results) - - - - - -.. rst-class:: sphx-glr-script-out - - .. code-block:: none - - - --------------------- RESULTS COMPARISON --------------------- - | TARGET | Mechanical APDL | RATIO - /INPUT FILE= LINE= 0 - R1, lb 900.0 900.0 1.0 - R2, lb 600.0 600.0 1.0 - ---------------------------------------------------------------- - - - - - -.. GENERATED FROM PYTHON SOURCE LINES 145-146 - -stop mapdl - -.. GENERATED FROM PYTHON SOURCE LINES 146-147 - -.. code-block:: default - - mapdl.exit() - - - - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 0.426 seconds) - - -.. _sphx_glr_download_vm-001-statically_indeterminate_reaction_force_analysis.py: - -.. only:: html - - .. container:: sphx-glr-footer sphx-glr-footer-example - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: vm-001-statically_indeterminate_reaction_force_analysis.py ` - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: vm-001-statically_indeterminate_reaction_force_analysis.ipynb ` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery `_ diff --git a/doc/source/verif-manual/vm-001/vm-001-statically_indeterminate_reaction_force_analysis_codeobj.pickle 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