3_Platte.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Platte\n",
    "\n",
    "Dr. Zoufiné Lauer-Baré, FEM course"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Steifigkeit einer linear elastischen Platte mit Höhe $h$ und Breite $2a$ ist nach dem vereinfachten 2D Kirchhof-Love-Plattenmodell gebeben durch $$D=\\frac{Eh^3}{12(1-\\nu^2)}.$$\n",
    "\n",
    "Wobei $E,\\nu$ wie beim Zugstab Materialkonstanten sind; siehe z.B. [Timoshenko, Woinowski-Krieger, 2016]. Das folgende Bild zeigt ein 3D Volumen, einen \"Flachen Zylinder\", solche Geometrien können in der technischen Mechanik durch Platten-Modelle Approximiert werden."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table><tr>\n",
    "<td> <img src=\"FIGURES/platteRandbedingungen.PNG\" width=\"500\" height=\"500\"/> </td>\n",
    "</tr></table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wenn $f$ eine Flächenlast (\"Druck\") ist, die in der Platte wirkt, dann ist die Durchbiegung $w$ der Platte gegeben durch $$D\\Delta^2 w=f.$$\n",
    "\n",
    "Wobei $$\\Delta^2 w=\\frac{\\partial^4 w}{\\partial x^4}+2\\frac{\\partial^4 w}{\\partial x^2 \\partial y^2}+\\frac{\\partial^4 w}{\\partial x^4}.$$\n",
    "\n",
    "Am Rand $\\sqrt{x^2+y^2}=a$ sei $w=0$ d.h. die Platte fixiert (Ableitung verschwindet Rand und in der Mitte).  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Radialkoordinaten formuliert ergibt sich $$D\\frac{1}{r}\\frac{\\partial}{\\partial r}\\left(\\frac{1}{r}\\frac{\\partial}{\\partial r}\\left(\\frac{1}{r}\\frac{\\partial}{\\partial r}\\left(r\\frac{\\partial w}{\\partial r}\\right)\\right)\\right)=f$$\n",
    "Nach [Timoshenko, Woinowski-Krieger, 2016] ergibt sich dann die Verschiebung $$w(r)=\\frac{f}{64D}\\left(a^2-r^2\\right)^2.$$\n",
    "\n",
    "Daraus ergibt sich die maximale Verschiebung in der Mitte\n",
    "\n",
    "$$w_{max}=\\frac{fa^4}{64D}$$\n",
    "\n",
    "und die maximale Spannung ergibt sich am Rand durch $$\\sigma_{max}=\\frac{3}{4}\\frac{fa^2}{h^2},$$\n",
    "\n",
    "siehe [Timoshenko, Woinowski-Krieger, 2016]; siehe auch [Landau, Lifschitz, 1975]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Konkretes Beispiel\n",
    "\n",
    "$h=1 m$, $a=30 m$, $f=7850\\cdot h\\cdot9.8066\\frac{N}{m^2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0531968363915625"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# h=1 und 0.75 z.B., Bild fuer h=1 m\n",
    "\n",
    "emod = 200 #stahl\n",
    "nu = 0.3\n",
    "A = np.pi*(30.)**2\n",
    "hoehe = 1\n",
    "a = 30\n",
    "E = emod*10**9\n",
    "\n",
    "\n",
    "f = 7850*hoehe*9.8066\n",
    "\n",
    "D=(E*hoehe**3)/(12*(1-nu**2))\n",
    "\n",
    "\n",
    "\n",
    "wmax = (f*a**4)/(64*D)\n",
    "\n",
    "wmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "51.96272175"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmamax=(3/4.)*(f*(a**2))/(hoehe**2)\n",
    "\n",
    "sigmamax*10**(-6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.196272175"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmamax*10**(-7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.567510665625e-08"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(f)/(64*D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table><tr>\n",
    "<td> <img src=\"FIGURES/plate_analytical_uz_scaled_3.PNG\" width=\"400\" height=\"200\"/> </td>\n",
    "<td> <img src=\"FIGURES/platte_ansys_w_seitlich.PNG\" width=\"450\" height=\"300\"/> </td>\n",
    "</tr></table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Verschiebungen können gut approximiert werden. Das linke Bild oben zeigt die analytische Approximation $w(r)=\\frac{f}{64D}\\left(a^2-r^2\\right)^2$, mit Paraview in der 3D Geometrie dargestellt. Auch die maximale Spannung wird relativ gut approximiert und tritt wie analytisch vorhergesagt, am Rand auf. Die Unterschiede zwischen 3D FEM und analytischer Approximation können analog zum Zugstabbeispiel durch genauere analytische Approximationen reduziert werden. Der Aufwand für genauere Approximationen ist bei Platten jedoch höher, da im Gegensatz zu Biegebalken, Zugstab, Torsionsttab, die Platte analytisch in 2D ist. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from matplotlib import ticker\n",
    "import numpy as np\n",
    "from scipy import integrate\n",
    "from fem.funktionen import *\n",
    "import seaborn as sns\n",
    "#sns.set()\n",
    "mpl.rcParams[\"figure.figsize\"] = (20,7)\n",
    "mpl.rcParams['lines.linewidth'] = 5\n",
    "mpl.rcParams['lines.markersize'] = 15\n",
    "#sns.set()\n",
    "farben = sns.color_palette()\n",
    "plt.style.use('seaborn-darkgrid')\n",
    "farben = sns.color_palette()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$w(r)=\\\\frac{f}{64D}\\\\left(a^2-r^2\\\\right)^2$')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1440x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.linspace(-30, 30)\n",
    "ax=plt.axes()\n",
    "ax.tick_params(labelsize=15)\n",
    "ax.plot(r, -f/(64*D)*(a**2-r**2)**2, label = r'w analytisch', color=farben[0]),\n",
    "ax.tick_params(labelsize=15)\n",
    "ax.set_xlabel(xlabel='x in m',fontsize=15)\n",
    "ax.set_ylabel(ylabel='u in m',fontsize=15)\n",
    "plt.legend(loc='best',fontsize=15)\n",
    "ax.set_title(r\"$w(r)=\\frac{f}{64D}\\left(a^2-r^2\\right)^2$\", fontsize=25)"
   ]
  }
 ],
 "metadata": {
  "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}