{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "vscode": {
     "languageId": "plaintext"
    }
   },
   "source": [
    "# Stress Strain Calculation of a Laminate\n",
    "\n",
    "This example presents the stress strain calculation of a Laminate using the CLT. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "from composipy import OrthotropicMaterial, LaminateProperty, LaminateStrength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Material\n",
    "E1 = 137.9e3\n",
    "E2 = 11.7e3\n",
    "v12 = 0.31\n",
    "G12 = 4.82e3\n",
    "t = 0.1524\n",
    "\n",
    "#Loads\n",
    "Nxx = 100\n",
    "Mxx = 20\n",
    "\n",
    "# Quasi laminate\n",
    "stacking = [45, -45, 90, 0]\n",
    "stacking += stacking[::-1]\n",
    "\n",
    "# Object definition\n",
    "material = OrthotropicMaterial(E1, E2, v12, G12, t)\n",
    "laminate = LaminateProperty(stacking, material)\n",
    "strength_analysis = LaminateStrength(laminate, Nxx=Nxx, Mxx=Mxx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating strains at the midplane $\\varepsilon_{0x}$, $\\varepsilon_{0y}$ and $\\gamma_{0xy}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.52630215e-03, -4.89003289e-04, -1.67758599e-20,  5.46178270e-03,\n",
       "       -2.99304212e-03, -6.90268796e-04])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "strength_analysis.epsilon0()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating strains ply by ply in analysis direction and material direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ply</th>\n",
       "      <th>position</th>\n",
       "      <th>angle</th>\n",
       "      <th>epsilonx</th>\n",
       "      <th>epsilony</th>\n",
       "      <th>gammaxy</th>\n",
       "      <th>epsilon1</th>\n",
       "      <th>epsilon2</th>\n",
       "      <th>gamma12</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>top</td>\n",
       "      <td>45</td>\n",
       "      <td>4.86e-03</td>\n",
       "      <td>-2.31e-03</td>\n",
       "      <td>-4.21e-04</td>\n",
       "      <td>1.06e-03</td>\n",
       "      <td>1.48e-03</td>\n",
       "      <td>-7.17e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>bot</td>\n",
       "      <td>45</td>\n",
       "      <td>4.02e-03</td>\n",
       "      <td>-1.86e-03</td>\n",
       "      <td>-3.16e-04</td>\n",
       "      <td>9.25e-04</td>\n",
       "      <td>1.24e-03</td>\n",
       "      <td>-5.88e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>top</td>\n",
       "      <td>-45</td>\n",
       "      <td>4.02e-03</td>\n",
       "      <td>-1.86e-03</td>\n",
       "      <td>-3.16e-04</td>\n",
       "      <td>1.24e-03</td>\n",
       "      <td>9.25e-04</td>\n",
       "      <td>5.88e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>bot</td>\n",
       "      <td>-45</td>\n",
       "      <td>3.19e-03</td>\n",
       "      <td>-1.40e-03</td>\n",
       "      <td>-2.10e-04</td>\n",
       "      <td>1.00e-03</td>\n",
       "      <td>7.90e-04</td>\n",
       "      <td>4.59e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>top</td>\n",
       "      <td>90</td>\n",
       "      <td>3.19e-03</td>\n",
       "      <td>-1.40e-03</td>\n",
       "      <td>-2.10e-04</td>\n",
       "      <td>-1.40e-03</td>\n",
       "      <td>3.19e-03</td>\n",
       "      <td>2.10e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3</td>\n",
       "      <td>bot</td>\n",
       "      <td>90</td>\n",
       "      <td>2.36e-03</td>\n",
       "      <td>-9.45e-04</td>\n",
       "      <td>-1.05e-04</td>\n",
       "      <td>-9.45e-04</td>\n",
       "      <td>2.36e-03</td>\n",
       "      <td>1.05e-04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ply position  angle  epsilonx  epsilony   gammaxy  epsilon1  epsilon2  \\\n",
       "0    1      top     45  4.86e-03 -2.31e-03 -4.21e-04  1.06e-03  1.48e-03   \n",
       "1    1      bot     45  4.02e-03 -1.86e-03 -3.16e-04  9.25e-04  1.24e-03   \n",
       "2    2      top    -45  4.02e-03 -1.86e-03 -3.16e-04  1.24e-03  9.25e-04   \n",
       "3    2      bot    -45  3.19e-03 -1.40e-03 -2.10e-04  1.00e-03  7.90e-04   \n",
       "4    3      top     90  3.19e-03 -1.40e-03 -2.10e-04 -1.40e-03  3.19e-03   \n",
       "5    3      bot     90  2.36e-03 -9.45e-04 -1.05e-04 -9.45e-04  2.36e-03   \n",
       "\n",
       "    gamma12  \n",
       "0 -7.17e-03  \n",
       "1 -5.88e-03  \n",
       "2  5.88e-03  \n",
       "3  4.59e-03  \n",
       "4  2.10e-04  \n",
       "5  1.05e-04  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_strain = strength_analysis.calculate_strain()\n",
    "df_strain.head(6) #display the first 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note\n",
    "The sequence of the DataFrame starts from the TOP OF THE LAYUP to the BOTTOM OF THE LAYUP, which is the reverse of the definition order.\n",
    "When defining the laminate, the first element of the list corresponds to the bottom-most layer. This is especially important for non-symmetric laminates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1dee71542e0>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_strain_top = df_strain[df_strain['position']=='top'] #filter the top position\n",
    "plt.grid()\n",
    "plt.xlabel('strain')\n",
    "plt.ylabel('ply number')\n",
    "plt.plot(df_strain_top['epsilonx'], df_strain_top['ply'], 'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating stresses ply by ply in analysis direction and material direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ply</th>\n",
       "      <th>position</th>\n",
       "      <th>angle</th>\n",
       "      <th>sigmax</th>\n",
       "      <th>sigmay</th>\n",
       "      <th>tauxy</th>\n",
       "      <th>sigma1</th>\n",
       "      <th>sigma2</th>\n",
       "      <th>tau12</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>top</td>\n",
       "      <td>45</td>\n",
       "      <td>121.68</td>\n",
       "      <td>52.57</td>\n",
       "      <td>65.77</td>\n",
       "      <td>152.89</td>\n",
       "      <td>21.36</td>\n",
       "      <td>-34.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>bot</td>\n",
       "      <td>45</td>\n",
       "      <td>103.94</td>\n",
       "      <td>47.25</td>\n",
       "      <td>57.58</td>\n",
       "      <td>133.17</td>\n",
       "      <td>18.02</td>\n",
       "      <td>-28.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>top</td>\n",
       "      <td>-45</td>\n",
       "      <td>124.02</td>\n",
       "      <td>67.33</td>\n",
       "      <td>-80.22</td>\n",
       "      <td>175.90</td>\n",
       "      <td>15.45</td>\n",
       "      <td>28.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>bot</td>\n",
       "      <td>-45</td>\n",
       "      <td>99.59</td>\n",
       "      <td>55.32</td>\n",
       "      <td>-64.48</td>\n",
       "      <td>141.93</td>\n",
       "      <td>12.97</td>\n",
       "      <td>22.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>top</td>\n",
       "      <td>90</td>\n",
       "      <td>32.52</td>\n",
       "      <td>-183.16</td>\n",
       "      <td>-1.01</td>\n",
       "      <td>-183.16</td>\n",
       "      <td>32.52</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3</td>\n",
       "      <td>bot</td>\n",
       "      <td>90</td>\n",
       "      <td>24.37</td>\n",
       "      <td>-122.78</td>\n",
       "      <td>-0.51</td>\n",
       "      <td>-122.78</td>\n",
       "      <td>24.37</td>\n",
       "      <td>0.51</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ply position  angle  sigmax  sigmay  tauxy  sigma1  sigma2  tau12\n",
       "0    1      top     45  121.68   52.57  65.77  152.89   21.36 -34.56\n",
       "1    1      bot     45  103.94   47.25  57.58  133.17   18.02 -28.35\n",
       "2    2      top    -45  124.02   67.33 -80.22  175.90   15.45  28.35\n",
       "3    2      bot    -45   99.59   55.32 -64.48  141.93   12.97  22.14\n",
       "4    3      top     90   32.52 -183.16  -1.01 -183.16   32.52   1.01\n",
       "5    3      bot     90   24.37 -122.78  -0.51 -122.78   24.37   0.51"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_stress = strength_analysis.calculate_stress()\n",
    "df_stress.head(6) #display the first 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note\n",
    "The sequence of the DataFrame starts from the TOP OF THE LAYUP to the BOTTOM OF THE LAYUP, which is the reverse of the definition order.\n",
    "When defining the laminate, the first element of the list corresponds to the bottom-most layer. This is especially important for non-symmetric laminates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1dee72b1790>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_stress_top = df_stress[df_stress['position']=='top'] #filter the top position\n",
    "plt.grid()\n",
    "plt.xlabel('stress MPa')\n",
    "plt.ylabel('ply number')\n",
    "plt.plot(df_stress_top['sigmax'], df_stress_top['ply'], 'k')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}