Replicate the experiments of J. D. Stachiw

This repo is a fork of https://github.com/timmaxw/os2cx and is designed to replicate the experiments done by J. D. Stachiw in Figure 7.12 from the following book:

Stachiw, J. D., Acrylic plastic viewports for ocean engineering applications (1977)
https://catalog.hathitrust.org/Record/008333526
Main Author:    Stachiw, J. D
Language(s):    English
Published:      San Diego, Calif. : Naval Undersea Center, 1977
Subjects:       Ocean engineering > Ocean engineering / Materials
Oceanographic submersibles > Oceanographic submersibles / Materials
Physical Description:   2 v. : ill. ; 28 cm

Link to Figure 7.12: https://babel.hathitrust.org/cgi/pt?id=uc1.31822009085754&view=1up&seq=337

In this book, Stachiw measures the deflection of 3 different sizes and thicknesses of acrylic over a flange over a range of pressures until imploision. My goal was to replicate these results in Calculix and then compare against the real-world experiments to see if they match.

How to compile and run

Code tested on Ubuntu 20.04:

./apt-get-deps
qmake
make
cd stachiw
# Perform calculations for different sizes, thickness, and pressure
./all_stachiw_multi.sh
# Generate graphs of experiments
./pandas-plot-stachiw.py
# Run GUI with single example
./gui_stachiw_single.sh

These plots compare the Stachiw results against those calculated from CalculiX, as well as using standard equations for circular plate with uniform load and edges simply supported. Both the CalculiX results and the equations are perfectly linear, while Stachiw's results are curves that stop when the acrylic burst open. So the results are close and useful for approximate calculations, but do not predict the burst pressure or change at the same rate with pressure.

Original README.md

Forked from original GitHub repository https://github.com/timmaxw/os2cx

OS2CX (short for "OpenSCAD-to-CalculiX") integrates the popular open-source CAD package OpenSCAD with the open-source analysis package CalculiX. OpenSCAD lets the user generate 3D models defined using a text-based input language. CalculiX simulates 3D models to predict physical properties such as strength, stiffness, etc. using finite element analysis. OS2CX interfaces OpenSCAD and CalculiX together, so that 3D models generated in OpenSCAD can be simulated in CalculiX.

OS2CX is an experimental, alpha-quality project. It's not particularly well-tested, and results may not be accurate. Don't use it for anything important!

Example

Suppose we want to calculate how much a 1-meter steel I-beam would flex if we anchored one end firmly in concrete and hung a 1-metric-ton car from the other end. We can model this I-beam in OpenSCAD like so:

length = 1;
width = 0.1;
height = 0.1;
thickness = 0.01;

module i_beam() {
    cube([length, thickness, height], center=true);
    translate([0, 0, height/2-thickness/2])
        cube([length, width, thickness], center=true);
    translate([0, 0, -height/2+thickness/2])
        cube([length, width, thickness], center=true);
}

Next, we need to tell OS2CX the parameters of the simulation. We do this using modules that OS2CX adds to OpenSCAD via a openscad2calculix.scad helper library:

include <../openscad2calculix.scad>

/* Declares a material object in OS2CX, called "steel". It has a Young's modulus
of 209 gigapascals, and a Poisson's ratio of 0.3. */
os2cx_material_elastic_simple(
    "steel",
    youngs_modulus=[209, "GPa"],
    poissons_ratio=0.3,
    density=[7600, "kg/m^3"]);

/* Declares a new mesh object in OS2CX. Its name will be "i_beam", and its shape
comes from the the OpenSCAD i_beam() module we defined above. */
os2cx_mesh("i_beam", material="steel") {
    i_beam();
}

/* Declares two selection objects in OS2CX. A selection object refers to part of
the surface or volume of a mesh object. It's defined by taking the intersection
of the declared mesh, with another OpenSCAD shape. */
os2cx_select_surface("anchored_end", [-1, 0, 0], 45) {
    translate([-length/2, 0, 0])
        cube([0.1, width+0.1, height+0.1], center=true);
}
os2cx_select_volume("loaded_end") {
    translate([length/2, 0, 0])
        cube([0.1, width+0.1, height+0.1], center=true);
}

/* Declares a load object in OS2CX, called "car_weight". It's defined as a
force of 9,800 newtons in the -Z direction, applied uniformly over the
"loaded_end" volume we defined above. */
weight = 1000;
gravity = 9.8;
os2cx_load_volume(
    "car_weight",
    "loaded_end",
    force_total=[[0, 0, -gravity*weight], "N"]);


/* Tell OS2CX to do a simple static deflection analysis using the objects we
just defined */
os2cx_analysis_static_simple(
    fixed="anchored_end",
    load="car_weight",
    length_unit="m"
);

/* Tell OS2CX to report the maximum deflection of the loaded end. */
os2cx_measure(
    "loaded_end_deflection",
    "loaded_end",
    "DISP");

Let's save this file as example.scad and open it using the OpenSCAD2CalculiX GUI application. After a few seconds of calculation, OS2CX will show us the results:

The bending is exaggerated by a factor of 50 in the visualization. Consulting the color scale on the left-hand side, we can see that the beam would bend approximately 3.50 millimeters. Theory predicts 3.48 millimeters; not bad!

Installing and running

OS2CX has been tested on Linux (Ubuntu 22.04). The dependencies are all cross-platform, so in principle it should be easy to get it working on other operating systems, but no guarantees.

Dependencies:

• OpenSCAD 2021.01 (sudo apt install openscad)
• CalculiX 2.17 (sudo apt install calculix-ccx)
• Qt 5.15
• CGAL 5.4 (sudo apt install libcgal-dev)
• tetgen 1.5.0 (as a library, not an executable) (sudo apt install libtet1.5-dev)
• Google Test (sudo apt-get install libgtest-dev)

Development notes:

• I develop OS2CX using Qt Creator.
• It's structured as a top-level QMake project with three sub-projects: a core project that contains the main logic, a gui project that defines the GUI application, and a test project that defines tests for core.
• Only gui makes significant use of Qt. core and test use nothing from Qt except QProcess.
• The test executable must be executed in the toplevel os2cx/ directory.