Doc/tech demos 21buckling pmh

.gitignore

@@ -88,4 +88,7 @@ venv/
 .vscode/
 
 # Pycharm local settings
-.idea/
+.idea/
+
+.vs
+.gitignore

doc/source/examples/technology_showcase_examples/README.txt

@@ -20,5 +20,7 @@ this project.
 +----------------------------+---------------------------------------------------------------------------------------------------------+
 | :ref:`tech_demo_20`        | Technology showcase demonstration example 20: Dynamic simulation of a printed circuit board assembly    |
 +----------------------------+---------------------------------------------------------------------------------------------------------+
+| :ref:`tech_demo_21`        | Technology showcase demonstration example 21: Buckling of a ring-stiffened cylinder                     |
++----------------------------+---------------------------------------------------------------------------------------------------------+
 | :ref:`tech_demo_28`        | Technology showcase demonstration example 28: Friction Stir Welding (FSW) Simulation                    |
 +----------------------------+---------------------------------------------------------------------------------------------------------+

examples/00-mapdl-examples/21-example-technology-showcase-buckling.py

@@ -0,0 +1,374 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Sep  2 14:24:13 2022
+
+@author: pmaroneh
+"""
+
+""".. _ref_buckling_postbuckling_ring_stiffened_cylinder:
+
+Buckling and post-buckling analysis of a ring-stiffened
+cylinder using nonlinear stabilization
+======================================================
+
+This examples shows how to use PyMAPDL to import an existing FE model and to
+perform a nonlinear buckling and postbuckling analysis using nonlinear
+stabilization. The problem uses a stiffened cylinder subjected to uniform
+external pressure to show how to find the nonlinear buckling loads,
+achieve convergence at the post-buckling stage, and interpret the results.
+
+This example is inspired from the model and analysis defined in Chapter 21 of
+the Mechanical APDL Technology Showcase Manual.
+
+"""
+
+###############################################################################
+# Setting up model
+# ----------------
+#
+# The original FE model is given in the Ansys Mechanical APDL Technology
+# Showcase Manual.  The .cdb contains a FE model of a ring-stiffened cylinder.
+#
+# A circular cylinder made of bare 2024-T3 aluminum alloy is stiffened inside
+# with five Z-section rings. Its ends are closed with thick aluminum bulkheads.
+# A riveted L section exists between the top plate and the top ring and the
+# bottom plate and bottom ring.
+# The cylinder is subjected to a differential external pressure. The pressure
+# causes a local buckling phenomenon characterized by buckling of the skin
+# between stiffening rings, leading eventually to collapse.
+#
+# The finite element model of the ring stiffened cylinder is meshed with
+# SHELL281 elements with an element size of 10 mm. The fine mesh is required
+# for buckling analysis, and a full 360-degree model is necessary because
+# the deformation is no longer axisymmetric after buckling occurs.
+#
+# All shell elements have uniform thickness. Five sections are created in the
+# model with no offsets, so the shell sections are offset to the midplane
+# by default.
+#
+# Starting MAPDL as a service and importing an external model
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#
+
+from ansys.mapdl.core import launch_mapdl
+from ansys.mapdl.core.examples import download_tech_demo_data
+
+# define geometric parameters
+bs = 95.3  # Ring spacing (mm)
+ts = 1.034  # Skin thickness (mm)
+tw = 0.843  # Ring thickness (mm)
+r = 344 * ts  # Radius of cylinder (mm)
+L = 431.8 + 2 * (19 - 9.5)  # Length of cylinder (mm)
+pext = 0.24  # Differential external pressure (MPa)
+
+# start MAPDL as a service
+mapdl = launch_mapdl()
+print(mapdl)
+
+mapdl.filname("buckling")  # change filename
+# mapdl.nerr(nmerr=200, nmabt=10000, abort=-1, ifkey=0, num=0)
+
+# enter preprocessor
+mapdl.prep7()
+
+# define material properties for 2024-T3 Alluminum alloy
+EX = 73000  # Young's Modulus (MPA)
+ET = 73  # Tangent modulus
+mapdl.mp("ex", 1, EX)  # Young's Modulus (MPA)
+mapdl.mp("prxy", 1, 0.33)  # Poisson's ratio
+EP = EX * ET / (EX - ET)
+mapdl.tb("biso", 1)
+mapdl.tbdata(1, 268.9, EP)
+# create material plot
+mapdl.show("png")
+mapdl.tbplot("biso", 1)
+mapdl.show("close")
+
+# define shell elements and their sections
+mapdl.et(1, 181)
+# cylinder
+mapdl.sectype(1, "shell")
+mapdl.secdata(ts, 1)
+# L
+mapdl.sectype(2, "shell")
+mapdl.secdata(ts + 1.64, 1)
+# Z shaped ring stiffener
+mapdl.sectype(3, "shell")
+mapdl.secdata(tw, 1)
+# Plate at z=0 with thickness=25 mm
+mapdl.sectype(4, "shell")
+mapdl.secdata(25, 1)
+# Plate at z=L  with thickness=25 mm
+mapdl.sectype(5, "shell")
+mapdl.secdata(25, 1)
+
+
+# read model of stiffened cylinder
+# download the cdb file
+ring_mesh_file = download_tech_demo_data(
+    "td-21", "ring_stiffened_cylinder_mesh_file.cdb"
+)
+
+# read in cdb
+mapdl.cdread("db", ring_mesh_file)
+mapdl.allsel()
+mapdl.eplot(background="w")
+mapdl.cmsel("all")
+
+###############################################################################
+# Define static prestress analysis
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# Displacement boundary conditions are defined to prevent the six rigid body
+# motions. A total of six displacements are therefore applied to three nodes
+# located on the top plate at 0, 90, and 270 degrees; the nodes are restricted
+# so that all rigid translations and rotations are not possible for the
+# cylinder.
+#
+# Loading consists of a uniformly distributed external differential
+# pressure: Pext = 0.24 MPa
+
+mapdl.csys(1)  # activate cylindrical coordinate system
+
+# Define pressure on plate at z=0
+mapdl.nsel("s", "loc", "z", 0)
+mapdl.esln("s", 1)
+mapdl.sfe("all", 2, "pres", 1, pext)
+mapdl.allsel()
+
+# Define pressure on the rim of plate at z=0
+mapdl.nsel("s", "loc", "z", 0)
+mapdl.nsel("r", "loc", "x", r - ts / 2, 760 / 2)
+mapdl.esln("s", 1)
+mapdl.sfe("all", 1, "pres", 1, pext)
+mapdl.allsel()
+
+# Define pressure on plate at z=L
+mapdl.nsel("s", "loc", "z", L)
+mapdl.esln("s", 1)
+mapdl.sfe("all", 2, "pres", 1, pext)
+mapdl.allsel()
+
+# Define pressure on the rim of plate at z=L
+mapdl.nsel("s", "loc", "z", L)
+mapdl.nsel("r", "loc", "x", r - ts / 2, 760 / 2)
+mapdl.esln("s", 1)
+mapdl.sfe("all", 1, "pres", 1, pext)
+mapdl.allsel()
+
+# Define pressure on cylinder
+mapdl.nsel("s", "loc", "x", r - ts / 2)
+mapdl.esln("s", 1)
+mapdl.sfe("all", 2, "pres", 1, pext)
+mapdl.allsel()
+
+# Define displacement BSs to avoid rigid body motion
+mapdl.csys(0)  # activate cartesian coordinate system
+mapdl.nsel("s", "loc", "x", r - ts / 2)
+mapdl.nsel("r", "loc", "y", 0)
+mapdl.nsel("r", "loc", "z", 0)
+mapdl.d("all", "ux", 0)
+mapdl.d("all", "uy", 0)
+mapdl.d("all", "uz", 0)
+mapdl.allsel()
+#
+mapdl.nsel("s", "loc", "x", 0)
+mapdl.nsel("r", "loc", "y", r - ts / 2)
+mapdl.nsel("r", "loc", "z", 0)
+mapdl.d("all", "uz", 0)
+mapdl.allsel()
+#
+mapdl.nsel("s", "loc", "x", 0)
+mapdl.nsel("r", "loc", "y", -(r - ts / 2))
+mapdl.nsel("r", "loc", "z", 0)
+mapdl.d("all", "uy", 0)
+mapdl.d("all", "uz", 0)
+mapdl.allsel()
+#
+
+# Print DOF constraints
+print(mapdl.dlist())
+
+# Solve static prestress analysis
+mapdl.slashsolu()
+mapdl.pstres("on")
+mapdl.antype("STATIC")
+output = mapdl.solve()
+print(output)
+
+# Plot total deformation
+mapdl.post1()
+mapdl.set("last")
+mapdl.post_processing.plot_nodal_displacement("NORM", smooth_shading=True)
+#%%
+###############################################################################
+# Run linear buckling analysis
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# This preliminary analysis predicts the theoretical buckling pressure of the
+# ideal linear elastic structure (perfect cylinder) and the buckled mode shapes
+# used in the next step to generate the imperfections.
+# It is also an efficient way to check the completeness and
+# correctness of modeling.
+# To run the linear buckling analysis, a static solution with prestress effects
+# must be obtained, followed by the eigenvalue buckling solution using the
+# Block Lanczos method and mode expansion.
+
+# Define and solve linear buckling analysis
+mapdl.slashsolu()
+mapdl.outres("all", "all")
+mapdl.antype("BUCKLE")
+mapdl.bucopt("lanb", "10")
+mapdl.mxpand(10)
+output = mapdl.solve()
+print(output)
+
+# Plot total deformation of first and 10th mode
+mapdl.post1()
+mapdl.set(1, 1)
+mapdl.post_processing.plot_nodal_displacement("NORM", smooth_shading=True)
+mapdl.set(1, 10)
+mapdl.post_processing.plot_nodal_displacement("NORM", smooth_shading=True)
+#%%
+###############################################################################
+# Generate imperfections
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# If a structure is perfectly symmetric, nonsymmetric buckling does not occur
+# numerically, and a nonlinear buckling analysis fails because
+# nonsymmetric buckling responses cannot be triggered. In this problem,
+# the geometry, elements, and pressure are all axisymmetric.
+# It is not possible, therefore, to simulate nonaxisymmetric buckling with
+# the initial model. To overcome this problem, small geometric imperfections
+# (similar to those caused by manufacturing a real structure) must be
+# introduced to trigger the buckling responses.
+# Because the radius of the cylinder is 355.69 mm and the maximum
+# displacement of a mode shape is 1 mm, a factor of 0.1 is applied when
+# updating the geometry with mode shapes. The factor assumes the manufacturing
+# tolerance of the radius to be on the order of 0.1.
+mapdl.finish()
+mapdl.prep7()
+for i in range(1, 11):
+    mapdl.upgeom(0.1, 1, i, "buckling", "rst")  # Add imperfections as a tenth of each
+    # mode shape
+mapdl.finish()
+#%%
+###############################################################################
+# Run nonlinear static analysis on geometry with imperfections
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# The nonlinear buckling analysis is a static analysis performed after adding
+# imperfections with large deflection active (NLGEOM,ON), extended to a point
+# where the stiffened cylinder can reach its limit load.
+# To perform the analysis, the load must be allowed to increase using very
+# small time increments so that the expected critical buckling load can
+# be predicted accurately.
+# Note - as this is a buckling analysis, divergence is expected.
+
+mapdl.slashsolu()
+mapdl.antype("STATIC")
+mapdl.nlgeom("on")
+mapdl.pred("on")
+mapdl.time(1)
+mapdl.nsubst(100, 10000, 10)
+mapdl.rescontrol("define", "all", 1)
+mapdl.outres("all", "all")
+mapdl.ncnv(2)  # Do not terminate the program execution if the solution diverges
+output = mapdl.solve()
+print(output)
+mapdl.finish()
+
+#%%
+###############################################################################
+# Post-buckling analysis
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# An unconverged solution of the nonlinear static analysis could mean that
+# buckling has occurred. In this example, the change in time (or load)
+# increment, and displacement value, occurs between substeps 10 and 11,
+# which corresponds to TIME = 0.51781 and TIME = 0.53806 and to a pressure
+# between 0.124 MPa and 0.129 MPa. It is therefore very likely that buckling
+# occurred at this time; to be sure, the analysis is continued. The goal is to
+# verify the assessment made at this stage by obtaining the load-displacement
+# behavior over a larger range. Because the post-buckling state is unstable,
+# special techniques are necessary to compensate, in this case, nonlinear
+# stabilization is used.
+
+mapdl.slashsolu()  # Restart analysis with stabilization
+mapdl.antype("static", "restart", 1, 10)
+mapdl.nsubst(100, 50000, 10)
+mapdl.rescontrol("define", "last")
+mapdl.stabilize("constant", "energy", 0.000143)  # Use energy option
+output = mapdl.solve()
+print(output)
+mapdl.finish()
+
+#%%
+###############################################################################
+# Postprocess buckling analysis in POST1
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#
+mapdl.post1()
+mapdl.set("last")
+mapdl.post_processing.plot_nodal_displacement("NORM", smooth_shading=True)
+mapdl.post_processing.plot_nodal_eqv_stress()
+mapdl.finish()
+#%%
+###############################################################################
+# Postprocess buckling analysis in POST26
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#
+mapdl.post26()
+
+
+mapdl.numvar(100)  # allow storage for 100 variables
+mapdl.enersol(13, "sene")  # store stiffness energy
+mapdl.enersol(14, "sten")  # store artificial stabilization energy
+
+# time history plot of stiffness and stabilization energies
+mapdl.show("png")
+mapdl.plvar(13, 14)
+mapdl.show("close")
+
+# pressure versus axial shortening for some nodes under the upper ring
+mapdl.nsol(2, 67319, "U", "Z", "UZ1")
+mapdl.prod(
+    ir=3, ia=2, ib="", ic="", name="strain1", facta="", factb="", factc=-1 / 431.8
+)
+mapdl.prod(ir=12, ia=1, ib="", ic="", name="Load", facta="", factb="", factc=0.24)
+mapdl.xvar(3)
+mapdl.show("png")
+mapdl.xrange(0.01)
+mapdl.yrange(0.24)
+mapdl.axlab("X", "Axial Shortening")
+mapdl.aylab("Y", "Applied Pressure ")
+mapdl.plvar(12)
+mapdl.show("close")
+mapdl.xvar(3)
+mapdl.show("png")
+mapdl.xrange(0.002)
+mapdl.yrange(1)
+mapdl.axlab("X", "Axial Shortening")
+mapdl.aylab("Y", "Time")
+mapdl.plvar(1)
+mapdl.show("close")
+
+# pressure versus radial displacement for the node with max. deformation
+mapdl.nsol(6, 65269, "U", "Y", "UY_1")
+mapdl.prod(ir=7, ia=6, ib=6, ic="", name="UY2_1")
+mapdl.nsol(8, 65269, "U", "X", "UX_1")
+mapdl.prod(ir=9, ia=8, ib=8, ic="", name="UX2_1")
+mapdl.add(10, 7, 9, "sum")
+mapdl.sqrt(ir=11, ia=10, name="Urad")
+mapdl.xvar(11)
+mapdl.show("png")
+mapdl.xrange(4)
+mapdl.yrange(0.24)
+mapdl.axlab("X", "Radial Displacement")
+mapdl.aylab("Y", "Applied Pressure")
+mapdl.plvar(12)
+mapdl.show("close")
+mapdl.finish()
+
+#%%
+###############################################################################
+# Exit MAPDL
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# Exit MAPDL instance
+
+mapdl.exit()