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Merge pull request #295 from TLCFEM/plugin-fibre-section
Plugin fibre section
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‎docs/examples.rst

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examples/analysis/warping_analysis
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examples/analysis/frame_analysis
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examples/analysis/stress_analysis
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examples/analysis/export_fibre_section
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Results
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-------

‎docs/examples/analysis/export_fibre_section.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "db82db5006f2f216",
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"metadata": {},
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"source": [
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"# Export to Fibre Section\n",
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"\n",
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"This example shows how to export a section to a fibre section that can be used in [suanPan](https://github.com/TLCFEM/suanPan).\n",
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"\n",
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"[suanPan](https://github.com/TLCFEM/suanPan) is a finite element analysis framework. Sections can be exported and used to perform nonlinear analysis of frame structures.\n",
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"\n",
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"There are three analysis types available.\n",
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"\n",
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"1. '2D' ---> 2D planar analysis (axial force, bending moment). Elements: `B21`, `F21`.\n",
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"2. '3D' ---> 3D spatial analysis (axial force, bending moment). Elements: `B31`, `F31`.\n",
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"3. '3DOS' ---> 3D spatial analysis with warping and torsion (axial force, bending moment, torsion). Elements: `B31OS`.\n",
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"\n",
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"The section is discretised into triangular elements in `sectionproperties`. Each triangle can be deemed as a small cell/fibre. Its area and properties at the centre of the triangle are calculated and exported to create a fibre section.\n",
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"\n",
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"For '2D' and '3D' analyses, the location and area are used. For '3DOS' analysis, the additional warping function and its derivatives are used.\n",
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"\n",
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"## The Export Function\n",
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"\n",
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"One shall call the function with a geometry object with mesh created."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "1fe6766c73110947",
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"metadata": {},
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"outputs": [],
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"source": [
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"from sectionproperties.post.fibre import to_fibre_section\n",
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"from sectionproperties.pre.library import i_section\n",
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"\n",
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"geom = i_section(d=203, b=133, t_f=7.8, t_w=5.8, r=8.9, n_r=8)\n",
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"geom.create_mesh(mesh_sizes=10)\n",
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"\n",
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"commands = to_fibre_section(geom, analysis_type='3DOS')\n",
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"\n",
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"print(commands[:3000])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3e59149a988e3681",
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"metadata": {},
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"source": [
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"The output can be saved to a file and later be used to create beam elements."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "e62e5df634d337ed",
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"metadata": {},
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"outputs": [],
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"source": [
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"from shutil import which\n",
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"\n",
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"# write the fibre section to a file\n",
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"with open('200UB25.4.sp', 'w') as f:\n",
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" f.write(commands)\n",
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"\n",
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"# write the main analysis file\n",
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"# since we assigned '3DOS' analysis type, we need to use compatible elements, for example, 'B31OS'.\n",
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"model = '''# Example torsion analysis\n",
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"node 1 0 0 0\n",
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"node 2 1 0 0\n",
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"material ElasticOS 1 200. .25\n",
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"file 200UB25.4.sp\n",
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"orientation B3DOSL 1 0. 0. 1.\n",
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"element B31OS 1 1 2 1 1 6\n",
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"fix2 1 E 1\n",
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"displacement 1 0 1E-1 4 2\n",
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"plainrecorder 1 Node RF4 2\n",
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"plainrecorder 2 Element BEAMS 1\n",
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"step static 1\n",
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"set ini_step_size 1E-1\n",
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"set fixed_step_size true\n",
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"converger RelIncreDisp 1 1E-10 5 1\n",
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"analyze\n",
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"save recorder 1 2\n",
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"exit\n",
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"'''\n",
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"with open('torsion_analysis.sp', 'w') as f:\n",
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" f.write(model)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e3a7872e157397ad",
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"metadata": {},
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"source": [
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"For further details, check [this](https://tlcfem.github.io/suanPan-manual/3.2/Example/Structural/Statics/thin-walled-section/) example."
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]
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},
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{
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"cell_type": "markdown",
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"id": "a905cac642f4ba76",
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"metadata": {},
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"source": [
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"## A Bit More Details\n",
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"\n",
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"### Shift Section\n",
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"\n",
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"As the header states, the function computes properties in the local coordinate system of the section.\n",
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"\n",
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"For the above I-section, one may want to shift the section to the centroid of the section.\n",
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"The user shall explicitly perform this step."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d0342167a9608431",
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"metadata": {},
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"outputs": [],
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"source": [
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"geom.plot_geometry()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "72fd533e96ae001c",
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"metadata": {},
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"outputs": [],
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"source": [
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"from sectionproperties.analysis import Section\n",
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"\n",
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"sec = Section(geom)\n",
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"sec.calculate_geometric_properties()\n",
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"x, y = sec.get_c()\n",
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"geom = geom.shift_section(-x, -y) # or whatever shift you want\n",
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"geom.create_mesh(mesh_sizes=5)\n",
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"geom.plot_geometry()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c0091da299e91349",
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"metadata": {},
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"source": [
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"### Overwrite Material\n",
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"\n",
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"Material names shall be converted to material tags.\n",
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"\n",
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"One can provide such a mapping dictionary to the function.\n",
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"With the shifted geometry, one can do the following."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "381c615fd4cf7f58",
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"metadata": {},
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"outputs": [],
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"source": [
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"commands = to_fibre_section(geom, analysis_type='3DOS', material_mapping={'default': 1})\n",
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"print(commands[:5000])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "6f3179efd747b6ff",
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"metadata": {},
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"source": [
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"## Run Analysis\n",
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"\n",
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"If `suanPan` is installed, one can run the analysis using the previously saved script."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "2997fa9f72909c12",
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"metadata": {},
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"outputs": [],
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"source": [
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"from os.path import exists\n",
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"\n",
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"# write the fibre section to a file with material tag replaced\n",
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"with open('200UB25.4.sp', 'w') as f:\n",
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" f.write(commands)\n",
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"\n",
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"# run the analysis\n",
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"if which('suanpan') is not None:\n",
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" from subprocess import run\n",
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"\n",
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" result_available = True\n",
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" run(['suanpan', '-f', 'torsion_analysis.sp'])\n",
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"else:\n",
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" result_available = exists('R1-RF42.txt')\n",
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" print('suanPan is not installed.')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d77fc35609b5228e",
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"metadata": {},
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"source": [
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"## Plot Results\n",
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"\n",
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"The results are stored in `R1-RF42.txt` (**R**ecorder **1** --> **RF4** for node **2**) and `R2-BEAMS1.txt` (**R**ecorder **2** --> **BEAMS** for element **1**).\n",
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"\n",
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"The sixth component of `BEAMS` is the St. Venant torsion."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "91298a718a2935a9",
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"metadata": {},
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"outputs": [],
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"source": [
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"if result_available:\n",
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" from matplotlib import pyplot as plt\n",
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" import numpy as np\n",
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"\n",
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" data = np.loadtxt('R1-RF42.txt')\n",
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" twist = data[:, 0] * .1\n",
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" torque = data[:, 1]\n",
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" plt.plot(twist, torque)\n",
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" plt.xlabel('twist (rad)')\n",
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" plt.ylabel('total torque')\n",
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" plt.legend(['200UB25.4'])\n",
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" plt.tight_layout()\n",
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" plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "e93238cf396c115d",
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"metadata": {},
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"outputs": [],
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"source": [
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"if result_available:\n",
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" data = np.loadtxt('R2-BEAMS1.txt')\n",
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" twist = data[:, 0] * .1\n",
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" torque = data[:, 6]\n",
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" ref_torque = twist * 80 * 62.7e3 # G=80, J=62.7\n",
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" plt.plot(twist, torque)\n",
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" plt.plot(twist, ref_torque)\n",
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" plt.xlabel('twist (rad)')\n",
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" plt.ylabel('St. Venant torsion')\n",
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" plt.legend(['numerical', 'theoretical'])\n",
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" plt.tight_layout()\n",
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" plt.show()"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 2
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython2",
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"version": "2.7.6"
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}
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"nbformat_minor": 5
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}

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