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This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -24,10 +24,21 @@ "name": "Calfem.ipynb", "provenance": [], "collapsed_sections": [], "toc_visible": true, "include_colab_link": true } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "view-in-github", "colab_type": "text" }, "source": [ "<a href=\"https://colab.research.google.com/gist/bagustris/3c0d97cdbc2944c64d527c7948c0c03a/calfem.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" ] }, { "cell_type": "markdown", "metadata": { -
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Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -0,0 +1,1063 @@ { "nbformat": 4, "nbformat_minor": 0, "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "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": "3.6.4" }, "colab": { "name": "Calfem.ipynb", "provenance": [], "collapsed_sections": [], "toc_visible": true } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "gFSDmEZytWMX" }, "source": [ "# What is CALFEM for Python" ] }, { "cell_type": "markdown", "metadata": { "id": "nWqS94s4tWMa" }, "source": [ "* Subset of CALFEM routines implemented in Python\n", "* Using NumPy for matrices\n", "* Additional mesh generation routines supporting Triangle and GMSH\n", "* Plotting with Matplotlib" ] }, { "cell_type": "markdown", "metadata": { "id": "H0G9jlwKtWMb" }, "source": [ "# CALFEM Python modules" ] }, { "cell_type": "markdown", "metadata": { "id": "lDlZ3786tWMc" }, "source": [ "* **calfem.core**\n", " * Element routines\n", " * System routines\n", "* **calfem.utils**\n", " * I/O routines\n", " * Misc. routines\n", "* **calfem.geometry**\n", " * Routines for defining problem geometry used for input in mesh generation\n", "* **calfem.mesh**\n", " * Mesh generation routines\n", "* **calfem.vis/calfem.vis_mpl**\n", " * Routines for visualising geometry, meshes and results." ] }, { "cell_type": "markdown", "metadata": { "id": "TmEFTEGmzvOA" }, "source": [ "# Installing CALFEM for Pyton" ] }, { "cell_type": "code", "metadata": { "id": "bUpWJT0Zzr2q", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "ae809070-721f-452e-de43-96d0e618ea43" }, "source": [ "!pip install calfem-python\n", "!pip install pyqt5" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "Collecting calfem-python\n", "\u001b[?25l Downloading https://files.pythonhosted.org/packages/b1/89/75feb11d12f8ac88feb6c745a7e37621caea6750a1242dd16f0bc5a91e70/calfem_python-3.5.3-py3-none-any.whl (70kB)\n", "\u001b[K |████████████████████████████████| 71kB 3.0MB/s \n", "\u001b[?25hCollecting visvis\n", "\u001b[?25l Downloading https://files.pythonhosted.org/packages/02/4e/e175ada34cb13967ed8b6597ba39ac737e191d7c5a64a1d0fd622c334a24/visvis-1.13.0.tar.gz (5.1MB)\n", "\u001b[K |████████████████████████████████| 5.1MB 7.1MB/s \n", "\u001b[?25hCollecting pyvtk\n", " Downloading https://files.pythonhosted.org/packages/6a/dc/d5ffc2cc50bdd7a2e7b435655ee5931d614f7c118624dd20c51440c79337/PyVTK-0.5.18.tar.gz\n", "Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from calfem-python) (3.2.2)\n", "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from calfem-python) (1.19.5)\n", "Requirement already satisfied: pyOpenGl in /usr/local/lib/python3.7/dist-packages (from visvis->calfem-python) (3.1.5)\n", "Requirement already satisfied: six in /usr/local/lib/python3.7/dist-packages (from pyvtk->calfem-python) (1.15.0)\n", "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->calfem-python) (2.8.1)\n", "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->calfem-python) (1.3.1)\n", "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->calfem-python) (2.4.7)\n", "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib->calfem-python) (0.10.0)\n", "Building wheels for collected packages: visvis, pyvtk\n", " Building wheel for visvis (setup.py) ... \u001b[?25l\u001b[?25hdone\n", " Created wheel for visvis: filename=visvis-1.13.0-cp37-none-any.whl size=4905513 sha256=8862b98830b4158cef834b2e7877c917651d8a08d4b66730ca1b0950a75ecced\n", " Stored in directory: /root/.cache/pip/wheels/30/c2/3e/d6ecf9ef400e03b84f3533211fa1a9cb21f828c12658508b44\n", " Building wheel for pyvtk (setup.py) ... \u001b[?25l\u001b[?25hdone\n", " Created wheel for pyvtk: filename=PyVTK-0.5.18-cp37-none-any.whl size=24735 sha256=39ad91270bf76f32d1ce69c27bb33c30b0a0dc0a704301978308779f2cae56ca\n", " Stored in directory: /root/.cache/pip/wheels/7d/73/d6/4c3ce104624b4459b6dbc3329235f68815d35e5d6c0f3aac83\n", "Successfully built visvis pyvtk\n", "Installing collected packages: visvis, pyvtk, calfem-python\n", "Successfully installed calfem-python-3.5.3 pyvtk-0.5.18 visvis-1.13.0\n", "Collecting pyqt5\n", "\u001b[?25l Downloading https://files.pythonhosted.org/packages/ed/62/cd9f10702c75b242f82da858668fba0cda04cda92133244d3d1555e530b4/PyQt5-5.15.4-cp36.cp37.cp38.cp39-abi3-manylinux2014_x86_64.whl (8.3MB)\n", "\u001b[K |████████████████████████████████| 8.3MB 4.1MB/s \n", "\u001b[?25hCollecting PyQt5-Qt5>=5.15\n", "\u001b[?25l Downloading https://files.pythonhosted.org/packages/83/d4/241a6a518d0bcf0a9fcdcbad5edfed18d43e884317eab8d5230a2b27e206/PyQt5_Qt5-5.15.2-py3-none-manylinux2014_x86_64.whl (59.9MB)\n", "\u001b[K |████████████████████████████████| 59.9MB 82kB/s \n", "\u001b[?25hCollecting PyQt5-sip<13,>=12.8\n", "\u001b[?25l Downloading https://files.pythonhosted.org/packages/31/24/f887203677955ba4d5d4efe9176ac7ed2bf84efce8c243ab91e63183ad9e/PyQt5_sip-12.8.1-cp37-cp37m-manylinux1_x86_64.whl (283kB)\n", "\u001b[K |████████████████████████████████| 286kB 27.1MB/s \n", "\u001b[?25hInstalling collected packages: PyQt5-Qt5, PyQt5-sip, pyqt5\n", "Successfully installed PyQt5-Qt5-5.15.2 PyQt5-sip-12.8.1 pyqt5-5.15.4\n" ], "name": "stdout" } ] }, { "cell_type": "markdown", "metadata": { "id": "QSmht_QotWMe" }, "source": [ "# General procedure for FE calculation" ] }, { "cell_type": "markdown", "metadata": { "id": "hOcQ1h_YtWMf" }, "source": [ "* Define the model\n", "* Generate element matrices\n", "* Assemble element matrices in the global stiffness matrix\n", "* Solve the system of equations\n", "* Calculate element forces" ] }, { "cell_type": "markdown", "metadata": { "id": "xWdbZzY9tWMg" }, "source": [ "# Example 1 - System of springs" ] }, { "cell_type": "markdown", "metadata": { "id": "JmL12HGVtWMg" }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "id": "bOzQsbQftWMh" }, "source": [ "First we import the required Python-modules:" ] }, { "cell_type": "code", "metadata": { "id": "vuiqm6cFtWMi" }, "source": [ "import numpy as np\n", "import calfem.core as cfc\n", "import calfem.vis_mpl as cfv\n", "import math" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "Jc13lKa4tWMm" }, "source": [ "Create the topology matrix. All input to CALFEM is NumPy arrays. Topology is defined by index 1." ] }, { "cell_type": "code", "metadata": { "id": "UsHJRBIVtWMn", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "9008bf91-4654-47dc-d8c5-7750f0ad501d" }, "source": [ "Edof = np.array([\n", " [1,2],\n", " [2,3],\n", " [2,3]\n", " ])\n", "print(Edof)" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "[[1 2]\n", " [2 3]\n", " [2 3]]\n" ], "name": "stdout" } ] }, { "cell_type": "markdown", "metadata": { "id": "cbxmq_WdtWMs" }, "source": [ "Stiffness matrix and force vector." ] }, { "cell_type": "code", "metadata": { "id": "k2eVblPhtWMt", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "21cc4090-e3cc-47eb-9dde-c396cef452bb" }, "source": [ "K = np.zeros((3,3))\n", "f = np.zeros((3,1))\n", "print(K)\n", "print(f)" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "[[0. 0. 0.]\n", " [0. 0. 0.]\n", " [0. 0. 0.]]\n", "[[0.]\n", " [0.]\n", " [0.]]\n" ], "name": "stdout" } ] }, { "cell_type": "markdown", "metadata": { "id": "W1WAd9vxtWMx" }, "source": [ "Element matrices." ] }, { "cell_type": "code", "metadata": { "id": "XaB3JJG2tWMy", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "e1c9fccf-b15a-437e-a48f-9561619fa588" }, "source": [ "k = 1500.0\n", "ep1 = k\n", "ep2 = 2.0*k\n", "Ke1 = cfc.spring1e(ep1)\n", "Ke2 = cfc.spring1e(ep2)\n", "print(Ke1)\n", "print(Ke2)" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "[[ 1500. -1500.]\n", " [-1500. 1500.]]\n", "[[ 3000. -3000.]\n", " [-3000. 3000.]]\n" ], "name": "stdout" } ] }, { "cell_type": "markdown", "metadata": { "id": "EosogK5itWM2" }, "source": [ "Assemble element matrices in global stiffness matrix." ] }, { "cell_type": "code", "metadata": { "id": "PnRJk8YxtWM2", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "52ebaf8d-e5e7-4fa8-c8e4-5cec55b246fe" }, "source": [ "cfc.assem(Edof[0,:], K, Ke2)\n", "cfc.assem(Edof[1,:], K, Ke1)\n", "cfc.assem(Edof[2,:], K, Ke2)\n", "\n", "print(K)" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "[[ 3000. -3000. 0.]\n", " [-3000. 7500. -4500.]\n", " [ 0. -4500. 4500.]]\n" ], "name": "stdout" } ] }, { "cell_type": "markdown", "metadata": { "id": "D_qDeNR0tWM5" }, "source": [ "Solving the equation system.\n", "\n", "bc is an array of prescribed degrees of freedom. Values to be specified are specified in a separate array. If all values are 0, they don't have to be specified. \n", "\n", "Note: NumPy index from 0 ie 1 here corresponds to degree of freedom 2" ] }, { "cell_type": "code", "metadata": { "id": "CS9_3q1OtWM6", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "0748a78d-35f0-4aed-ee4b-e8a08342aead" }, "source": [ "bc = np.array([1,3])\n", "\n", "f[1] = 100.0\n", "\n", "# Solve equation system \n", "\n", "a, r = cfc.solveq(K, f, bc)\n", "\n", "print(\"Displacements:\")\n", "print(a)\n", "print(\"Reaction forces:\")\n", "print(r)" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "Displacements:\n", "[[0. ]\n", " [0.01333333]\n", " [0. ]]\n", "Reaction forces:\n", "[[-40.]\n", " [ 0.]\n", " [-60.]]\n" ], "name": "stdout" } ] }, { "cell_type": "markdown", "metadata": { "id": "fkayC2m3tWM9" }, "source": [ "Calculating element forces." ] }, { "cell_type": "code", "metadata": { "id": "RkzQgzz8tWM-" }, "source": [ "ed1 = cfc.extractEldisp(Edof[0,:], a)\n", "ed2 = cfc.extractEldisp(Edof[1,:], a)\n", "ed3 = cfc.extractEldisp(Edof[2,:], a)\n", " \n", "es1 = cfc.spring1s(ep2, ed1)\n", "es2 = cfc.spring1s(ep1, ed2)\n", "es3 = cfc.spring1s(ep2, ed3)" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "D-eJKUm9tWNB" }, "source": [ "print(\"N1 =\", es1)\n", "print(\"N2 =\", es2)\n", "print(\"N3 =\", es3)" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "GmhChjXUtWNI" }, "source": [ "# Example 2 - Bars" ] }, { "cell_type": "markdown", "metadata": { "id": "_2kdcB0ItWNJ" }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "id": "ceRrvOKwtWNK" }, "source": [ "Define element topology. Element number are not used in the **Edof** matrix in CALFEM for Python." ] }, { "cell_type": "code", "metadata": { "id": "558bhYPmtWNK" }, "source": [ "Edof = np.array([\n", " [1,2,5,6],\n", " [5,6,7,8],\n", " [3,4,5,6]\n", "])" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "I70w6CUmtWNN" }, "source": [ "Stiffness matrix and load vector." ] }, { "cell_type": "code", "metadata": { "id": "tBslPdwutWNP" }, "source": [ "K = np.matrix(np.zeros((8,8)))\n", "f = np.matrix(np.zeros((8,1)))" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "3Qr3rjgqtWNS" }, "source": [ "Element properties." ] }, { "cell_type": "code", "metadata": { "id": "TpnMqyK5tWNT" }, "source": [ "E = 2.0e11\n", "A1 = 6.0e-4\n", "A2 = 3.0e-4\n", "A3 = 10.0e-4\n", "ep1 = [E, A1] # Vanliga listor kan användas för att definiera element-\n", "ep2 = [E, A2] # egenskaper\n", "ep3 = [E, A3]" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "IXOMKpPltWNV" }, "source": [ "Element coordinates." ] }, { "cell_type": "code", "metadata": { "id": "F_StF3g2tWNW" }, "source": [ "ex1=np.array([0.,1.6])\n", "ex2=np.array([1.6,1.6])\n", "ex3=np.array([0.,1.6])\n", "\n", "ey1=np.array([0.,0.])\n", "ey2=np.array([0.,1.2])\n", "ey3=np.array([1.2,0.])" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "2tvMp03ftWNZ" }, "source": [ "Element matrices." ] }, { "cell_type": "code", "metadata": { "id": "g2a2lkAstWNa" }, "source": [ "Ke1 = cfc.bar2e(ex1, ey1, ep1)\n", "Ke2 = cfc.bar2e(ex2, ey2, ep2)\n", "Ke3 = cfc.bar2e(ex3, ey3, ep3)" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "NITmOQq_tWNd" }, "source": [ "Assemble stiffness matrix." ] }, { "cell_type": "code", "metadata": { "id": "A_0HwLpstWNd" }, "source": [ "cfc.assem(Edof[0,:],K,Ke1)\n", "cfc.assem(Edof[1,:],K,Ke2)\n", "cfc.assem(Edof[2,:],K,Ke3)" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "d9Y6ne2MtWNh" }, "source": [ "Solve the equation system." ] }, { "cell_type": "code", "metadata": { "id": "51LIp0LetWNi" }, "source": [ "bc = np.array([1,2,3,4,7,8])\n", "f[5] = -80e3\n", "\n", "a, r = cfc.solveq(K, f, bc)\n", "\n", "print(\"Displacements:\")\n", "print(a)\n", "print(\"Reaction forces:\")\n", "print(r)" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "CR94WSfgtWNk" }, "source": [ "Calculate element forces." ] }, { "cell_type": "code", "metadata": { "id": "2PKnGVP8tWNl" }, "source": [ "ed1=cfc.extractEldisp(Edof[0,:],a);\n", "N1=cfc.bar2s(ex1,ey1,ep1,ed1)\n", "ed2=cfc.extractEldisp(Edof[1,:],a);\n", "N2=cfc.bar2s(ex2,ey2,ep2,ed2)\n", "ed3=cfc.extractEldisp(Edof[2,:],a);\n", "N3=cfc.bar2s(ex3,ey3,ep3,ed3)\n", "print(\"N1=\",N1)\n", "print(\"N2=\",N2)\n", "print(\"N3=\",N3)" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "50NnInZYtWNn" }, "source": [ "# Example 3 - More bars" ] }, { "cell_type": "markdown", "metadata": { "id": "6IInWnYItWNo" }, "source": [ "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "NPABtMlktWNo" }, "source": [ "Element topology." ] }, { "cell_type": "code", "metadata": { "id": "SI9pBAoEtWNp" }, "source": [ "Edof = np.array([\n", " [1, 2, 5, 6],\n", " [3, 4, 7, 8],\n", " [5, 6, 9, 10],\n", " [7, 8, 11, 12],\n", " [7, 8, 5, 6],\n", " [11, 12, 9, 10],\n", " [3, 4, 5, 6],\n", " [7, 8, 9, 10],\n", " [1, 2, 7, 8],\n", " [5, 6, 11, 12]\n", "])" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "heukZGRHtWNr" }, "source": [ "Stiffness matrix and element properties." ] }, { "cell_type": "code", "metadata": { "id": "U4mPbBxUtWNs" }, "source": [ "K=np.zeros([12,12])\n", "f=np.zeros([12,1])\n", "\n", "A = 25.0e-4\n", "E = 2.1e11\n", "ep = [E,A]" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "1cIl24vRtWNu" }, "source": [ "Element coordinates." ] }, { "cell_type": "code", "metadata": { "id": "bDoWJp60tWNv" }, "source": [ "ex = np.array([\n", " [0., 2.],\n", " [0., 2.],\n", " [2., 4.],\n", " [2., 4.],\n", " [2., 2.],\n", " [4., 4.],\n", " [0., 2.],\n", " [2., 4.],\n", " [0., 2.],\n", " [2., 4.]\n", "])\n", "\n", "ey = np.array([\n", " [2., 2.],\n", " [0., 0.],\n", " [2., 2.],\n", " [0., 0.],\n", " [0., 2.],\n", " [0., 2.],\n", " [0., 2.],\n", " [0., 2.],\n", " [2., 0.],\n", " [2., 0.]\n", "])\n" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "0P_ELf50tWNy" }, "source": [ "Assemble elements using a loop." ] }, { "cell_type": "code", "metadata": { "id": "L3rEx4AgtWNz" }, "source": [ "for elx, ely, eltopo in zip(ex, ey, Edof):\n", " Ke = cfc.bar2e(elx, ely, ep)\n", " cfc.assem(eltopo, K, Ke)" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "5FVk7ApvtWN1" }, "source": [ "Solve the equation system." ] }, { "cell_type": "code", "metadata": { "id": "o0GxDoYvtWN2" }, "source": [ "bc = np.array([1,2,3,4])\n", "\n", "f[10]=0.5e6*math.sin(math.pi/6)\n", "f[11]=-0.5e6*math.cos(math.pi/6)\n", "\n", "a, r = cfc.solveq(K,f,bc)" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "-_08WXh0tWN5" }, "source": [ "Calculating element forces." ] }, { "cell_type": "code", "metadata": { "id": "BUHPtrhVtWN6" }, "source": [ "ed=cfc.extractEldisp(Edof,a) # Extraherar alla elementförskjutningar\n", "\n", "N=np.zeros([Edof.shape[0]]) # Array för att lagra elementkrafter\n", "\n", "print(\"Element forces:\")\n", "\n", "i = 0\n", "for elx, ely, eld in zip(ex, ey, ed):\n", " N[i] = cfc.bar2s(elx, ely, ep, eld)\n", " print(\"N%d = %g\" % (i+1,N[i]))\n", " i+=1" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "vJl2zY8TxK4F" }, "source": [ "# Example 6 - Frame and bars" ] }, { "cell_type": "markdown", "metadata": { "id": "V9BJFzhhx1KC" }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "id": "dywtvOaOyKhQ" }, "source": [ "System matrices" ] }, { "cell_type": "code", "metadata": { "id": "Od0OlgUXsSVy" }, "source": [ "K = np.zeros([18,18])\n", "f = np.zeros([18,1])\n", "f[12,0] = 1.0\n", "\n", "coord = np.array([\n", " [0.0, 0.0],\n", " [1.0, 0.0],\n", " [0.0, 1.0],\n", " [1.0, 1.0],\n", " [0.0, 2.0],\n", " [1.0, 2.0]\n", "])\n", "\n", "dof1 = np.array([\n", " [1, 2, 3],\n", " [4, 5, 6],\n", " [7, 8, 9],\n", " [10, 11, 12],\n", " [13, 14, 15],\n", " [16, 17, 18]\n", "])\n", "\n", "dof2 = np.array([\n", " [1, 2],\n", " [4, 5],\n", " [7, 8],\n", " [10, 11],\n", " [13, 14],\n", " [16, 17]\n", "])" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "uAIQvIuB0KmG" }, "source": [ "Element properties, topology and coordinates" ] }, { "cell_type": "code", "metadata": { "id": "7HdJM9lxytXS" }, "source": [ "ep1 = [1.0, 1.0, 1.0]\n", "\n", "edof1 = np.array([\n", " [1, 2, 3, 7, 8, 9],\n", " [7, 8, 9, 13, 14, 15],\n", " [4, 5, 6, 10, 11, 12],\n", " [10, 11, 12, 16, 17, 18],\n", " [7, 8, 9, 10, 11, 12],\n", " [13, 14, 15, 16, 17, 18]\n", "])\n", "\n", "ex1, ey1 = cfc.coordxtr(edof1, coord, dof1);\n", "\n", "ep2 = [1.0, 1.0]\n", "\n", "edof2 = np.array([\n", " [1, 2, 10, 11],\n", " [7, 8, 16, 17],\n", " [7, 8, 4, 5],\n", " [13, 14, 10, 11]\n", "])\n", "\n", "ex2, ey2 = cfc.coordxtr(edof2, coord, dof2);" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "_b_ofF4l2EOW" }, "source": [ " Create and assemble element matrices" ] }, { "cell_type": "code", "metadata": { "id": "uL8CUlIM1NrM" }, "source": [ "for elx, ely, eltopo in zip(ex1, ey1, edof1):\n", " Ke = cfc.beam2e(elx, ely, ep1)\n", " cfc.assem(eltopo, K, Ke)" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "e7VVWmw42RZU" }, "source": [ "for elx, ely, eltopo in zip(ex2, ey2, edof2):\n", " Ke = cfc.bar2e(elx, ely, ep2)\n", " cfc.assem(eltopo,K,Ke)" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "F0hFDqb32scN" }, "source": [ "Solve equation system" ] }, { "cell_type": "code", "metadata": { "id": "-GdjFV6P2o7r" }, "source": [ "bc_prescr = np.array([1, 2, 3, 4, 5, 6])\n", "a, r = cfc.solveq(K, f, bc_prescr)" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "Axe1ELYJ272x" }, "source": [ "print(a)" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "wJ1U3vF-2-oA" }, "source": [ "" ], "execution_count": null, "outputs": [] } ] }