docs/nusa-info/es/beam-element.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Elemento `Beam`\n",
    "\n",
    "## Fundamento teórico\n",
    "\n",
    "El elemento `Beam` (viga) es un elemento finito bidimensional donde las coordenadas locales y globales coinciden. Está caracterizado por una función de forma lineal. El elemento `Beam` tiene un modulo de elasticidad *E*, momento de inercia *I* y longitud *L*. Cada elemento `Beam` tiene dos nodos y se asume horizontal como se muestra en la figura. En este caso la matriz de rigidez del elemento está dada por la matriz siguiente, asumiendo que la deformación axial es despreciable:\n",
    "\n",
    "$$\n",
    "k = \\frac{EI}{L^3}\n",
    "\\begin{bmatrix}\n",
    "12 & 6L & -12 & 6L \\\\\n",
    "6L & 4L^2 & -6L & 2L^2 \\\\\n",
    "-12 & -6L & 12 & -6L \\\\\n",
    "6L & 2L^2 & -6L & 4L^2 \n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "<img src=\"src/beam-element/beam_element.PNG\" width=\"200px\"> </img>\n",
    "\n",
    "Está claro que el elemento `Beam` tiene cuatro grados de libertad, dos en cada nodo: un desplazamiento transversal y una rotación. La convención de signos utilizada es la tradicional: los desplazamientos son positivos hacia arriba y las rotaciones cuando son antihorario."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplos resueltos\n",
    "\n",
    "**Ejemplo 1**. Viga en voladizo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1.1)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from nusa import *\n",
    "import itertools\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def pairwise(iterable):\n",
    "    #~ \"s -> (s0,s1), (s1,s2), (s2, s3), ...\"\n",
    "    a, b = itertools.tee(iterable)\n",
    "    next(b, None)\n",
    "    return zip(a, b)\n",
    "\n",
    "# Input data \n",
    "E = 210e9 # Pa\n",
    "I = 1e-5\n",
    "L = 1\n",
    "P = 10e3\n",
    "\n",
    "nelm = 10\n",
    "parts = np.linspace(0,L,nelm)\n",
    "\n",
    "nodos = []\n",
    "for xc in parts:\n",
    "    cn = Node((xc,0))\n",
    "    nodos.append(cn)\n",
    "\n",
    "elementos = []\n",
    "for x in pairwise(nodos):\n",
    "    ni,nj = x[0], x[1]\n",
    "    ce = Beam((ni,nj),E,I)\n",
    "    elementos.append(ce)\n",
    "\n",
    "m = BeamModel()\n",
    "\n",
    "for n in nodos: m.add_node(n)\n",
    "for e in elementos: m.add_element(e)\n",
    "\n",
    "m.add_constraint(nodos[0], ux=0, uy=0, ur=0)\n",
    "m.add_force(nodos[-1], (-P,))\n",
    "m.plot_model()\n",
    "m.solve()\n",
    "m.plot_disp(1)\n",
    "xx = np.linspace(0,L)\n",
    "d = ((-P*xx**2.0)/(6.0*E*I))*(3*L - xx)\n",
    "plt.plot(xx,d)\n",
    "plt.axis(\"auto\")\n",
    "plt.xlim(0,1.1*L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ejemplo 2**. Determine los desplazamientos nodales y rotaciones, fuerzas nodales globales, y fuerzas en elementos para la viga mostrada en la figura. Se ha discretizado la viga como se indica en la numeración nodal. La viga está fija en los nodos 1 y 5, y tiene un soporte de rodillo en el nodo 3. Las cargas verticales de 10 000 lb cada una son aplicadas en los nodos 2 y 4. Sea E=300x10<sup>6</sup> psi and I=500 in<sup>4</sup>.\n",
    "\n",
    "<img src=\"src/beam-element/logan_E42.PNG\" width=\"400px\"> </img>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Desplazamientos nodales y rotaciones\n",
      "UY \t UR\n",
      "0 \t 0\n",
      "-0.048 \t 1.665334536937735e-20\n",
      "0 \t -6.66133814775094e-20\n",
      "-0.04800000000000001 \t 1.665334536937735e-20\n",
      "0 \t 0\n",
      "\n",
      "Fuerzas nodales globales\n",
      "FY \t M\n",
      "5000.0 \t 299999.99999999994\n",
      "-10000.0 \t 0.0\n",
      "10000.0 \t -1.9828229724794254e-11\n",
      "-10000.0 \t 0.0\n",
      "5000.0 \t -300000.0\n",
      "\n",
      "Fuerzas en elementos\n",
      "\n",
      "FY:\n",
      "[[ 5000.]\n",
      " [-5000.]] \n",
      " M:\n",
      "[[300000.]\n",
      " [300000.]]\n",
      "\n",
      "\n",
      "FY:\n",
      "[[-5000.]\n",
      " [ 5000.]] \n",
      " M:\n",
      "[[-300000.]\n",
      " [-300000.]]\n",
      "\n",
      "\n",
      "FY:\n",
      "[[ 5000.]\n",
      " [-5000.]] \n",
      " M:\n",
      "[[300000.]\n",
      " [300000.]]\n",
      "\n",
      "\n",
      "FY:\n",
      "[[-5000.]\n",
      " [ 5000.]] \n",
      " M:\n",
      "[[-300000.]\n",
      " [-300000.]]\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Logan, D. (2007). A first course in the finite element analysis.\n",
    "Example 4.2 , pp. 166.\n",
    "\"\"\"\n",
    "from nusa.core import *\n",
    "from nusa.model import *\n",
    "from nusa.element import *\n",
    "\n",
    "# Input data \n",
    "E = 30e6\n",
    "I = 500.0\n",
    "P = 10e3\n",
    "L = 10*(12.0)  # ft -> in\n",
    "# Model\n",
    "m1 = BeamModel(\"Beam Model\")\n",
    "# Nodes\n",
    "n1 = Node((0,0))\n",
    "n2 = Node((10*12,0))\n",
    "n3 = Node((20*12,0))\n",
    "n4 = Node((30*12,0))\n",
    "n5 = Node((40*12,0))\n",
    "# Elements\n",
    "e1 = Beam((n1,n2),E,I)\n",
    "e2 = Beam((n2,n3),E,I)\n",
    "e3 = Beam((n3,n4),E,I)\n",
    "e4 = Beam((n4,n5),E,I)\n",
    "\n",
    "# Add elements \n",
    "for nd in (n1,n2,n3,n4,n5): m1.add_node(nd)\n",
    "for el in (e1,e2,e3,e4): m1.add_element(el)\n",
    "\n",
    "m1.add_force(n2,(-P,))\n",
    "m1.add_force(n4,(-P,))\n",
    "m1.add_constraint(n1, ux=0,uy=0,ur=0) # fixed \n",
    "m1.add_constraint(n5, ux=0,uy=0,ur=0) # fixed\n",
    "m1.add_constraint(n3, uy=0, ur=0) # fixed\n",
    "m1.add_constraint(n2, ur=0)\n",
    "m1.add_constraint(n4, ur=0)\n",
    "m1.plot_model()\n",
    "m1.solve() # Solve model\n",
    "\n",
    "# Desplazamientos nodales y rotaciones\n",
    "print(\"Desplazamientos nodales y rotaciones\")\n",
    "print(\"UY \\t UR\")\n",
    "for node in m1.get_nodes():\n",
    "    print(\"{0} \\t {1}\".format(node.uy, node.ur))\n",
    "\n",
    "# Fuerzas nodales globales\n",
    "print(\"\\nFuerzas nodales globales\")\n",
    "print(\"FY \\t M\")\n",
    "for node in m1.get_nodes():\n",
    "    print(\"{0} \\t {1}\".format(node.fy, node.m))\n",
    "\n",
    "# Fuerzas en elementos\n",
    "print(\"\\nFuerzas en elementos\")\n",
    "for element in m1.get_elements():\n",
    "    print(\"\\nFY:\\n{0} \\n M:\\n{1}\\n\".format(element.fy, element.m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dibujando diagramas de cortante y momento flexionante\n",
    "m1.plot_shear_diagram()\n",
    "m1.plot_moment_diagram()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplo 3. \n",
    "\n",
    "![](src/beam-element/P913_beer.PNG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Beer & Johnston. (2012) Mechanics of materials. \n",
    "Problem 9.13 , pp. 568.\n",
    "\"\"\"\n",
    "# Input data \n",
    "E = 29e6\n",
    "I = 291 # W14x30 \n",
    "P = 35e3\n",
    "L1 = 5*12 # in\n",
    "L2 = 10*12 #in\n",
    "# Model\n",
    "m1 = BeamModel(\"Beam Model\")\n",
    "# Nodes\n",
    "n1 = Node((0,0))\n",
    "n2 = Node((L1,0))\n",
    "n3 = Node((L1+L2,0))\n",
    "# Elements\n",
    "e1 = Beam((n1,n2),E,I)\n",
    "e2 = Beam((n2,n3),E,I)\n",
    "\n",
    "# Add elements \n",
    "for nd in (n1,n2,n3): m1.add_node(nd)\n",
    "for el in (e1,e2): m1.add_element(el)\n",
    "    \n",
    "m1.add_force(n2, (-P,))\n",
    "m1.add_constraint(n1, ux=0, uy=0) # fixed \n",
    "m1.add_constraint(n3, uy=0) # fixed\n",
    "m1.solve() # Solve model\n",
    "\n",
    "m1.plot_shear_diagram()\n",
    "m1.plot_moment_diagram()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23333.333333333358"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n1.fy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplo 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Beer & Johnston. (2012) Mechanics of materials. \n",
    "Problem 9.13 , pp. 568.\n",
    "\"\"\"\n",
    "\n",
    "# Datos\n",
    "P1 = 3e3\n",
    "P2 = 3e3\n",
    "M1 = 450\n",
    "E = 200e9\n",
    "I = (1/12)*(50e-3)*(60e-3)**3\n",
    "\n",
    "n1 = Node((0,0))\n",
    "n2 = Node((0.3,0))\n",
    "n3 = Node((0.5,0))\n",
    "n4 = Node((0.7,0))\n",
    "n5 = Node((1,0))\n",
    "\n",
    "e1 = Beam((n1,n2), E, I)\n",
    "e2 = Beam((n2,n3), E, I)\n",
    "e3 = Beam((n3,n4), E, I)\n",
    "e4 = Beam((n4,n5), E, I)\n",
    "\n",
    "model_cp = BeamModel()\n",
    "\n",
    "for nodo in (n1,n2,n3,n4,n5): model_cp.add_node(nodo)\n",
    "for el in (e1,e2,e3,e4): model_cp.add_element(el)\n",
    "\n",
    "model_cp.add_constraint(n1, ux=0, uy=0)\n",
    "model_cp.add_constraint(n5, uy=0)\n",
    "model_cp.add_force(n2, (-P1,))\n",
    "model_cp.add_force(n4, (-P2,))\n",
    "model_cp.add_moment(n3, (-M1,))\n",
    "\n",
    "model_cp.solve()\n",
    "model_cp.plot_shear_diagram()\n",
    "model_cp.plot_moment_diagram()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [],
   "source": [
    "uy = []\n",
    "for n in model_cp.get_nodes():\n",
    "    uy.append(n.fy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x251f208c908>]"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(uy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}