diff --git a/docs/Example/Structural/Statics/thin-walled-section.ipynb b/docs/Example/Structural/Statics/thin-walled-section.ipynb index cc0e3a43a6..1cf7cfc869 100644 --- a/docs/Example/Structural/Statics/thin-walled-section.ipynb +++ b/docs/Example/Structural/Statics/thin-walled-section.ipynb @@ -93,16 +93,24 @@ }, { "cell_type": "code", - "execution_count": 137, + "execution_count": 25, "id": "dab5b9ac8c86f07e", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-09-26T13:37:14.535410900Z", - "start_time": "2023-09-26T13:37:14.215241400Z" + "end_time": "2023-09-27T01:51:36.305236200Z", + "start_time": "2023-09-27T01:51:35.914460Z" } }, "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + }, { "data": { "text/plain": "
", @@ -115,7 +123,7 @@ "data": { "text/plain": "" }, - "execution_count": 137, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } @@ -146,13 +154,13 @@ }, { "cell_type": "code", - "execution_count": 138, + "execution_count": 26, "id": "3f55a26243dcadae", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-09-26T13:37:14.551028200Z", - "start_time": "2023-09-26T13:37:14.535410900Z" + "end_time": "2023-09-27T01:51:36.320853800Z", + "start_time": "2023-09-27T01:51:36.305236200Z" } }, "outputs": [ @@ -187,13 +195,13 @@ }, { "cell_type": "code", - "execution_count": 139, + "execution_count": 27, "id": "bc9dbbcc42a1a8f8", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-09-26T13:37:14.660404100Z", - "start_time": "2023-09-26T13:37:14.551028200Z" + "end_time": "2023-09-27T01:51:36.461475900Z", + "start_time": "2023-09-27T01:51:36.320853800Z" } }, "outputs": [ @@ -227,13 +235,13 @@ }, { "cell_type": "code", - "execution_count": 140, + "execution_count": 28, "id": "6ee9cef09d277fc1", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-09-26T13:37:14.676029100Z", - "start_time": "2023-09-26T13:37:14.566685600Z" + "end_time": "2023-09-27T01:51:36.477103100Z", + "start_time": "2023-09-27T01:51:36.336476500Z" } }, "outputs": [ @@ -265,13 +273,13 @@ }, { "cell_type": "code", - "execution_count": 141, + "execution_count": 29, "id": "a39b669ef8c0eb57", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-09-26T13:37:15.481537500Z", - "start_time": "2023-09-26T13:37:14.582312Z" + "end_time": "2023-09-27T01:51:37.295912700Z", + "start_time": "2023-09-27T01:51:36.352107200Z" } }, "outputs": [ @@ -320,13 +328,13 @@ }, { "cell_type": "code", - "execution_count": 142, + "execution_count": 30, "id": "17e2210c33e9c4f0", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-09-26T13:37:15.497151700Z", - "start_time": "2023-09-26T13:37:15.481537500Z" + "end_time": "2023-09-27T01:51:37.311554400Z", + "start_time": "2023-09-27T01:51:37.295912700Z" } }, "outputs": [ @@ -376,13 +384,13 @@ }, { "cell_type": "code", - "execution_count": 143, + "execution_count": 31, "id": "11d3383864c87bee", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-09-26T13:37:15.544016700Z", - "start_time": "2023-09-26T13:37:15.497151700Z" + "end_time": "2023-09-27T01:51:37.374040300Z", + "start_time": "2023-09-27T01:51:37.311554400Z" } }, "outputs": [], @@ -462,13 +470,13 @@ }, { "cell_type": "code", - "execution_count": 144, + "execution_count": 32, "id": "5d93eaa7d593df9b", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-09-26T13:37:16.721571500Z", - "start_time": "2023-09-26T13:37:15.512801300Z" + "end_time": "2023-09-27T01:51:38.360980400Z", + "start_time": "2023-09-27T01:51:37.327168300Z" } }, "outputs": [], @@ -531,13 +539,13 @@ }, { "cell_type": "code", - "execution_count": 145, + "execution_count": 33, "id": "8972a1b23b6585ce", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-09-26T13:37:17.651864500Z", - "start_time": "2023-09-26T13:37:16.721571500Z" + "end_time": "2023-09-27T01:51:39.243347300Z", + "start_time": "2023-09-27T01:51:38.360980400Z" } }, "outputs": [ @@ -697,7 +705,7 @@ }, { "cell_type": "code", - "execution_count": 146, + "execution_count": 34, "outputs": [ { "name": "stdout", @@ -740,8 +748,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-09-26T13:37:17.792491500Z", - "start_time": "2023-09-26T13:37:17.651864500Z" + "end_time": "2023-09-27T01:51:39.368518Z", + "start_time": "2023-09-27T01:51:39.243347300Z" } }, "id": "3d6b5f8485c55665" @@ -753,15 +761,144 @@ "Due to the existence of bi-moments, the torque is not linearly proportional to the rotation.\n", "If one records the `BEAMS` output, the St. Venant torsion would be $$GJ\\phi'$$.\n", "\n", + "## Flat Bar Example\n", + "\n", + "We show another example with analytical solution.\n", + "This example is taken from this [paper](https://doi.org/10.1061/(ASCE)0733-9445(2005)131:7(1135))." + ], + "metadata": { + "collapsed": false + }, + "id": "595639805b88b538" + }, + { + "cell_type": "code", + "execution_count": 35, + "outputs": [ + { + "data": { + "text/plain": "
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3XLlyBdu2bYOnpyd69epV3Y+uSjt27EC/fv3g6emJ/v37w93dHXp6esLIE+fPn0f//v2F+mPHjsXevXsxefJknDlzBi4uLiguLsbdu3exd+9eHD9+HF26dHmvx7B27Vp0794dHTp0gI+PDywtLZGSkoJLly7hyZMnuHXrFgDA3t4eysrKWLJkCTIyMiCRSNC7d280a9asyn106tQJ7du3FxqPdO7cuc7iZx+OsnfqpFKpgiNhjV3ZNVZYWFj13f/3kGiyf6j79++Tj48PmZubk1gsJi0tLXJxcaE1a9bIdDWBCu7YEZXe+fDw8CBNTU2SSqXUq1cvmW4uiIh++OEHcnR0JF1dXVJXV6d27dpRSEgIFRQUEFHpXzq+vr7Url070tDQIB0dHXJycqK9e/dWeQwpKSkUGhpKbm5uZGxsTCoqKqSnp0e9e/emX3/9VW59X19fMjU1JVVVVTIyMqI+ffrQxo0bZerl5OTQvHnzyMLCQqj36aefynTtcvHiRXJwcCCxWFytDoqDg4OF7Zmamlbaue/bqnvHjqi0e5NVq1aRs7MzaWtrk4qKChkZGdHAgQNp586d5f6iLCgooCVLlpCtrS1JJBLS09MjBwcHCg4OpoyMjDo7BnnXkbw7dkSl/dSNGzeOjIyMSFVVlZo3b04DBw4s95lu2rSJLC0tSVlZWW4HxZVZunQpAaBFixZVWo81XLm5uRQTE1PuiQBjda0m15qIqIo3phljjNXY6tWr8fXXXyMxMVFuS2TW8OXl5eHBgwewsLD4IIZAZI1XTa417seOMcbqGBFhy5YtcHNz46SONTrh4eHQ1dVVdBisApzYMcZYHcnOzsauXbvw5Zdf4vbt2/j6668VHRJj5Xh7e0MkEkEkEkEsFqN169ZYuHAhioqKqrX+iBEjcP/+/Rrts2fPnpg5c+Y7RCvr6tWrcHFxgYaGBpo1a4ZPP/20WnEHBQUJx/zmdOrUqVrHVJXExESIRCJERUXV+74A7u6EMcbqzPPnzzF69Gjo6upi7ty5GDRokKJDYkyufv36ISwsDPn5+Thy5Ah8fX2hqqqKgICAKtdVV1evVd+jtTFixAi0bdsW165dQ0lJidz+Ritia2tbLpEr64i+MeE7dowxVkfMzc1BREhLS0NISIiiw2GsQhKJBEZGRjAzM8NXX30Fd3d3/Oc//wFQOlLLuHHjoKenB6lUiv79+8sM2fj2o9igoCDY29tj+/btMDc3h46ODkaOHCmMQOTt7S2M2FN2pywxMRFpaWkYM2YMDAwMoK6ujjZt2iAsLKzSuJWUlDB06FBYW1vD1tYWvr6+1R7FR0VFBUZGRjKTWCzG9u3b0aVLF2hpacHIyAijR48W+o0rc+fOHQwcOBDa2trQ0tJCjx49kJCQICzfvHkzrK2toaamhnbt2uFf//qXsKxslJpOnTpBJBKhZ8+eAICzZ8/C0dERGhoa0NXVhYuLS7lRdt5Fvd6xCwoKQnBwsEyZlZUV7t69W5+7ZYwxxt47+m9nsu/i8OHDOH/+PFxdXTFgwIAar1/bzpHV1dXx8uVLAKWJWFxcHP7zn/9AW1sbs2fPxv/93/8hJiamwk7VExISEBERgUOHDiEtLQ2fffYZQkNDERISgtWrV+P+/fto3749Fi5cCKC0E/oZM2YgJiYGR48eRdOmTREfHy8ztKM8gwcPxg8//IC+ffvC3Nz8nY/3TYWFhfj+++9hZWWF1NRU+Pn5wdvbWxjD+unTp3B1dUXPnj1x+vRpaGtr48KFC8Ij4J07d+K7777Dzz//jE6dOuHmzZvw8fGBhoYGvLy8cOXKFTg6OuLUqVOwtbWFWCxGUVERPD094ePjg127dqGgoABXrlypkw6u6/1R7Nu3PmsyPmZJSQmePXsGLS0t7s2bMcbYe0dEeP36NUxMTKCkVPlDrpycHGhqatZqf2vXrn2n9bKysqChoVHj9YgIkZGROH78OKZNmyYkdBcuXEC3bt0AlCYupqamiIiIwPDhw+Vup6SkBOHh4cKY0mPHjkVkZCRCQkKgo6MDsVgMqVQqjM8NAI8ePUKnTp3QpUsXAKgyUdu2bRvCw8Ph7+8PNzc3HD16FDY2NgCA5cuXIywsrNLhLG/fvi3z+djY2ODKlSv44osvhDJLS0v89NNP6Nq1K7KysqCpqYm1a9dCR0cHu3fvFhLbtm3bCusEBgZi+fLlGDp0KIDSO3QxMTHYsGEDvLy8hLGymzRpIhz/q1evkJGRgYEDB6JVq1YAIDPqTm3Ue2JXduuzOvLz85Gfny/MP336VPjQGGOMMUV5/PgxWrRooegw6syhQ4egqamJwsJClJSUYPTo0QgKCkJkZCRUVFTg5OQk1G3SpAmsrKwQGxtb4fbMzc2FpA4oHfrq7ceZb/vqq68wbNgw3LhxA3379oWnp6eQTL6tpKQEc+bMwffff48pU6bAwMAArq6uOHToED766CPcvn0bPXr0qHR/VlZWwuNmoPRxNABcv34dQUFBuHXrFtLS0oQxpR89egQbGxtERUWhR48ecu9WZmdnIyEhARMmTICPj49QXlRUBB0dnQpj0dfXh7e3Nzw8PPDxxx/D3d0dn332WfWGDKtCvSd2cXFxMDExgZqaGpydnbF48eIKm/8vXry43KNboPQHSltb+51j+Oijjyq9IBljjDVOHTt2xPnz5995/czMTJiamsokLRWRSqXIysqq8T4OHz6MESNGQFlZGcXFxdizZ0+NH8fWdPSLXr16Yd26dRCLxTAxManR0zR53k56RCKRkCBVpH///nj48CGOHDmCkydPok+fPvD19cWPP/5Yrm5qaiqSk5PRqVMnAMCECRPw+vVruLu7Y/Pmzdi/fz8iIyMr3V9ZC+A3ZWdnw8PDAx4eHti5cycMDAzw6NEjeHh4oKCgAAAqbShS9nlv2rRJJhkGUOUIEWFhYZg+fTqOHTuGPXv2YP78+Th58iQ++uijSterSr0mdk5OTggPD4eVlRWSkpIQHByMHj16IDo6Wu4PSUBAAPz8/IT5sh8obW3tWiV2AwYMkEns/P39ERgY+M7bY6yh2rBBBatXqyIlRYQOHUrw448F6NKl8i9fxhqSefPmYfXq1cL8gAEDavX7o0x1XgcSiUTv9Dj0s88+g5qaGs6ePYuePXu+l9bUGhoa5ZIcoPRxYFFRES5fvizcPXv58iXu3btXqydoYrEYxcXF5coNDAzg5eUFLy8v9OjRA/7+/nITOz09Pairq+P8+fNwdnYGAMycOROvX7/GqFGjMGjQIDg6OtY4rrt37+Lly5cIDQ2FqakpAODatWsydezs7LBt2zYUFhaWS2ANDQ1hYmKCv//+G2PGjKnw2AHIPf5OnTqhU6dOCAgIgLOzM3755ZcPO7F7c8xIOzs7ODk5wczMDHv37sWECRPK1ZdIJMKt0boUFBQkXCj+/v4y44wy9k+xZw8QEACsXw84OQGrVinD01Md9+4B1Rj+lLEGoexlfaD0+76htE4eNGjQB9E9Tps2bTB48GD4+Phgw4YN0NLSwpw5c9C8eXMMHjz4nbdrbm6Oy5cvIzExEZqamtDX10dQUBAcHBxga2uL/Px8HDp0qML3zCQSCWbMmIHg4GBIpVL069cPycnJiIqKgoaGBn7//Xfcu3cPVlZWNYqrZcuWEIvFWLNmDSZPnozo6Gh8//33MnWmTp2KNWvWYOTIkQgICICOjg7+/PNPODo6wsrKCsHBwZg+fTp0dHTQr18/5Ofn49q1a0hLS4Ofnx+aNWsGdXV1HDt2DC1atICamhpevXqFjRs3YtCgQTAxMcG9e/cQFxeHcePGvfM5LvNeuzvR1dVF27ZtER8f/z53K4Pv1LF/qhUrAB8fYPx4wMamNMGTSoGtWxUdGWP1g7/v301YWBgcHBwwcOBAODs7g4hw5MiRClvEVsc333wDZWVl2NjYCI87xWIxAgICYGdnB1dXVygrK2P37t0VbiMkJAQrV67Exo0bYWdnh9GjR8PU1BSJiYlwdHTEgAED8OLFixrFZWBggPDwcOzbtw82NjYIDQ0td8ewSZMmOH36NLKysuDm5gYHBwds2rRJOB8TJ07E5s2bERYWhg4dOsDNzQ3h4eFCNycqKir46aefsGHDBpiYmGDw4MGQSqW4e/cuhg0bhrZt22LSpEnw9fXFl19+WcMzW957HSs2KysLLVu2RFBQEKZPn15l/czMTOjo6CAjI6NWt9Kzs7OFljDv2nKIsYasoKA0ifv1V8DT83/lXl5Aejpw8KCiImOsbtX1931lv4d4rFj2vnwwY8V+8803OHfuHBITE3Hx4kUMGTIEysrKGDVqVH3uljH2lhcvgOJiwNBQttzQEEhOVkxMjDHG6l69vmP35MkTDBo0CJmZmQBKm/du2rRJ6NOFMVZ/4uJKH7MmJgJNmig6GsYYY+9Dvd6xGzJkCPLy8rB161bcuXMHw4YNw4QJE6rs24YxVjthYUC7dsCyZcDevcC6daXlu3bJ1ktJAarZzSRjjLEGoF4TuxUrVsDHxwfjx4+HjY0N1q9fD6lUiq38tjZj9SYuDpg4ESgpKX38WlJSOgHAmjVAWdulkhIgMhL4b88BjDHGGoF6S+wKCgpw/fp1uLu7/29nSkpwd3fHpUuX5K6Tn5+PzMxMmYkxVjNbtwKVdbk1cyYQGwt89RWQnV3aSpYxxljjUG+J3YsXL1BcXAzDt97WNjQ0RHIFb2svXrwYOjo6wlTWWSBjrPoSE4GK2rqLRMCZM4C9PRAVBRw7Vr5BBWOMsYbrvfZjV5WAgABkZGQI0+PHjxUdEmMNjrl5xXfslJSA6dOB/Hzg8uXSjooZY4w1HvWW2DVt2hTKyspISUmRKU9JSYFRBW9rSyQSYfiw2g4jxtg/1RdfVHzHjgiQM+gLY4yxRqLeEjuxWAwHBweZQXlLSkoQGRkpjPPGGKt7bdoAW7aU3p1TVpb9d8sWQM7wkIwxxhqJeu3Hzs/PD15eXujSpQscHR2xatUqZGdnYzy/rc1YvfL2Brp3L03kEhNLH89OmMBJHWOs4Tp79ix69eqFtLQ06Orq1ss+vL29kZ6ejoiIiHrZ/vtQr4ndiBEj8Pz5c3z33XdITk6Gvb09jh07Vq5BBWOs7rVuDSxerOgoGGNVebMzcXPz0tcp2rSp330mJycjJCQEhw8fxtOnT9GsWTPY29tj5syZ6NOnT53tp2fPnrC3t8eqVavqbJuVMTc3x8OHDwEAUqkUVlZWCAgIwPDhw6u1/urVq1HTkVZFIhEOHDgAzzfHa1Sgekvs3jy5ZYYMGQInflubMcYYA1DamfjEiaUNnohK/126tPRuu7d3/ewzMTERLi4u0NXVxbJly9ChQwcUFhbi+PHj8PX1xd27d+tnxxUgIhQXF0NFpW5SkoULF8LHxweZmZlYvnw5RowYgebNm6Nbt25Vrqujo1MnMShSvd6xKzu5ZbS0tOpzdxV6M/ueN28eQkJCFBIHY4yx+pWdnS38PygoCMuWLVNgNJV7szPxt02YUPo6RX28PjFlyhSIRCJcuXIFGhoaQrmtrS2++OILYf7Ro0eYNm0aIiMjoaSkhH79+mHNmjXCU7egoCBERERg1qxZWLBgAdLS0tC/f39s2rQJWlpa8Pb2xrlz53Du3DmsXr0aAPDgwQMkJiaiV69eOHLkCObPn4/bt2/jxIkTcHZ2hr+/P3bv3o3MzEx06dIFK1euRNeuXWt0fFpaWjAyMoKRkRHWrl2LHTt24P/9v/+Hbt264fbt25gxYwYuXboEqVSKYcOGYcWKFdDU1ARQ/lFsz549YWdnBzU1NWzevBlisRiTJ09GUFAQgNKbWEDpjSsAMDMzQ2JiIm7duoWZM2fi2rVrEIlEaNOmDTZs2IAuXbrU+POqMaonZmZmtHLlyhqtk5eXRxkZGcL0+PFjAkAZGRm1imXGjBkEgCeeeOKJp3/YNHfu3Fr9/sjIyCBA/u+h3NxciomJodzc3Hfa9pw5RMrKRED5SVm5dHlde/nyJYlEIlq0aFGl9YqLi8ne3p66d+9O165doz///JMcHBzIzc1NqBMYGEiampo0dOhQun37Np0/f56MjIyEc56enk7Ozs7k4+NDSUlJlJSUREVFRXTmzBkCQHZ2dnTixAmKj4+nly9f0vTp08nExISOHDlCd+7cIS8vL9LT06OXL18SEQnrpaWlVRi3vNxDR0eH/Pz8KCsri4yNjYV4IyMjycLCgry8vIS6Xl5eNHjwYGHezc2NtLW1KSgoiO7fv0/btm0jkUhEJ06cICKi1NRUAkBhYWGUlJREqampRERka2tLn3/+OcXGxtL9+/dp7969FBUVVcWnU7GaXGv1mtgZGhqSvr4+2dvb09KlS6mwsLDSdQIDA+X+YD5+/Fgm4avpZG1trfAvF5544oknnt7/1LFjx1r9/ii7wZCenl7ud1ZtE7uRI4mUlOQndkpKpcvr2uXLlwkA/fbbb5XWO3HiBCkrK9OjR4+Esjt37hAAunLlChGV/s6WSqWUmZkp1PH39ycnJydh3s3NjWbMmCGz7bIELSIiQijLysoiVVVV2rlzp1BWUFBAJiYmtHTpUpn1qpvY5efn06JFiwgAHTp0iDZu3Eh6enqUlZUl1D98+DApKSlRcnIyEclP7Lp37y6zj65du9Ls2bOFeQB04MABmTpaWloUHh5eYZw1VZNrrd4exU6fPh2dO3eGvr4+Ll68iICAACQlJWHFihUVrhMQEAA/Pz9h/unTp7CxseERKBhjjL2TW7du1cl7U69fv67z968q60xcJCpdXteomg0DYmNjYWpqKvP718bGBrq6uoiNjRUej5qbm8u8ZmVsbIzU1NRq7ePNx5IJCQkoLCyEi4uLUKaqqgpHR0fExsZWa3tlZs+ejfnz5yMvLw+ampoIDQ3FgAED4Ofnh44dO8o8fnZxcUFJSQnu3btXYcNOOzs7mfnqHKOfnx8mTpyI7du3w93dHcOHD0erVq1qdBzvqkaJ3Zw5c7BkyZJK68TGxqJdu3YyCZqdnR3EYjG+/PJLLF68GBKJRO66EolEZpmmpiYeP34MLS0tiCob/LIaMjMzYWpqisePHzfIjo8bcvwcu+I05PgbcuxAw46/IccO1G38RITXr1/DxMSkjqL7ny++KG0oIX+/9dOZeJs2bSASieqsgYSqqqrMvEgkQom8lwbleDPBqkv+/v7w9vaGpqYmDA0Na50/vMsxBgUFYfTo0Th8+DCOHj2KwMBA7N69W3gXrz7VKLGbNWsWvKtopmNpaSm33MnJCUVFRUhMTISVlVW19qekpIQWLVrUJMQqNfQRLRpy/By74jTk+Bty7EDDjr8hxw7UXfz11VKyrDPxCRNkW8US1V9n4vr6+vDw8MDatWsxffr0cslVeno6dHV1YW1tjcePH+Px48fCXbuYmBikp6fDxsam2vsTi8UoLi6usl6rVq0gFotx4cIFmJmZAQAKCwtx9epVzJw5s/oHiNKRr1rLOXnW1tYIDw9Hdna2cNwXLlyAkpJStfMSeVRVVeUeY9u2bdG2bVt8/fXXGDVqFMLCwj68xM7AwAAGBgbvtKOoqCgoKSmhWbNm77Q+Y4wx1tgoojPxtWvXwsXFBY6Ojli4cCHs7OxQVFSEkydPYt26dYiNjYW7uzs6dOiAMWPGYNWqVSgqKsKUKVPg5uZWo5ad5ubmuHz5MhITE6GpqQl9fX259TQ0NPDVV1/B398f+vr6aNmyJZYuXYqcnBxMqKNbl2PGjEFgYCC8vLwQFBSE58+fY9q0aRg7dmyt+tc1NzdHZGQkXFxcIJFIoKamBn9/f3z66aewsLDAkydPcPXqVQwbNqxOjqMq9fKO3aVLl3D58mX06tULWlpauHTpEr7++mt8/vnn0NPTq49dMsYYYw3S++5M3NLSEjdu3EBISAhmzZqFpKQkGBgYwMHBAevWrQNQ+rjx4MGDmDZtGlxdXWW6O6mJb775Bl5eXrCxsUFubi4ePHhQYd3Q0FCUlJRg7NixeP36Nbp06YLjx4/XWd4glUpx/PhxzJgxA127dpXp7qQ2li9fDj8/P2zatAnNmzfH/fv38fLlS4wbNw4pKSlo2rQphg4diuDg4Do5jirVWZONN1y/fp2cnJxIR0eH1NTUyNramhYtWkR5eXn1sbtqycvLo8DAQIXGUBsNOX6OXXEacvwNOXaihh1/Q46d6P3FX9tWsYxVV02uNRFRDcfOYIwxxhjy8vLw4MEDWFhYQE1NTdHhsEasJtea0nuKiTHGGGOM1TNO7BhjjDHGGglO7BhjjDHGGglO7BhjjLFa4FfVWX2ryTXGiR1jjDH2DspGJMjJyVFwJKyxK7vG3h4FQ55GmdiFhISgW7dukEql0NXVlVvn0aNHGDBgAKRSKZo1awZ/f38UFRXJ1Dl79iw6d+4MiUSC1q1bIzw8vP6Df2v/IpFI7nT16lUAQGJiotzlf/7553uNtSLm5ublYgsNDZWp89dff6FHjx5QU1ODqakpllY0xs57lJiYiAkTJsDCwgLq6upo1aoVAgMDUVBQIFPnQz73a9euhbm5OdTU1ODk5IQrV64oOiS5Fi9ejK5du0JLSwvNmjWDp6cn7t27J1OnZ8+e5c7z5MmTFRTx/wQFBZWLq127dsLyvLw8+Pr6okmTJtDU1MSwYcOQkpKiwIhlyfv5FIlE8PX1BfBhnffz58/jk08+gYmJCUQiESIiImSWExG+++47GBsbQ11dHe7u7oiLi5Op8+rVK4wZMwba2trQ1dXFhAkTkJWV9c4xKSsrQ1dXF6mpqXj58iVyc3ORl5fHE091NuXm5uLly5dITU2Frq4ulJWVq7wu66WDYkUrKCjA8OHD4ezsjC1btpRbXlxcjAEDBsDIyAgXL15EUlISxo0bB1VVVSxatAgA8ODBAwwYMACTJ0/Gzp07ERkZiYkTJ8LY2BgeHh7v5Ti6deuGpKQkmbIFCxYgMjKyXM/fp06dgq2trTDfpEmT9xJjdSxcuBA+Pj7C/JsDRmdmZqJv375wd3fH+vXrcfv2bXzxxRfQ1dXFpEmTFBEuAODu3bsoKSnBhg0b0Lp1a0RHR8PHxwfZ2dn48ccfZep+iOd+z5498PPzw/r16+Hk5IRVq1bBw8MD9+7d++BGfzl37hx8fX3RtWtXFBUVYe7cuejbty9iYmJkhjvy8fHBwoULhXmpVKqIcMuxtbXFqVOnhHkVlf99rX799dc4fPgw9u3bBx0dHUydOhVDhw7FhQsXFBFqOVevXpUZCik6Ohoff/wxhg8fLpR9KOc9OzsbHTt2xBdffIGhQ4eWW7506VL89NNP2LZtGywsLLBgwQJ4eHggJiZG6B5izJgxSEpKwsmTJ1FYWIjx48dj0qRJ+OWXX945LiMjIwCo9sD3jL0LXV1d4VqrUv12qadYYWFhpKOjU678yJEjpKSkRMnJyULZunXrSFtbm/Lz84mI6NtvvyVbW1uZ9UaMGEEeHh71GnNlCgoKyMDAgBYuXCiUPXjwgADQzZs3FRZXZczMzGjlypUVLv/Xv/5Fenp6wnknIpo9ezZZWVm9h+hqZunSpWRhYSHMf8jn3tHRkXx9fYX54uJiMjExocWLFyswqupJTU0lAHTu3DmhzM3NjWbMmKG4oCoQGBhIHTt2lLssPT2dVFVVad++fUJZbGwsAaBLly69pwhrZsaMGdSqVSsqKSkhog/3vAOgAwcOCPMlJSVkZGREy5YtE8rS09NJIpHQrl27iIgoJiaGANDVq1eFOkePHiWRSERPnz6tdUxFRUWUm5vLE091PhUVFdXoWvxHJnYLFiwo92X8999/EwC6ceMGERH16NGj3Bfa1q1bSVtbu56irdqvv/5KSkpK9PjxY6GsLLkwNTUlAwMDcnFxoYMHDyosxreZmZmRoaEh6evrk729PS1dupQKCwuF5WPHjqXBgwfLrHP69GkCQK9evXrP0VZu3rx55ODgIMx/qOc+Pz+flJWVZX7xERGNGzeOBg0apJigaiAuLo4A0O3bt4UyNzc3atq0KTVp0oRsbW1pzpw5lJ2drcAoSwUGBpJUKiVjY2OysLCg0aNH08OHD4mIKDIykgBQWlqazDotW7akFStWKCDayuXn51OTJk0oJCREKPtQz/vbiV1CQoLcP7JcXV1p+vTpRES0ZcsW0tXVlVleWFhIysrK9Ntvv9V3yIy9N43yUWxVkpOTyw34WzafnJxcaZ3MzEzk5uZCXV39/QT7hi1btsDDwwMtWrQQyjQ1NbF8+XK4uLhASUkJ+/fvh6enJyIiIjBo0KD3HuPbpk+fjs6dO0NfXx8XL15EQEAAkpKShLH5kpOTYWFhIbPOm5/FhzK2cHx8PNasWSPzGPZDPfcvXrxAcXGx3Ov37t27CoqqekpKSjBz5ky4uLigffv2Qvno0aNhZmYGExMT/PXXX5g9ezbu3buH3377TYHRAk5OTggPD4eVlRWSkpIQHByMHj16IDo6GsnJyRCLxeXe8zU0NBS+Zz4kERERSE9Ph7e3t1D2oZ73t5WdT3nX/Jvf6W+/hqCiogJ9ff0P8vNg7F01mMRuzpw5WLJkSaV1YmNjZV5c/lC9y7E8efIEx48fx969e2XqNW3aFH5+fsJ8165d8ezZMyxbtqzekouaxP9mbHZ2dhCLxfjyyy+xePFiSCSSeomvMu9y7p8+fYp+/fph+PDhMu8KKuLcN3a+vr6Ijo7GH3/8IVP+5vuWHTp0gLGxMfr06YOEhAS0atXqfYcp6N+/v/B/Ozs7ODk5wczMDHv37lXIH3+1sWXLFvTv3x8mJiZC2Yd63hljFWswid2sWbNk/pKUx9LSslrbMjIyKtdCsKylWtnLiUZGRuVar6WkpEBbW7vWX9jvcixhYWFo0qRJtRIGJycnnDx5sjYhVqo2n4WTkxOKioqQmJgIKyurCs8zgOq/KFoDNY392bNn6NWrF7p164aNGzdWuf36PvfV0bRpUygrK8s9r/VxTuvK1KlTcejQIZw/f17mrrQ8Tk5OAErvpH5ICYauri7atm2L+Ph4fPzxxygoKEB6errMXbsP8XN4+PAhTp06VeWduA/1vJedz5SUFBgbGwvlKSkpsLe3F+q83cChqKgIr169+uA+D8Zqo8EkdgYGBjAwMKiTbTk7OyMkJASpqanCrfmTJ09CW1sbNjY2Qp0jR47IrHfy5Ek4OzvXev81PRYiQlhYmNBytypRUVEyX251rTafRVRUFJSUlITz7uzsjHnz5qGwsFA4tpMnT8LKyqpeHsPWJPanT5+iV69ecHBwQFhYGJSUqu4dqL7PfXWIxWI4ODggMjISnp6eAEofcUZGRmLq1KkKjU0eIsK0adNw4MABnD17ttyjeXmioqIAQOHn+m1ZWVlISEjA2LFj4eDgAFVVVURGRmLYsGEAgHv37uHRo0d18j1Sl8LCwtCsWTMMGDCg0nof6nm3sLCAkZERIiMjhUQuMzMTly9fxldffQWg9LsmPT0d169fh4ODAwDg9OnTKCkpERJWxhoFRb/kVx8ePnxIN2/epODgYNLU1KSbN2/SzZs36fXr10RU2nqpffv21LdvX4qKiqJjx46RgYEBBQQECNv4+++/SSqVkr+/P8XGxtLatWtJWVmZjh079t6P59SpUwSAYmNjyy0LDw+nX375hWJjYyk2NpZCQkJISUmJtm7d+t7jfNvFixdp5cqVFBUVRQkJCbRjxw4yMDCgcePGCXXS09PJ0NCQxo4dS9HR0bR7926SSqW0YcMGBUZO9OTJE2rdujX16dOHnjx5QklJScJU5kM+97t37yaJRELh4eEUExNDkyZNIl1dXZmW4B+Kr776inR0dOjs2bMy5zknJ4eIiOLj42nhwoV07do1evDgAR08eJAsLS3J1dVVwZETzZo1i86ePUsPHjygCxcukLu7OzVt2pRSU1OJiGjy5MnUsmVLOn36NF27do2cnZ3J2dlZwVHLKi4uppYtW9Ls2bNlyj+08/769WvhuxwArVixgm7evCk0VgkNDSVdXV06ePAg/fXXXzR48GCysLCg3NxcYRv9+vWjTp060eXLl+mPP/6gNm3a0KhRoxRyPIzVl0aZ2Hl5eRGActOZM2eEOomJidS/f39SV1enpk2b0qxZs2RaaxIRnTlzhuzt7UksFpOlpSWFhYW93wP5r1GjRlG3bt3kLgsPDydra2uSSqWkra1Njo6OMt0rKNL169fJycmJdHR0SE1NjaytrWnRokWUl5cnU+/WrVvUvXt3kkgk1Lx5cwoNDVVQxP8TFhYm9xp682+hD/ncExGtWbOGWrZsSWKxmBwdHenPP/9UdEhyVXSey37eHj16RK6urqSvr08SiYRat25N/v7+lJGRodjAqbQLJGNjYxKLxdS8eXMaMWIExcfHC8tzc3NpypQppKenR1KplIYMGSLzx8GH4Pjx4wSA7t27J1P+oZ33M2fOyL1OvLy8iKi0y5MFCxaQoaEhSSQS6tOnT7ljevnyJY0aNYo0NTVJW1ubxo8fL/zBz1hjISLiQe4YY4wxxhqDRjmkGGOMMcbYPxEndowxxhhjjQQndowxxhhjjQQndowxxhhjjQQndowxxhhjjQQndowxxhhjjQQndowxxhhjjQQndowxxhhjjQQndowxxhhjjQQndowxxhhjjQQndowxxhhjjcT/B1aMhcFPrjVzAAAAAElFTkSuQmCC" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "b = 200\n", + "d = 10\n", + "\n", + "points = [\n", + " [-b / 2, -d / 2],\n", + " [b / 2, -d / 2],\n", + " [b / 2, d / 2],\n", + " [-b / 2, d / 2],\n", + "]\n", + "\n", + "facets = [\n", + " [0, 1],\n", + " [1, 2],\n", + " [2, 3],\n", + " [3, 0]\n", + "]\n", + "\n", + "holes = []\n", + "control_points = [[0, 0]]\n", + "geometry = Geometry.from_points(points, facets, control_points)\n", + "geometry.create_mesh(mesh_sizes=[2])\n", + "geometry.plot_geometry()\n", + "to_file(to_cell3dos(geometry), \"flat.sp\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-09-27T01:51:41.071158400Z", + "start_time": "2023-09-27T01:51:39.399583600Z" + } + }, + "id": "23400ded8d28bd56" + }, + { + "cell_type": "markdown", + "source": [ + "Use the following model to apply an end twist.\n", + "\n", + "```text\n", + "# flat bar\n", + "node 1 0 0 0\n", + "node 2 1000 0 0\n", + "material ElasticOS 1 200 .25\n", + "file flat.sp\n", + "orientation B3DOSL 1 0. 0. 1.\n", + "element B31OS 1 1 2 1574 1 6\n", + "fix2 1 E 1\n", + "displacement 1 0 1.4 4 2\n", + "hdf5recorder 1 Node RF4 2\n", + "step static 1\n", + "set ini_step_size 1E-2\n", + "set fixed_step_size true\n", + "converger RelIncreDisp 1 1E-10 5 1\n", + "analyze\n", + "save recorder 1\n", + "exit\n", + "```\n", + "\n", + "Use the following script to plot the results." + ], + "metadata": { + "collapsed": false + }, + "id": "1f6e7db7e19b740" + }, + { + "cell_type": "code", + "execution_count": 36, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with h5py.File('R1-RF4.h5', 'r') as f:\n", + " data = f['/R1-RF4/R1-RF42']\n", + " x = data[:, 0] * 1.4\n", + " plt.plot(x, data[:, 1] / 1000, label='B31OS')\n", + " ref = [z * .080 * 66.667 + .100 * 17.778 * z ** 3 for z in x]\n", + " plt.plot(x, ref, label='theoretical')\n", + " plt.legend()\n", + " plt.xlabel('rotation (rad)')\n", + " plt.ylabel('torque (kNm)')\n", + " plt.tight_layout(pad=.2)\n", + " plt.show()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-09-27T01:51:41.211981300Z", + "start_time": "2023-09-27T01:51:41.071158400Z" + } + }, + "id": "60cd4dd159b84495" + }, + { + "cell_type": "markdown", + "source": [ + "The discretisation introduces some errors. With mesh refinement, the numerical result approaches the analytical solution.\n", + "\n", "## Closing Remarks\n", "\n", "1. `Cell3DOS` is the basic building block. `Fibre3DOS` collects all cells and defines the section. `B31OS` is the corresponding element.\n", - "2. Sectional integration is always about the origin of the local coordinate system. Shifting of axis can be accounted for by directly defining the section in the shifted position.\n" + "2. Sectional integration is always about the origin of the local coordinate system. Shifting of axis can be accounted for by directly defining the section in the shifted position." ], "metadata": { "collapsed": false }, - "id": "595639805b88b538" + "id": "59ab091899487f1e" } ], "metadata": { diff --git a/docs/Example/Structural/Statics/thin-walled-section.md b/docs/Example/Structural/Statics/thin-walled-section.md index 09c49f69c6..86226a1d41 100644 --- a/docs/Example/Structural/Statics/thin-walled-section.md +++ b/docs/Example/Structural/Statics/thin-walled-section.md @@ -85,6 +85,12 @@ section.plot_mesh(title="Circular Section Mesh") + +![png](thin-walled-section_files/thin-walled-section_3_1.png) + + + + @@ -484,8 +490,92 @@ We shall see the initial stiffness is $$74.93$$, which is close to the torsional Due to the existence of bi-moments, the torque is not linearly proportional to the rotation. If one records the `BEAMS` output, the St. Venant torsion would be $$GJ\phi'$$. +## Flat Bar Example + +We show another example with analytical solution. +This example is taken from this [paper](https://doi.org/10.1061/(ASCE)0733-9445(2005)131:7(1135)). + + +```python +b = 200 +d = 10 + +points = [ + [-b / 2, -d / 2], + [b / 2, -d / 2], + [b / 2, d / 2], + [-b / 2, d / 2], +] + +facets = [ + [0, 1], + [1, 2], + [2, 3], + [3, 0] +] + +holes = [] +control_points = [[0, 0]] +geometry = Geometry.from_points(points, facets, control_points) +geometry.create_mesh(mesh_sizes=[2]) +geometry.plot_geometry() +to_file(to_cell3dos(geometry), "flat.sp") +``` + + + +![png](thin-walled-section_files/thin-walled-section_25_0.png) + + + +Use the following model to apply an end twist. + +```text +# flat bar +node 1 0 0 0 +node 2 1000 0 0 +material ElasticOS 1 200 .25 +file flat.sp +orientation B3DOSL 1 0. 0. 1. +element B31OS 1 1 2 1574 1 6 +fix2 1 E 1 +displacement 1 0 1.4 4 2 +hdf5recorder 1 Node RF4 2 +step static 1 +set ini_step_size 1E-2 +set fixed_step_size true +converger RelIncreDisp 1 1E-10 5 1 +analyze +save recorder 1 +exit +``` + +Use the following script to plot the results. + + +```python +with h5py.File('R1-RF4.h5', 'r') as f: + data = f['/R1-RF4/R1-RF42'] + x = data[:, 0] * 1.4 + plt.plot(x, data[:, 1] / 1000, label='B31OS') + ref = [z * .080 * 66.667 + .100 * 17.778 * z ** 3 for z in x] + plt.plot(x, ref, label='theoretical') + plt.legend() + plt.xlabel('rotation (rad)') + plt.ylabel('torque (kNm)') + plt.tight_layout(pad=.2) + plt.show() +``` + + + +![png](thin-walled-section_files/thin-walled-section_27_0.png) + + + +The discretisation introduces some errors. With mesh refinement, the numerical result approaches the analytical solution. + ## Closing Remarks 1. `Cell3DOS` is the basic building block. `Fibre3DOS` collects all cells and defines the section. `B31OS` is the corresponding element. 2. Sectional integration is always about the origin of the local coordinate system. Shifting of axis can be accounted for by directly defining the section in the shifted position. - diff --git a/docs/Example/Structural/Statics/thin-walled-section.zip b/docs/Example/Structural/Statics/thin-walled-section.zip index 70ab0a9dc2..ae7f6666b6 100644 Binary files a/docs/Example/Structural/Statics/thin-walled-section.zip and b/docs/Example/Structural/Statics/thin-walled-section.zip differ diff --git a/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_25_0.png b/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_25_0.png new file mode 100644 index 0000000000..9a5d0744cd Binary files /dev/null and b/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_25_0.png differ diff --git a/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_27_0.png b/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_27_0.png new file mode 100644 index 0000000000..97eb12a282 Binary files /dev/null and b/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_27_0.png differ diff --git a/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_3_0.png b/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_3_0.png index e682602f3b..055974129d 100644 Binary files a/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_3_0.png and b/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_3_0.png differ diff --git a/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_3_1.png b/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_3_1.png new file mode 100644 index 0000000000..e682602f3b Binary files /dev/null and b/docs/Example/Structural/Statics/thin-walled-section_files/thin-walled-section_3_1.png differ