AE-245 - Lista 02 - Q4 - Literal.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix([[43*L*Q/160], [83*L**2*Q/2560], [7*L*Q/160], [-19*L**2*Q/1536]])\n"
     ]
    }
   ],
   "source": [
    "# BIBLIOTECAS\n",
    "from sympy import *\n",
    "import numpy as np\n",
    "import numpy.ma as ma\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# DECLARA SIMBOLOS\n",
    "x, y, a1, a2, a3, Q, L, E, I = symbols('x y a1 a2 a3 Q L E I')\n",
    "\n",
    "# CARREGAMENTO\n",
    "q   = a3*x**2 + a2*x + a1\n",
    "eq1 = q.subs(x,0) - Q\n",
    "a1_ = solve(eq1,a1)[0]\n",
    "q = q.subs(a1, a1_)\n",
    "eq2 = q.subs(x,L/3) - Q/2\n",
    "eq3 = q.subs(x,L)\n",
    "system = [eq2, eq3]\n",
    "var = [a2, a3]\n",
    "sol = solve(system, var)\n",
    "a2_ = sol[a2]\n",
    "a3_ = sol[a3]\n",
    "q = q.subs([(a2, a2_), (a3, a3_)])\n",
    "\n",
    "# MATRIZ DE RIGIDEZ\n",
    "K = E*I/L**3*Matrix([[12, 6*L, -12, 6*L], [6*L, 4*L**2, -6*L, 2*L**2], [-12, -6*L, 12, -6*L], [6*L, 2*L**2, -6*L, 4*L**2]])\n",
    "\n",
    "# VETOR DE CARREGAMENTO\n",
    "phi = Matrix([[2*x**3/L**3-3*x**2/L**2+1],[x - 2*x**2/L+x**3/L**2],[3*x**2/L**2 - 2*x**3/L**3],[x**3/L**2 - x**2/L]])\n",
    "F = integrate(q*phi,(x,0,L/2))\n",
    "print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q - \\frac{7 Q x}{4 L} + \\frac{3 Q x^{2}}{4 L^{2}}$"
      ],
      "text/plain": [
       "Q - 7*Q*x/(4*L) + 3*Q*x**2/(4*L**2)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ELIMINAÇÃO DE LINHAS E COLUNAS\n",
    "F = F.row_del(0)\n",
    "F = F.row_del(0)\n",
    "\n",
    "K.row_del(0)\n",
    "K.row_del(0)\n",
    "K.col_del(0)\n",
    "K.col_del(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{7 L Q}{80}\\\\- \\frac{L^{2} Q}{48}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  7*L*Q/80],\n",
       "[-L**2*Q/48]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{215}{8}\\\\\\frac{415}{128}\\\\\\frac{35}{8}\\\\- \\frac{475}{384}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   215/8],\n",
       "[ 415/128],\n",
       "[    35/8],\n",
       "[-475/384]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F.subs({L: 1, Q: 100}).simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{12 E I}{L^{3}} & - \\frac{6 E I}{L^{2}}\\\\- \\frac{6 E I}{L^{2}} & \\frac{4 E I}{L}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[12*E*I/L**3, -6*E*I/L**2],\n",
       "[-6*E*I/L**2,     4*E*I/L]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = linsolve((K, F))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left\\{\\left( 8.92857142857143 \\cdot 10^{-14}, \\  1.09126984126984 \\cdot 10^{-13}\\right)\\right\\}$"
      ],
      "text/plain": [
       "FiniteSet((8.92857142857143e-14, 1.09126984126984e-13))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u.subs({L: 1, Q: 100, E: 210e9, I: 100})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Bibliotecas\n",
    "from sympy import *\n",
    "from sympy.interactive import printing\n",
    "printing.init_printing(use_latex = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, L, E, I, Q = symbols('x L E I Q')\n",
    "f = Function('f')(x)\n",
    "q = Q + 3*Q*x**2/4/L**2 - 7*Q*x/4/L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$\\displaystyle E I \\frac{d^{4}}{d x^{4}} f{\\left(x \\right)} - Q + \\frac{7 Q x}{4 L} - \\frac{3 Q x^{2}}{4 L^{2}} = 0$"
      ],
      "text/plain": [
       "      4                          2    \n",
       "     d              7⋅Q⋅x   3⋅Q⋅x     \n",
       "E⋅I⋅───(f(x)) - Q + ───── - ────── = 0\n",
       "      4              4⋅L        2     \n",
       "    dx                       4⋅L      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ics = {f.subs(x,0): 0, f.diff(x).subs(x,0): 0, f.diff(x,x).subs(x,L): 0, f.diff(x,x,x).subs(x,L): 0}\n",
    "ode = Eq(E*I*f.diff(x,x,x,x)- q,0)\n",
    "display(ode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle f{\\left(x \\right)} = \\frac{Q x^{2} \\left(L^{2} \\left(25 L^{2} - 30 L x + 20 x^{2}\\right) - 7 L x^{3} + x^{4}\\right)}{480 E I L^{2}}$"
      ],
      "text/plain": [
       "          2 ⎛ 2 ⎛    2                2⎞        3    4⎞\n",
       "       Q⋅x ⋅⎝L ⋅⎝25⋅L  - 30⋅L⋅x + 20⋅x ⎠ - 7⋅L⋅x  + x ⎠\n",
       "f(x) = ────────────────────────────────────────────────\n",
       "                                   2                   \n",
       "                          480⋅E⋅I⋅L                    "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fsol = dsolve(ode, f, ics = ics)\n",
    "fsol.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle f{\\left(L \\right)} = \\frac{3 L^{4} Q}{160 E I}$"
      ],
      "text/plain": [
       "           4  \n",
       "        3⋅L ⋅Q\n",
       "f(L) = ───────\n",
       "       160⋅E⋅I"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fsol.subs(x,L)"
   ]
  },
  {
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}