Lagrange_constraints.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "93781b2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "6383ad0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "E = 210e9\n",
    "A = 0.05**2\n",
    "h_1 = 0.5\n",
    "h_2 = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "6b29a91b",
   "metadata": {},
   "outputs": [],
   "source": [
    "K_el = lambda h: E*A/h * np.matrix([[1,-1],[-1,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "95c7b2d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.05e+09, -1.05e+09,  0.00e+00],\n",
       "       [-1.05e+09,  2.10e+09, -1.05e+09],\n",
       "       [ 0.00e+00, -1.05e+09,  1.05e+09]])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_ref = np.zeros((3,3))\n",
    "K_ref[0:2,0:2] += K_el(h_1)\n",
    "K_ref[1:3,1:3] += K_el(h_2)\n",
    "K_ref"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "3b75bbb5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([      0.,       0., 1000000.])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RHS_ref = np.zeros(3)\n",
    "RHS_ref[-1] = 1e6\n",
    "RHS_ref"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "86b77cc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.01064312e+08, 2.74893569e+09, 1.00000000e+00])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_ref[0,:] = 0\n",
    "K_ref[0,0] = 1\n",
    "RHS_ref[0] = 0\n",
    "np.linalg.eigvals(K_ref)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "2b1e8389",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.82762768e-21  9.52380952e-04  1.90476190e-03]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2935c015760>]"
      ]
     },
     "execution_count": 126,
     "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": [
    "u = np.linalg.solve(K_ref,RHS_ref)\n",
    "print(u)\n",
    "plt.plot(u,marker='d',ls='--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "21210d8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.05e+09, -1.05e+09,  0.00e+00,  0.00e+00],\n",
       "        [-1.05e+09,  1.05e+09,  0.00e+00,  0.00e+00],\n",
       "        [ 0.00e+00,  0.00e+00,  1.05e+09, -1.05e+09],\n",
       "        [ 0.00e+00,  0.00e+00, -1.05e+09,  1.05e+09]])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_sys = np.block([[K_el(h_1),np.zeros_like(K_el(h_1))],[np.zeros_like(K_el(h_1)),K_el(h_2)]])\n",
    "K_sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "e351ef81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([      0.,       0.,       0., 1000000.])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RHS_sys = np.zeros(4)\n",
    "RHS_sys[-1] = 1e6\n",
    "RHS_sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "a811edfb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.00e+00,  0.00e+00,  0.00e+00,  0.00e+00],\n",
       "        [-1.05e+09,  1.05e+09,  0.00e+00,  0.00e+00],\n",
       "        [ 0.00e+00,  0.00e+00,  1.05e+09, -1.05e+09],\n",
       "        [ 0.00e+00,  0.00e+00, -1.05e+09,  1.05e+09]])"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_sys[0,:] = 0\n",
    "K_sys[0,0] = 1\n",
    "RHS_sys[0] = 0\n",
    "K_sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "347893d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.e+00,  1.e+08, -1.e+08,  0.e+00]])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k_spring = 1e8\n",
    "C = np.array([[0,1,-1,0]])*k_spring\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "1e9cd8a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7.65181397e+07,  6.46881782e+07,  1.05943820e+09,  2.10239176e+09,\n",
       "        1.00000000e+00])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_lagr = np.zeros((5,5))\n",
    "K_lagr[0:4,0:4] += K_sys\n",
    "K_lagr[4:5,0:4] += C\n",
    "K_lagr[0:4,4:5] += C.T\n",
    "K_lagr\n",
    "np.linalg.eigvals(K_lagr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "cef2a1a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([      0.,       0.,       0., 1000000.,  -10000.])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RHS_lagr = np.append(RHS_sys,-1e-4*k_spring)\n",
    "RHS_lagr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "8dd70e48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.15426621e-19,  9.52380952e-04,  1.05238095e-03,  2.00476190e-03,\n",
       "       -1.00000000e-02])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_lagr=np.linalg.solve(K_lagr,RHS_lagr)\n",
    "u_lagr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "8534e1b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2935d108070>]"
      ]
     },
     "execution_count": 139,
     "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": [
    "plt.plot(u,marker='d',ls='--')\n",
    "plt.plot(u_lagr[0:-1],marker='d',ls='--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e6fd7ba8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}