Plugin fibre section

docs/examples.rst

@@ -37,6 +37,7 @@ Analysis
     examples/analysis/warping_analysis
     examples/analysis/frame_analysis
     examples/analysis/stress_analysis
+    examples/analysis/export_fibre_section
 
 Results
 -------

docs/examples/analysis/export_fibre_section.ipynb

@@ -0,0 +1,278 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "db82db5006f2f216",
+   "metadata": {},
+   "source": [
+    "# Export to Fibre Section\n",
+    "\n",
+    "This example shows how to export a section to a fibre section that can be used in [suanPan](https://github.com/TLCFEM/suanPan).\n",
+    "\n",
+    "[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",
+    "\n",
+    "There are three analysis types available.\n",
+    "\n",
+    "1. '2D' ---> 2D planar analysis (axial force, bending moment). Elements: `B21`, `F21`.\n",
+    "2. '3D' ---> 3D spatial analysis (axial force, bending moment). Elements: `B31`, `F31`.\n",
+    "3. '3DOS' ---> 3D spatial analysis with warping and torsion (axial force, bending moment, torsion). Elements: `B31OS`.\n",
+    "\n",
+    "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",
+    "\n",
+    "For '2D' and '3D' analyses, the location and area are used. For '3DOS' analysis, the additional warping function and its derivatives are used.\n",
+    "\n",
+    "## The Export Function\n",
+    "\n",
+    "One shall call the function with a geometry object with mesh created."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1fe6766c73110947",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from sectionproperties.post.fibre import to_fibre_section\n",
+    "from sectionproperties.pre.library import i_section\n",
+    "\n",
+    "geom = i_section(d=203, b=133, t_f=7.8, t_w=5.8, r=8.9, n_r=8)\n",
+    "geom.create_mesh(mesh_sizes=10)\n",
+    "\n",
+    "commands = to_fibre_section(geom, analysis_type='3DOS')\n",
+    "\n",
+    "print(commands[:3000])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3e59149a988e3681",
+   "metadata": {},
+   "source": [
+    "The output can be saved to a file and later be used to create beam elements."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e62e5df634d337ed",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from shutil import which\n",
+    "\n",
+    "# write the fibre section to a file\n",
+    "with open('200UB25.4.sp', 'w') as f:\n",
+    "    f.write(commands)\n",
+    "\n",
+    "# write the main analysis file\n",
+    "# since we assigned '3DOS' analysis type, we need to use compatible elements, for example, 'B31OS'.\n",
+    "model = '''# Example torsion analysis\n",
+    "node 1 0 0 0\n",
+    "node 2 1 0 0\n",
+    "material ElasticOS 1 200. .25\n",
+    "file 200UB25.4.sp\n",
+    "orientation B3DOSL 1 0. 0. 1.\n",
+    "element B31OS 1 1 2 1 1 6\n",
+    "fix2 1 E 1\n",
+    "displacement 1 0 1E-1 4 2\n",
+    "plainrecorder 1 Node RF4 2\n",
+    "plainrecorder 2 Element BEAMS 1\n",
+    "step static 1\n",
+    "set ini_step_size 1E-1\n",
+    "set fixed_step_size true\n",
+    "converger RelIncreDisp 1 1E-10 5 1\n",
+    "analyze\n",
+    "save recorder 1 2\n",
+    "exit\n",
+    "'''\n",
+    "with open('torsion_analysis.sp', 'w') as f:\n",
+    "    f.write(model)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e3a7872e157397ad",
+   "metadata": {},
+   "source": [
+    "For further details, check [this](https://tlcfem.github.io/suanPan-manual/3.2/Example/Structural/Statics/thin-walled-section/) example."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a905cac642f4ba76",
+   "metadata": {},
+   "source": [
+    "## A Bit More Details\n",
+    "\n",
+    "### Shift Section\n",
+    "\n",
+    "As the header states, the function computes properties in the local coordinate system of the section.\n",
+    "\n",
+    "For the above I-section, one may want to shift the section to the centroid of the section.\n",
+    "The user shall explicitly perform this step."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d0342167a9608431",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "geom.plot_geometry()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "72fd533e96ae001c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from sectionproperties.analysis import Section\n",
+    "\n",
+    "sec = Section(geom)\n",
+    "sec.calculate_geometric_properties()\n",
+    "x, y = sec.get_c()\n",
+    "geom = geom.shift_section(-x, -y)  # or whatever shift you want\n",
+    "geom.create_mesh(mesh_sizes=5)\n",
+    "geom.plot_geometry()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c0091da299e91349",
+   "metadata": {},
+   "source": [
+    "### Overwrite Material\n",
+    "\n",
+    "Material names shall be converted to material tags.\n",
+    "\n",
+    "One can provide such a mapping dictionary to the function.\n",
+    "With the shifted geometry, one can do the following."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "381c615fd4cf7f58",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "commands = to_fibre_section(geom, analysis_type='3DOS', material_mapping={'default': 1})\n",
+    "print(commands[:5000])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6f3179efd747b6ff",
+   "metadata": {},
+   "source": [
+    "## Run Analysis\n",
+    "\n",
+    "If `suanPan` is installed, one can run the analysis using the previously saved script."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2997fa9f72909c12",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from os.path import exists\n",
+    "\n",
+    "# write the fibre section to a file with material tag replaced\n",
+    "with open('200UB25.4.sp', 'w') as f:\n",
+    "    f.write(commands)\n",
+    "\n",
+    "# run the analysis\n",
+    "if which('suanpan') is not None:\n",
+    "    from subprocess import run\n",
+    "\n",
+    "    result_available = True\n",
+    "    run(['suanpan', '-f', 'torsion_analysis.sp'])\n",
+    "else:\n",
+    "    result_available = exists('R1-RF42.txt')\n",
+    "    print('suanPan is not installed.')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d77fc35609b5228e",
+   "metadata": {},
+   "source": [
+    "## Plot Results\n",
+    "\n",
+    "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",
+    "\n",
+    "The sixth component of `BEAMS` is the St. Venant torsion."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "91298a718a2935a9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "if result_available:\n",
+    "    from matplotlib import pyplot as plt\n",
+    "    import numpy as np\n",
+    "\n",
+    "    data = np.loadtxt('R1-RF42.txt')\n",
+    "    twist = data[:, 0] * .1\n",
+    "    torque = data[:, 1]\n",
+    "    plt.plot(twist, torque)\n",
+    "    plt.xlabel('twist (rad)')\n",
+    "    plt.ylabel('total torque')\n",
+    "    plt.legend(['200UB25.4'])\n",
+    "    plt.tight_layout()\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e93238cf396c115d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "if result_available:\n",
+    "    data = np.loadtxt('R2-BEAMS1.txt')\n",
+    "    twist = data[:, 0] * .1\n",
+    "    torque = data[:, 6]\n",
+    "    ref_torque = twist * 80 * 62.7e3  # G=80, J=62.7\n",
+    "    plt.plot(twist, torque)\n",
+    "    plt.plot(twist, ref_torque)\n",
+    "    plt.xlabel('twist (rad)')\n",
+    "    plt.ylabel('St. Venant torsion')\n",
+    "    plt.legend(['numerical', 'theoretical'])\n",
+    "    plt.tight_layout()\n",
+    "    plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
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+ "nbformat_minor": 5
+}