Commit 738b27ee authored by Jeremy BLEYER's avatar Jeremy BLEYER

Update demo_barrage_Ternay.ipynb XDMF export

parent 6ad50c0c
{"metadata":{"language_info":{"name":"python","version":"3.7.8","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kernelspec":{"name":"python3","display_name":"Python 3","language":"python"}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"code","source":"# -*- coding: utf-8 -*-\n\"\"\"\nBarrage du Ternay (calcul élastique linéaire, HPP)\n\nCreated on Wed Oct 11 12:46:22 2017\n@author: Jeremy Bleyer, Xavier Chateau\nEcole des Ponts ParisTech, Laboratoire Navier (ENPC,IFSTTAR,CNRS UMR 8205)\n@email: jeremy.bleyer@enpc.fr, xavier.chateau@enpc.fr\n\"\"\"\nfrom dolfin import *\nimport subprocess\nimport matplotlib.pyplot as plt\n\n# Unités : longueurs en m\n# efforts en MN, contraintes en MPa\n\n\n# masse volumique béton\nrhob = Constant(2.5e3)\n# masse volumique eau\nrhow = Constant(1e3)\n# accélération de la pesanteur\ng = Constant(9.81e-6)\n# vecteur forces volumiques\nrhoF = rhob*g*Constant((0, -1.))\n\n# Pression de l'eau\nPw = Expression(\"rho*g*(H-x[1])\", rho=rhow, g=g, H=40., degree=1)\n\n# propriétés élastiques du béton\nE = Constant(30e3)\nnu = Constant(0.25)\nlmbda = E*nu/(1+nu)/(1-2*nu)\nmu = E/2./(1+nu)\n\n## MAILLAGE\n# nom du fichier .geo\nfname = \"Ternay\"\n# appel de Gmsh, génération du fichier .msh (ancien format \"msh2\")\nsubprocess.call([\"gmsh\", \"-2\", fname+\".geo\", \"-format\", \"msh2\"])\n# appel de dolfin-convert pour conversion en .xml \n# (on peut aussi passer par meshio cf. https://fenicsproject.discourse.group/t/transitioning-from-mesh-xml-to-mesh-xdmf-from-dolfin-convert-to-meshio/412)\nsubprocess.call([\"dolfin-convert\", fname+\".msh\", fname+\".xml\"])\n\n## Lecture du maillage généré\nmesh = Mesh(fname+\".xml\")\n# On récupère également les physical regions\nsubdomains = MeshFunction(\"size_t\", mesh, fname+\"_physical_region.xml\")\n# ainsi que les facet regions\nboundaries = MeshFunction(\"size_t\", mesh, fname+\"_facet_region.xml\")\n# Et on génère les normales aux facets pour l'application de la pression\nn = FacetNormal(mesh)\n# élément d'intégration sur le volume\ndx = Measure(\"dx\")\n# élément d'intégration sur le bord du domaine\nds = Measure(\"ds\",subdomain_data=boundaries)\n\n# Définition de l'espace d'interpolation pour le déplacement\nV = VectorFunctionSpace(mesh,\"CG\",degree=2)\n# Définition de fonctions tests (champs de vitesse virtuels)\nu_ = TestFunction(V)\nv = TrialFunction(V)\n# fonction où l'on va stocker la solution\nu = Function(V, name=\"Deplacement\")\n\n# Fonction utiles à l'écriture du problème\ndef eps(w):\n return sym(grad(w))\ndef sigma(w):\n # loi de comportement élastique linéaire isotrope (état initial naturel)\n return lmbda*tr(eps(w))*Identity(2) + 2*mu*eps(w)\n\n# Définition du travail virtuel de déformation\nWdef = inner(sigma(v), eps(u_))*dx\n# Définition du travail des efforts extérieurs\nWext = dot(rhoF, u_)*dx + dot(-Pw*n, u_)*ds(1)\n#\n\n# Définition des conditions aux limites sur la surface \"2\" (y=0)\nbc = DirichletBC(V, Constant((0, 0)), boundaries, 2)\n\n# Résolution du problème\nsolve(Wdef == Wext, u, bc)\n\n# Tracé de la déformée\nplot(u, mode = \"displacement\")\nplt.show()\n\n# Evaluation du déplacement en x=0 y=H\nprint(\"Deplacement en (0,40):\", u(0, 40))\n\n# Posttraitement des contraintes (projetées sur un espace continu linéaire/élement)\nVsig = TensorFunctionSpace(mesh, \"CG\", degree=1)\nsig = Function(Vsig, name=\"Contraintes\")\nsig.assign(project(sigma(u), Vsig))\n# tracé de la contrainte sigma_{yy}\nplot(sig[1, 1], mode=\"color\", title=\"sigma_yy\")\nplt.show()\n# tracé de la contrainte sigma_{xy}\nplot(sig[0, 1], mode=\"color\", title=\"sigma_xy\")\nplt.show()\n# évaluation de sigma en x=L,y=0\nprint(\"Contrainte en (-4,0):\", sig(-4, 0))\n\n# Sauvegarde de la solution au format VTK (pour Paraview)\nu_file = File(\"Ternay/xi.pvd\")\nu_file << u\nsig_file = File(\"Ternay/sig.pvd\")\nsig_file << sig\n\n# ou dans un seul fichier au format XDMF (pour Paraview également)\nffile = XDMFFile(\"Ternay/results.xdmf\")\nffile.write(u, 0)\nffile.write(sig, 0)\n\n## QUELQUES COMPLEMENTS\n# Calcul de l'effort vertical résultant en y=0 via les contraintes\nprint(\"Rx(y=0) via contraintes:\", assemble(-sig[1, 0]*ds(2)))\n# Calcul de l'effort horizontal résultant en y=0\nprint(\"Ry(y=0) via contraintes:\", assemble(-sig[1, 1]*ds(2)))\n# Calcul du moment/O autour de z en y=0\nprint(\"Mz/O(y=0) via contraintes:\", assemble(-Expression(\"x[0]\", degree=1)*sig[1, 1]*ds(2)))\n\n# Calcul de la résultante au pied du barrage via le travail des efforts intérieurs\nbc_pied_x = DirichletBC(V, Constant((1., 0.)), boundaries, 2)\nbc_pied_y = DirichletBC(V, Constant((0., 1.)), boundaries, 2)\nbc_pied_m = DirichletBC(V, Expression((\"0.\", \"x[0]\"), degree=1), boundaries, 2)\nv_x = Function(V)\nbc_pied_x.apply(v_x.vector())\nv_y = Function(V)\nbc_pied_y.apply(v_y.vector())\nv_m = Function(V)\nbc_pied_m.apply(v_m.vector())\nWreac = action(Wdef, u) - Wext\nprint(\"Rx(y=0) via travail:\",assemble(action(Wreac,v_x)))\nprint(\"Ry(y=0) via travail:\",assemble(action(Wreac,v_y)))\nprint(\"Mz/O(y=0) via travail:\",assemble(action(Wreac,v_m)))\n\n# Assemblage de la matrice de rigidité et du vecteur des forces nodales\nK, F = assemble_system(Wdef, Wext, bc)\n# vecteur solution\nU = u.vector()\n# On verifie que KU = F\nres = K*U - F\nprint(\"Norme du résidu:\", res.norm(\"l2\"))\n\n# Calcul de l'énergie mécanique (F^T,U)/2.\n# 1ere solution : méthode \"inner\" de F ou de U\nprint(0.5*F.inner(U))\nprint(0.5*U.inner(F))\n# 2eme solution : on convertit F et U en Numpy array puis\nU_numpy = U.get_local()\nF_numpy = F.get_local()\nprint(0.5*F_numpy.dot(U_numpy))\n# ou encore\nimport numpy as np\nprint(0.5*np.dot(F_numpy.T,U_numpy))\n# 3ème solution : on évalue le travail virtuel des efforts extérieurs pour la solution\nprint(assemble(action(0.5*Wext,u)))\n","metadata":{"trusted":true},"execution_count":5,"outputs":[{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 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\n"},"metadata":{"needs_background":"light"}},{"name":"stdout","text":"Deplacement en (0,40): [0.00309074 0.00022182]\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 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\n"},"metadata":{"needs_background":"light"}},{"output_type":"display_data","data":{"text/plain":"<Figure 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9EwrwFpqUl7HQNAp93rs5Fk2b+vzOiYBnSN0RAyu+Esc1onklSsNljicJtTafI4gM/LsO4yOJhL9q49uX4aL7FGig4S28iDICHHrGzMgDG48M1UrePAIE2LLmSppfOmIbLwfDz66Y+Shnz2WHh0ktHfNNUqebeeta/GYCptSGgd6JpASEpQ05FCL91FXVobAcweOsfvFo0t5oT1a0DlCu0GhLxDT2AGhN7HuCZpeC1e5Jfc+aEFHBoIhtyNIjUbwA8qUTvrQ473sWG50jtBuUFgbSWEWwRHVvxcKN58AvgCvs8Zk23QgEJ40Y2WIXx7sCb3s6Byhta3kV9N43zPEp1ohRpZ470VkZxIj6geCzSAfBLYtG3fu4/DxPmq4nOgcoSUMAPEv4WH2g4E3wF5uQKiQ6weEXmZE+5zSPJrCuxFTSVuWh57aucRX3MOic4R28CO+KT8Vy1tdhZRlFN6LaW8cH6qOyE3QyEE/j7HO4Q74ypO97FhOdJLQMjCDQPCuNX+pXlvHlNAopsPOfp0tOFMQVyv8DBaS5fbLI1uf4/S56SW93h4JnSS0ixSamStQ+OgKF7V/46me1mVev5zYmXWucIPFAcxozdef2b2Yl9fjApjNjJXvEpEHRGSLr8vxPr/+QyLygog86Ze3L353Lw7VJllWbTI3NAQrK2hjZrSEV+vCI98v+xzdd25pKpfQFJKa/vTeby3GpfWYBWZTOWkI/EtVfVxE1gOPici9ftvvqupHFq97lw6RykZLAIW6gapxA8OqitUMmkb9LS0FmcuIXxg9pnaKRg+IXbSCrfsOc+rcedatXbPIV9ujxGzqcuxT1cf9+5PAFuDVi92xeSP4nhtfvLGq/LTYNA50iXRmsBgGhSFpqSgPlurhkeYiFoNCgKEqf/3kd5bkMnvkuCQNLSI34aZjPeJXvVdEnhaRj40rBbbUdTlUNRZlLNUCYYZ3+BRmhvv8D1F1S6M+okjyhPjjlaU+7KGjh6SCOx/dvDgX2OOCmDWhRWQd8Fngl1X1BPCHwOtx5cH2Ab/dtt9S1+UQo48j8eqaEDXUukFDWHscjBtbxVX+jwY8zHzJkqDMIHHgLPeTe/ax61Cf27HUmG3lpFU4Mv+5qt4OoKoHfAGaBvgj4E2L183Zw3UHkrmMG/L1EIlo3dIxqT8rH21cIgKuSA0Z0UcmBgjc+dgzC3txPS6K2Xg5BPgTYIuq/o5Zf6Np9lPApoXv3qVDpOWSzIwUETNZtkz3NJl1ar0dkqKIKiHtvzge3kVo/NJ3PfEMddPPZFlKzMbL8UPAPwQ2+vp2AL8C/IyI3IKjxm7gPYvSw7nCD/Zc3Wdxjzlm4DbZdo2iU+kmkFggzEcXFZdaVxT8t1IjufLyQeLBk6d5ePse/s73vG7xrrNHhtnU5fga7YrznoXvzvyhIwEVdf5oz0i1YhhDVHHrVKv02R9GRR1LTeQw7aIpN9qQPkwCuP2JzT2hlxCdixRKCKiETLqQYTc1yDwaqaK/ZLdrmGUYXXTBxweZa8+OHFU1hcULq/3lZ3dy/Oy5JbjyHtBBQjvvgydr06ScjOiCk0w7R3mc9nb62YwtAxqMrAibxIw7/WdL7Jmm5vOb+jIHS4UOEtpb6ECzaKk9uX0edJj/p7GsLlGqhGFekCXiTW40vNZjFwz1gIzM1l/96Sc2LsmV9+gkoXM4q+kfPq+KaOOJqOYB95LvEDSyimtnGVw89zCb1RJgZIcKbD14mCdf3Lfg19ZjFB0ktCZ9LOI0tZUcMaufWOE/eeWSey4dTqJCCTZa1S+hTVXsVh6iUj7+xJP0WHx0kNBOUqSSBTaVFFJN6GRao50OhC8CidGx4a26qObb/c1gajyaY7uD3b31WQ6c6qdnLTa6R+jw1CvzOGO32tO2qlAffGkRHNEzYqOGtsKS4AaMWXg97ktmmVMeiDLUmo8/1VvpxUb3CC2STX6NHg9vpVUkyQs/6ItuaXW6OZcOmpKW1LUOcpqkXrKIenwVtT8EfHLjU5ydmVm0S+/RRUIHWCZF9eEkQxzI2SCJCcaIaH5TpMOkiQCVJHdfYaxzCRLkiXL87Fluf7bPwltMdI7QmullyHRA+ByKzGBWZ1ETk3rqH94ZqS2SH1KjqgCrrUPVUnsOgT998nGavmTYoqFzhE4PDcIlKgXLGxKUKhctjBIiFqJhJELi7XWUIUF6mPh5fnKfpYpJTy3r2Ow8dpQHn9u1aNf/ckfnCB2fJFuZR2pWZpbJwEVAogfPI1jpRHCfmOQZWVnuZk4Sfxb1X2Zj7orI+RB9cUGcjz396EJecg+DzhE6PEnWRcAFmRpEfRymT4384Eu0xcSZLlFKqNHGXm40xkhjJEjksBkh2rN5JfTV5/ew5chEPNaxc+gcoQFHyvAcb0ieDsFPmPXSIzC1VBE+vpIMbLK6QRZnEj0dxpFWJQVa1HhVmuA+VP7Fg3cv1tW/rNE5QkfJYVNIy/B0ppcVtEE0M7tutxrEzi30xKw0rbf5HIIgjT9ZRmpv3UnK/DvHD7Pn5LEFvfYeHSS0SMi/IAVXBgP/3r96k5z7ICRZ4khCN2E2hMYjQYXiYZ7+eKE2Xp3ahv2yXwCBRpXfe/rrS/a9vFwwn0Iz14jIvSKyzb+2zvpecijIqik/+MPVtouPp8A4i8msbmR34yx2ML+Z5y8MEtVb44zkkpHXSmgN1trngQRJcsf2Tb2VXmDMxkKHQjPfB7wZ+EUReQPwAeA+Vb0ZuM9/Xn5UAqtXe93srXJYX0KjHyRl4SFeTmhq4kmvpQWvwTzrLUKCJGkkWXRMIMYPGhtt+P1NDy/UlfdgfoVm3gHc5pvdBrxzsTp5KVBALr8MLlvrZ6mQT5L1XgubERpcdGEAGD1tja/RUTfQeP1rvHJActM1bpHGu/gC94VY42PEfa3CHTs28typ3kovFOZTaOYGVd0HjvTA9WP2WdJCM0eOnIIrLkPWrEam3JRJjbIikE9N4n/SB6XutZ9RdXMGYxBGowsvDg5x77XB/a41IE2aZS4qXvkkedKo8gebeyu9UJhPoZlZYakLzWx/dj+6ZgpdPRWLk9vM0fCMlZjXEQMhSTkEb3XwXEd3XJOii05WaEorNfeLUxjen9GA1kQLbt2C+D7dsfPp3kovEOZcaAY4EGpz+NeJiBR8+Yub0MGAcu5ggqa/kXSJ4EHf2sFgZQeQZn0Mbwe5kbnp/DqCtRdoJHpAks6Gpm54/yN3LcK38fLDnAvNAJ8DbvXvbwUm4j9y/tx0SuAfDFLBmCxv2eZk+M0NvqadC0+rd8sFPZ1kSAiuJOJXGpwmVr5oRu4oYerKO1HE+6oFqHj88F62nZgIm7CiMRsLHQrN/EhRC/rDwFtFZBvwVv95WTF9fsiubQcI8/60EhhUjjvGosY3jUZDG2WJGItqLHWQGBQBkuTxUKORybZZCAq1RM+gqsSb5yObvrw4X8zLCPMpNAPwloXtzvywa8cBTxRPU1OTLuXOeUuK809Lo66gkgqqDeqrK0Xz3MSd0EZgqO64lSe3n+qVPCPu0DZ8nvu7g1vQZAX6Uzz04jYeObSLv/2K1y3+l9VRdCpSuHnj815OeEtbJUKHB8+rD4zoiNejSbJD07xB8YNG0SAtYoXolCVqXYFBOytQe89GSGqK1Zy8hW5Ibj916z+y6Us0seBkj0tFpwj98H3PhNGeX+OtdFVcplh7bVZX4j0RLqIXI4KWX5mXwgwgm1KeeH90GGhSugPDA4uESn0OiMLmY/v4qxcmou7likSnCH3m9HmAZI3D7BUwmXfi2/hE/+B6kyC9HePSs4bUz/TGWWIJkUEbIfRRwEZHtJkEf7TxgDjN7W6eyg4a/ed//8yXOV/3cw/ngs4QemamZtd27yUIAzExSwGJf/JE/jgFNpLPS4bG7xCq+9fJowEaKyakQIyXKQ0uRN4QZ7Roo6m4U1hf4waLQ+GFk8f58MYvLNRX87JCZwi9c9t+mrqJehYwZA4ujCJRCYyuJb6KyaATn0WXngAOVcjCa9TrbmKYPB423BDiXYLGCrvoIWhdUTdCrRVN4943jdDogDv3PMnh8ycX90vrIDpD6Cce2TlS9ChOaI3MomiAIbTXuVEXu6pLya1nAzVOemR50Y0LnFAr1NFzOBIdDINLZ52FZjhwpEZoqGioUBVqav791i8u/BfVcXSG0E8+ugswHAZnZKVcmRx3ThYnT4eYbDrFZdelWS3ZnRJdbnaAWPl9nXcE7NMxxi4NNDMVw7pCG/GLQiPcvfdJnjq2e2G+oJcJOkPo40dOY0t1hboYrQ70Nl0toYadJ3+YwZ0t5Y0B+UQBD0PqFBb3VU01X9yRxEUQg3fFP9dCFX5r8+epezferNEJQk9PD9mz0w0IM3IZiRCefeLMqcQEotTUtPVL+ZgVmibdCGNC27ZORyjNEUid3SQ+AJQm3gpN7ay6GzQ6a/2dl/Zx+95H6DE7dILQu7YdcE+FxTg2ysQkO1IM8RY7o9vU83CfSQETP0AkFEK3KaTGu5GI6g9qCR+s9ZBE7Cx8rjTDiqZ2j6PVRtBa0Lri97b8FfvP9I+Imw06QeiHH9iSkdGpA2teA4PJpYYpwhgTOTBtAmkDybMad75hoZPFuPTieNScOkYUa1z+R508H6hQ+xuiaaBRoVHh9HDI72z93Py+pJcJOkHoF/YcztnDGO0MxeCu4LffbmemOD57V18gsA9dZwT1p3eTdCWTIgQ/dlgnuOjgUJJ3JPirhxUzQ6FpgivPufO+enALjxx5dr5fVefRCULv3XXYJAGNRusylHnSMto66OlkVY2m8MwNgZToCYzaWb2fOvmiKx+RzGRJsMqN9VO7m6GppxjWEi20qtBoxb995nbODM/P56vqPFY8oaenh+zdczjXzHHqSAu1CwttpWyQHWIHiOVUK1unIxygMQfxzePzwm2b4ehAMvmpc6teD6cYDivq2g0Om0Z48fRxPraz901fCCue0Lu2HaAZOs9FgLPWOkJegKwATVrp9gv7hIw8LzXidKtAVisxNFnizIj7nmRejyA9/KJmsBiL2hiPyHC6Yjh0/XARROG/7PkaTxzbtiDfXRex4gn91fs250J4HJHDNvsRRgeKsdxBki7xwfTWlef93SGhKYbBlejFiFrcW2oBKluNKb5K5taTJvipK2+phboOC/z6xk8w3Qwv+bt6OWA2U7A+JiIHRWSTWfchEXmhmMGyLDh66GQicXSzeYwjNiQrbeWD2+A3p4Gh9S9Hz0dxmBAjD89UsdIiBGziXk3yU9OY4xflw4IUGQ4H1M2Auq5otOLI+TP851299GjDbCz0nwFva1n/u6p6i1+W7THJm57Yk6+40ICv+Cyt2417I2N6cNFpy03g0TgPifV+QCBrXlIs5nU0EskctbT3fLh7VJipB36Q6D0fdcWf7/oKW0/saenEyxuzKTTzEDCRXv3p6SEH9x2Pn2frqrPEFrM96mG/JQ/QOMubrD/ml8G0szo47BZkSEgj1aKdqROptSTVFBOeKoZDF2wJGXnDBv6fZz7F+Xp6Vt/VywXz0dDvFZGnvSQZW9duMQvNuAghkVhZQj9c2Ntht4c2QWUEI5w9j9AJaU3FO8yAsLDapWzA3iikGTBBcw/DoNDPjvF50dZaN01FgyO0Wyp2nzzMr2+67dK/uA5jroT+Q+D1wC3APuC3xzVczEIzDz+wJcsITdFtyV9dRxKBDdEVTOGN3IMX3XZxRZ6IFIMu1hvirXWo5l8peS2OcHwrO1TiJABpcAGXWpJFb3DW2YfG68Zl503XFQ8f2sJjR/uAS8CcCK2qB1S1VtUG+CPgTQvbrdnh2OH0IEsBM9C7uLvOGVY1nyVOolU/qXa0JkGSFiHih7rRnVhTHJ4IYN14DUitae5hkfMhfjZ4CLa4aKSx0MOK6eGA6WaK6XqKmWbAsHGDxQ8/8ylOzJye03fYNcyJ0KFiksdPAcsyq/Oxr29rH5zNQmKIFO1K1x/GZhuz7ep2JO2c+Z9Vs4T+sm/ho1gXnSd88EXHVNPGW2lPaBdBrJgZJgtdNxW1Vhw4d4oPb/lkdoO+XDEbt92ngG8A3ysiz4vIzwH/VkQ2isjTwN8F/sUi93ME09NDjh4yjxo2rrux7jorRYLllJb9gRCyNqYq/DcAACAASURBVH43cwMEmeEJnpUiiFvNrO9AXMmsdlUMFGOQJc4zFF+UJljrimZGmJmpOD90no9A7ocPPsudz39tHt9oNzCbQjM/07L6TxahL5eEXdsOZDkXGcbWtSvamL3DA4OUyPcs4d8NFtVn8QXrnHzVqvhHxuWGuVKXOaeD0Midz9eiiUGWNPD0siSop0ZcyqkIDECkohm6wenZRoBp1ky5/v/+ti/wA1e/nr+x7lWz+g67iBUbKfzW177TviGQuc3bEbbbdWWkkLR6ZB+CtyLTJ8na+/faaK46/LkqJaWWFm675Jc23hOTtIQve6CN9bYI52dWMWwqZpqKMzMN//fGT3C2fvkmMK1YQh/ef2K8vLDSwhaasYPCUEUpfraW1Xo/yIIkTmn4D409t6YDePOeBVGsrAjHM8QNHo7SPx0mFGgDOkzyQ2uhqZ2uPjezimFdMWwG7DhxhPc/vuw/oMuGFUvobzywJVrjiw6GyhyOEY+HFM2Nfy3MGYw6hChLRIxf2rrkxEmAlnFh8nCQSA2J8GF91UBVe89HLVRaQVOhM26qFgjqc6ZnZgacmZ7i/IwwbCoePbqHu1/49oW/k45iRRJ6enrIyRNn3YdxHg0LS2CRUj7j2FhY9ZDQH8uGZQeMGjvNFHfZcOFwWuSVpDK8pKlf4ZRWEdl8jgaYwSQu+TmIw8pZ66Gf2VILw+EUw2aKmeGAmbritzbfwcbjuy/+3XQMK5LQu7cdQOsmEuOClG7JsNPgihPxD+BMZE5SI3kxsv2Dj9q68zRY5QQpTbPX1iOuPsznKDH8MQguPGIEMaT+aV25ZTiIEuT89BRnZwYM6ynOzAjv+/afcWLmzIW+nc5hRRL60a9dQj5wObdwTG0DRyyNUcOYKxS9ILFR64DR+S80M/rxWYa22AxBN5tt1ifdkHzPTShDJn6CAHGSrZMolUtiqitUK7QZMBxOOZdeU3FseoZfe/IzL6tqpiuS0Af3H89XWJlQhr3Nei1mdlvRq2YfLZ1vYcAY2+EesplpCs9ZT1Txd0AW7vYZe2XJA1uBKZBcanKrDVRaxaBL8HqEDqUiNcLMcIrz0wPOzwy4f98OfvXJ8BSR7mNFEvrr92+5cIOWXI7oPiuCK3Yf+5ChaMmDLA67EQhvNlbmIZzhtOGz1+Ku0AzGp00q/EgicCB4yAGJnpFA4BAeH/rF53xoDU0NTSNora4Skw5omoq7dm/k3hcv8p11BCuO0NPTQ06fPDu7xjbUDWOtd8jbSOIhkFO8NZZExHHFaay1tu674NqLVh4jP4ycgei2i2XE/PuqkTyCGCxz7Vx5TV2hjVua4YCmdklMMzPiluEU//zrt7PtpcV/rN5yY8URetszL1DXs3TTBQlhfc7R8hot7RI0ksGWZJEjxn1TnqAaSZrex9B4aBoGsXZQGCSGJBkS9XTYN7TRYkJA0NYjudUCXlNrM3CTBBrlfd+8nbPDbtedXnGE3vLU3ktqr+ZvvsH5r63TIRBdo2XWjNhpupUmD0gcb5lfg3gwZ2nVnqAcn9mBYUPe1ZGBZFpSbohQxVRT/0tS+3C7jyyG988eP8Q/efBTs/zmViZWHKH37JjFo898ZDAGULx7LpMFVVofXM6l98PX+HdPkA1WPrQLVllSW/8mO04mY/z7bKa42SXeILWx1H73WMMjHK6cPV5XnuAVErwfUbqkAeO3Dj3Hnbs3Xvw7XKFYcYR+5MGWZPa24IrxPsSl8g8PqtKEVc3NcyI4LbIDMgsqlomR6ElIR1+0ddOFGTAKaN4mVmMy3o5Y6T94Qmo/QMw8JV6gzzjrHJ5cq02F+nrTintEhyq8/5HPs72jenpFEXp6esjpU+eT1S3cdCpC411rKlVmKa0+zqw2eO8GyfccB3CF3s5cder2A2J4PD9TlDK+4Gnmq5a8adLT4bUO4W+yykrWteduDIkTAgjej7pyaae10My4SKLWvg3CsFF+6et3cq6DenpFEfrZjXup6wsHCTJvRhS6Pq0zuwEwpJbU1hK+vCG0GEhm1ZrCIezxTYg7ygeJU7eil0PNYcOrJbu55EjuMP8wS2LygZiaWMWUkAMy9AGYoSP3s8cO8q4H/+KC3+VKxFzrclwjIveKyDb/OnaS7EJi57YDY7clCzwiYImuN09uFWdd7cOsdIRR6Xj5dKxAfnPykV8CU9C8bGfJ7Xfw6iMdwHg/4oWF5H81zwuv3YCwqqt0viacn2xOYpjSpZr09DcPPMcdu7r1CLm51uX4AHCfqt4M3Oc/LzqeeeLSPBzAqMUVEPvcwtKdR8rnCIS3UDQnv2Vm1ipwM90AWakP67ozCf2ZRg8a2VtltfuZvA9pFBmKC4uHKKJWSFO5wWKsxOS3a+V1tvB/fuNudrx0+JK+0knGXOtyvAO4zb+/DXjnAverFU88smNkneVILieIZM7zns2AMGwrrPWoVZV0nDKk3tKfrB8anqCV2jrpYTwfQsqHDta5vLgsZO7C3/GBncE3bQeVNSkSWZvFH1NxdT6GTcMvfrU7enquGvoGVd0H4F+vH9dwoepyTE8POXXCRAitQWz5WXdjJBm1pmEcV1ptiP7n6OIjSYEw7It17srjVG6457icmBgJFnSFleHFtbT8IORj0cbsV1h7DUTP6ntU0WVHYx5K5AeQYVb51mOH+CcPfKb1e19pWPRB4ULV5fjOphfcYydCMMTqYkNMu95Zvypa1+hHriQjLeDXO1KHJbbzfujoajYWWLI7i+Sb9lpZzYYs79lb74yU/jXT0VZ2NMl6B1KLIbJ611+suuQtdXg6gC0KGfzT4e78+v493LFz5evpuRL6QChl4F9nEe2YH3Zt3w8UStXOLPEEldKl502c5W7mwqtMLQ4c//GVFB2f1EQOIWbchf2NWR1VISZvL+wbXHzlIBBywpttGTLtTC5FfAXUKnhFgrzQ0E6crm4qF0KHmNxELfwfX/sC21860vb1rxjMldCfA271728F7lqY7oxHzIG2+jRUPIq/4RI3AVE7q8mky6J9UGjnZJ3jYyiK9pbEMWDhz21r0oX9g8FO0Zr0onaFfxvkRbT0oWG6N1M9aUPqkIUX3HYhoQmc1s4GkmEZejJ7K1038M8euIOzMyu3Xt5c63J8GHiriGwD3uo/Lyqe3fSC64/tm08HtRbWSovkjh5Vponk5LNWALFyJHMDmpupFLxGaqjkj4RTwZRcSDdd+PLLMHeIGNpDl1JEIJubWCGZBGmfeFv5PGqJwReaKkkRhe3Hj/Cer9zBSsVc63IAvGWB+zIW09NDTrx01ngnPDHK2zFa1GgX8/B1i5VNbXx7OyCM7awXpDiutfAGpVLIuhnqe7j70Q84zQ3lD6CNk0DW3Reld9ilwX0PjZNb7tciD+ioAIPUYW3USStN54m/bhU8+PwePv2dp/kH3/PfXuAqJhMrIlK4feuLKUIo3prmv+CZPAjWNyzRCyECgyqFrKMZNxo5K87oz5GF7azEseM6TT7q+JDPdJxIMP8mWOWiFmROMqOVbTKTQko7tfMQo6WX9Nr4J9hmWjvsEyy5xPchD+SDD3+R7cdXnp5eEYTetXV/sabQzdbLEdaN7hE1bSQ+xiJb91s4ziBk2uEGiRXJZx1QEjf2IVn4oKFjNFCibDUChNyzEdYaKRJ0sE0pEcw+dqAYFjSfv9gESZKmcrnHyZGKQ6owrJV/dt/K80+vCEI/9OXN5pNmlmoElWGWTUIKRIypoBUMQgEaRucImoy88kYILEtBmOTmi+LBWlvb92JbuLOym8Ais7yj68a1s49cjkGYcMNYi+8GHtH1Fyfj1rDt6BF+/ksrS0+vCEK/8Jz76XPfvxQEk5jbPKJrPZGdS9ZLEHG5HEkWWFni11WjmtmRNfjATVg8sjfBDVBzM6qQJy4FBCveopPbtmdVmKzF9kulIEMKqaKuBJkPpsTSCIb8seKpnWleC199fjf/ZevTc//nLTEmntC2ymjQoepJl8mDTAsX7jnBFTqsyLaH/5uqXRd1gA+LO0dAnqCUzKWadlZ2BNmTLG4c0uZJekXdkNLjgZI/9N4erpAhto0Yy1tpFaOHVTy2pOBKoz7vWswEg1Sv+lcfunfF6OmJJ/Su7+yLA0IVQ5ZIWDEkD+Ry2lfFSIFgbaWYoRJuDqNrrfXNNLn5HIls9XgMgScjbGvixQEhaV20oCUsMf3nrD5eeB8OW5I9vDa40gqkfQiF18PgMOhofxNEve0/D4fKe/76rhWhpyee0Nu27I8ElhD4sASKhMz90YC7uoEhpZURYggY5EkmXxztki/bvMYbyyxjkErypkGhhr+B+UZOWGRW2rRVTHvr5TAkt9O4YhKTHRiG/OkgMazG9trb+a3dNew4epRf+NLnL/bvWnZMPKHv/8JT7k342a8so4gEDrnsEqxslCOSBookS57cA2Rk1aJNlqlHWhf90WFjtOJWn7fcEPFtstRZELHF0kYFo+nwubRIGnrEhZcNFsXPGjfZeZq+ikD6UENEwA8q3f73797JpzZPtp6eeEIfP3YmWbHwUuZrVFX8+XeutbC3GQhGv3SFEqZqSXTFpRsGMzgklx5VIjXmVb12iDJHwzqjyZPszoeQ0eKa8jXNyCmy9pnG9m3UEJNwT1ndbbV4MajMLHedBo15fWr3+dcevJftxyZXT080oaenh+x73qVit2nZ3NOAkROSCAkZKbN9SsJ6U2g9ImT7JGufkTL8Eozo5bzNOAgm9N4ipwu1k5O0zRLH2d6JtNETUgcJQswHoQ7WWL2m1lzKhPM10NTKe+6eXD090YTetW2/TxnFkaYSF+wQcfkWVZXSQCubUISJEpIs5SBsI9fKURPLCBmjd6MMqGCkh9HUJR9HLK0US3ZAMyjVYrMnlpr3JaGjHAmHLok/0jNJOjq67Ig+7LTeJTtVvjTCzmPH+IV7JlNPTzShtz2zLxE5E6FhGpSG/0nKVwhWOgZYIBSMiZY2SAxTbyNMBojtYs50Wp+OR17no4WgyWcdPmPeWHbld0F2GEPIeLlabDNtQ46H9YCEWh5WjmQpqPbGwFjyxj53PA1oQ+LTAzt38edPP8WkYaIJfd/d7gsT/9+R4ImI0qMllB3JZnI5gs+6IoazYzqp1c6BW5UjZIPmEiVa8YLMjEqQkZUZU/1ANsW+IwG1JOwYAgvEqqVxJov1R1u5EAgcumAsehzDhkFhkCuF1g4FIm3w5UP338+Oo5P11OyJJvSZc9OkqVQSUxKynIsQ6Rs4+aGDFDRJS3DliZ8Uba13stwaWALZjZKS/Ykkb/NZJ6+GL1EQyO4lRIgeRsdiKTlIhIzW9QKaOrPg1oqH4wTtbLR0JlUaTA43eR6IqXxq5zvafetG+ad33TlR+dMTS+jp8zPs3n4QSBY2RQdD6FnQQSJslBA2sjeQ6LlQS04rI2x7qvyGMdo8ShlLRHscjCEtmiHhj58y60y02WZQWmNL8rC9Me3sL4KVD/ZYJmGpMtKlzOSLPmmSJc4sea2J3A3sPnqcX77nr5gUTCyhd20/SMqHMEQK9VMGzhpTuQpJQUZEixmIHCxpFcgtkcCa3SCG+KETLRYU0s3QFNY5/Apklhm7rWVsZuYVqjmnUhByDFnzJKPRpcx8tVo+dt1m51kNbuSKs+R+9rq6aV5VA9IoX962gz997PH2L2uJMS9Ci8hu/0TZJ0Xk0YXqFMCWjXuN7lTzfzVywYu/mGtBIqqVERomuvojlIk/aYs3fCZVNCOrIWgw5COkt5o6bNfUNitnMOaGwV3WCPnaBnGjd4i5tEIrRyliyD5O0kgmV9LTuEJ+SIQfJP7m/V9hx5Hl19MLYaH/rqreoqpvXIBjRTx47zPeLWckwKDy4ezgLnOBEict/LaRGhuSoocCjVTesksiamVJbEwXJKtWpXZxgxBlQ+yPJX2BtCrph6yZJSq0knXUwiedW1rmEfKbc8SuW3910T6r5+5lSNLQhtzqXNg//5d3cmZ6efX0xEqOc2fPm+/O6NkwCDRyIrw2XkJINmhUJw0gly3Geidt7PKkY14H5FY5I2vYbvOmPVHM/z2eh7RYLaxAmZwUrXF5UxlLDdiZZq3djMe7mBwpboJomcM24/mQlgFiSD/de/wl3n/Pl1hOzJfQCnxJRB4TkXe3NZhLoZmZ6SG7trvKCC7DLuhl3OvAh7AD0cPMkpBl5+d9uulWjqA6EE94EqlJhEsdThfmbhKyGyAndbzIC39DxQc1N4ME18gFpAMkyZB5MaAoY5CTLZuLWBJ2nPW2MF6Winy/THOb839xyzZue3T59PR8Cf1DqvqDwE8Avygif6dsMJdCMzu3HaAJ9Ss8GYGUkyESk8Gy/A1/NcFV1/j8CiqNU6nCALAxN0kmJ8rPQfuO4ezIr3niqn/Tqj7Cl+OaGBkgJclokSWmibX2kfCljDD51NHqBrlBbpEz62u2jVj28NqMnuM3732IHYeXR0/Pi9Cq+qJ/PQjcAbxpITq18Yk9JJdbGphlUbugpQdeKmCz7ryl9hNiVYIOJ08wCscRs04La1xGGb2MKV13rb/1drt/I4aRLdzN0aR2GYrTW0mSny8nfLY0+TmyNoboMempOEY2Q6bJ12mjvOuTn+X0MujpORNaRK4QkfXhPfBjwILUkvr6Q88SB4I2Sy7IDztHUIh+Zx2QBncDMQRMbZqiXdS3Pm9ay28kBFewBHQZezESSbLMrbLEMNImMTmSaLyZ1OwzQqLyfXHcoKetLCnbhI+ljBk5D4wOFo28oNgnEDveDAr7T5ziX99zH0uNi9bluABuAO7wWWJTwCdV9a8XolNnzk7nUUAz56+pkl7GEzRpZ0MuQ4xIlIr0jxPzzw0krswe9pmG8RgS31sLWSYtxfZme+iHjGnfup9/dVaPxL5AKiHW54gWWorXoq8jnbcNbHu7Tos+Z3dF0WlznLs3buX1117NL/yPbx53uQuOORNaVXcCP7CAfQFcyuiunQe9lABnAgxhrcYNZBaizrZWWcp/hDdhkfCN4qoclSZVctFckqD4Sc8eHtRCGCmI1mK4s3ZtMmSEp8WxQj/ivg1pAOzbK+kmyC6vIfOoYG8UGd0m5r01EG0+7d/7yjf58e/7Hl5/3TUtV7XwmDi33e4dB2kajT/pjV90Srz/GQiDwoG4oEogf5XIKl5mNCaymJEZ/M3g5UPQ4GTT6WI9FiBZMPuPa7POav7pdlejA9p0cXgVkhxoO0cpE8ruRJKbpCRM+xEZU/Q1O5eRFbF/pQQad1x1+R4/9/HPcvr8+fYTLDAmjtBRP3vry6ByZPauOJ3yCUhTYeBHro+D5vbejFiNlFQgyC4x2mcWGwHMtlejbaGF08X6aFHj5/Q7PU596LgPBWkEkheipR9S7mO7b3UyRiM3+WHiQ0WNWzAmMDWj51A7SGxg/0un+NDd94+50oXFxBF6x44DhNzmNJgT6krQVY7MtdfSzVTwL5NyOwYkS2wDKNBKxgt6J9rQYtG0OJaMI/wYKzgy69tYu8z/rKPHKuUsBTmtSy4M3NqMcvBoxM9mEFiZY2WWWHIpFH5ZrNIJDT7/9Fb+44OPjPkCFg4TR+j9L77kpMZA0NWVc70NnGVuQi7zakGn8IRVE7Ym3gRN6ckorGsgePwftljqVrJX+fpWSzpOBAeCj5y85Rgtu5eSJ7OmhRUee1xDzLZIYeuotP0y0n5trr9iUYX/8MA32Hlocf3TE0Xo6ekhz+094iTDqopmUNGscpY5WOxmIK4K7ED8UnkZkkuPTC8XJC6t6DgZGDGO3O2rHC5Erni4QnZ462nruLd5EPQCxCu1e7au2GdcF0eiiUWwRdu+qJaby7YTdfMR3/Wnf8nZ6cWbjzhRhN614yBD1CcheckxFYgL9WqhXgWswkkL4/FowgCw0LpKkh3Wqmb/zDayXoSQ5e6t+xkrOJJgXx7DRA1H1FA528ScMKnxlv5cgLTxXCU5y5uhOJ+VPuNulPC5KtsCB0+e5t98fvH09EQR+qsPbo1auMHrYh+pawagU9Cs8vpZWkhcgQ7aS9oK5FbaBFUWGhc9phWYGRkMmw0xAnHaCizBhYlpo33jOjgux6O0sOMuRcpj2P6XSwN3Pf4M//H+b7YfcJ6YKELv2x/0MzRTMFwF9SphuFqoV0lMTGIKmMLJDJ90ZGvT5dlu7j+RPhcnLQeNHmp3Kr0IF5MTLTKhOLw5hmbbSx1rm2X+4OIa4suF+laQduRXqty95eYo9fNYvVbIICn2/4MHHmHnwYXX0xNF6O07nYejXlPRrK1glaCrQFcLzSrvzZDcP20TiVLwxcxc8eZZCxkS0Ua28nNpNS/0j2w7mN1UkErinTMGhZW2p5AW8oTPtgsy8qblY8t52uRMOPbYxRsAe2NaSx9ysIfDhn/8R5/h3Myw5aLnjokh9PT0kL37jztX3Gqh9tq5nqqc3BgQtXQKlhAHg9ngTyAm2/tkJLH/GktAGSVGZmHbSNs2OLREDUlFgbTm2PY86WchmUct2slI+0uAvWRLsPK6LoDWwWlbERqzQ0nwOA4oru3wyTP8xp0Lq6cnhtA7dx50z7FZXUXf8nC1kx71lB8QrvEa2ssNmzlX+oJj4lJY5/81baFpIPsH2595C2tV22Z4lP8wa9hHxpyWrCFmLcWNN+bGaT2nvXna+l68v5CmvijaBtBhGReZDLs2+fd4+6Ob+b0vff0SOzAeE0Pohx7+jpMaq4XhAOq1QrNWaFaBrsZJj1VWWiQr3djP/njlP2xEEVhiFtvacpLDRin4NvJzG45pPRFjdGU6Rl75U/wDRrObTPN+j9Ot5QOGsnOW13WRGzges2X12PZtOt/0R4pmAH/8wLcXTE9PDKGPHDsVXXPDy9zSTEG9RhiuEuopUsBkkCxwdgVavpX8n93SLn4ulnzk75kyQjQdKVgeUM6kHqe7R3zKvtsSLPfIgc2Lkk/Une3gsO2Q5ntq0+utO13oly58bCF2+T0Phw3/+A8/vSB6emII/egze6nXwLlrK6avFIZXCDMbhOFa0DU4z8bAvdr85iQpGM0MK77cyn6RRRtRn54UXo1IHA1kJGI7zdxEZkp4JT6SM/ZnxPqX5Ck+u2Nrem/RRhQY9Rn71/A9ZYPJtkNe6Ka4hJtEi/OPJDSFfvnPR0+e5Tdun7+enk8+9IJhembIi6dPMlwnzKxXdJWbPhXm2qUnOvnXYB2aZCRU3LY4w0K8ZfXr4892QaxsZrN/dZCRET+pKcEF4F4k25gVbjTtwr4jv8qlO6HULP5jZu2qtC1OSdT0XZQWNF5Lsa4ce4xcbFuny+3ltpZfHCtv4iCR9H8QgTu/tZnrN1zBL/3EDzFXTISF3r7nENPrhOl1MH0lzKyDZjWoGfxlJQQKsmQyIYzA62BZU6rmSNAAEDQ9dwRIrEhvY+KOOQ/F4CYOhlp/n9PB4vi0/JUwsNWKxPdRVNsHouGtFu9bjjtyuoJ8wYravOqRGTjjyNy22txY2tbc9s//3z5277fZdWDuenpehBaRt4nIsyKyXUQ+MNfjfOvZTTTrhPpKgVVKM1CaNUq9qqGZany0UBMRNCdnzCjzBA7/fDffTTItG628/aeHusiNEirWR9KWM5sDeQtyxT40xfumyfsLrZbSnieDsWyhKLpdXxI3/Dq1ES2S3RNMtb3dRTHOkl/EwmdBrWr0fyEK9Yzyrv/vM3PO95jPnMIB8Pu4Gd9vAH5GRN4wl2N99/W7ePMP7ubyV55h6qppZHWdsuc0/SPCxWcVOkPubeiXsWwjWtQP7DRo4FqpbH6vSqazUXzhcPWeh3SuqiD7CMHaCJfp7nSs+H8e0f+JqdJiHstxQDjFOOscrSa0DiYvhFQvMO1jT3HBSy/Uk+1QtNwN8bkwx146zb/71AMX71QL5mOh3wRsV9WdqjoN/AXwjrkc6Mq1T/F9rznEG15zkGpNzWC1//32D4wMzwXJrGELicMAKisD6xcbe6nQuC6z+CP7qZ8O6/f11h9t0qDP/hqU5wy/EMUxw8DTann7K5N442eJe+aKN9UZMcNiZYwlUEHssdxtkxZ+EGktq53NE6xuptlbykC0pe9ij0E6lwCDIXzuwU18c+Pucb0di/kMCl8N7DWfnwf+dtnIF6B5N8BrX/va1gP9Nzf/U65+1R7+5umKW46u5YbV1/Di0TNcf9k6Tp09TzOjXHP5Zew7eoJXb9jAkRNnWDs1xeWrV/Hi4Zd4zbVXcfzkWVYPBly+eoqDx07xyms2cPDISa5at5aqqjh6/DQ3XLueA4dPcu2Vl6MKx0+c5fpr1nHoyCmu3nAZqurWXbueQ0dOcc2VlzMzrDlx+hzXX7OeA4dOcN2165iZqXnp1FluuHYD+w+f4Ibr1nPi1HlQZcP6tew/cpJXXrueE6fOQSWsv2INB46c5JWv2MDh46dZu2aKy9au5vCx0+5cx06y/vK1rFo14PBLp7j+mg0cPH7K9X0gHH7pNK+8dgMHj53kynWXISIcPnGaG6/dwP5jJ7nuyiuYHtacOneeV1y1jn3HTnDDVes4Mz3Duekh1155BfuPneSGq9Zx6vw052aGvGLDFbx47ASvvHo9J85NU9c1V19xOftOnOBVV21g/4lTXHXZGlavmmL/iVPceOV6Dp08zRVrV7NmasChk6d55ZXrOXjiFFdevpaBVBw6dZobr1zPgZdOcc0Vl6HAsdNnuWHDOg4eP8m16y5n2Cgnzpzj+g3rOHD8JK9YfwXnpoecOTvN9RvWsf/wCW68cj2i8Ia/8cpLJuV8CN12s4/80KnqR4GPArzxjW9s+SGENWtv4XVrb+F118KPtHO+R49ZYT6S43ngu8zn1wAvzq87PXrMD/Mh9LeBm0XkdSKyGvhp4HML060ePeaG+dTlGIrIe4Ev4mJ4H1PVzQvWsx495oB5RQpV9R7gngXqS48e88ZERAp79Fgo9ITu0Sn0hO7RVgo3RgAAAdJJREFUKfSE7tEpyLgE9UU5mcghYM8SnOo64PASnGex0YXrWKxr+G5VHXkkxJISeqkgIo8u9FO5lgNduI6lvoZecvToFHpC9+gUukrojy53BxYIXbiOJb2GTmroHi9fdNVC93iZoid0j06hc4ReqIm7Sw0R+ZiIHBSRTWbdNSJyr4hs869XL2cfLwYR+S4ReUBEtojIZhF5n1+/ZNfRKUIv5MTdZcCfAW8r1n0AuE9Vbwbu858nGUPgX6rq9wFvxj0u+w0s4XV0itAs4MTdpYaqPgSUBSneAdzm398GvHNJO3WJUNV9qvq4f38S2IKbe7pk19E1QrdN3H31MvVlIXCDqu4DRxbg+mXuz6whIjcBfwt4hCW8jq4RelYTd3ssLkRkHfBZ4JdV9cRSnrtrhO7axN0DInIjgH89uMz9uShEZBWOzH+uqrf71Ut2HV0jdNcm7n4OuNW/vxW4axn7clGIe2j6nwBbVPV3zKaluw71NY67sgBvB74D7AB+dbn7cwn9/hSwD5jB/dL8HHAtziuwzb9es9z9vMg1/DBO4j0NPOmXty/ldfSh7x6dQtckR4+XOXpC9+gUekL36BR6QvfoFHpC9+gUekL36BR6QvfoFP5/V3XGyaQmcYEAAAAASUVORK5CYII=\n"},"metadata":{"needs_background":"light"}},{"name":"stdout","text":"Contrainte en (-4,0): [0.43550639 0.84015827 0.84015827 1.5452058 ]\nRx(y=0) via contraintes: -7.872121063829414\nRy(y=0) via contraintes: 12.48889308588453\nMz/O(y=0) via contraintes: 172.8054660254949\nRx(y=0) via travail: -7.848000000096919\nRy(y=0) via travail: 12.535936298799605\nMz/O(y=0) via travail: 172.69938227720974\nNorme du résidu: 1.1151204272763373e-12\n0.002866757084281998\n0.002866757084281998\n0.002866757084281998\n0.002866757084281998\n0.002866757084281998\n","output_type":"stream"}]},{"cell_type":"code","source":"","metadata":{},"execution_count":null,"outputs":[]}]}
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{"metadata":{"language_info":{"name":"python","version":"3.7.8","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kernelspec":{"name":"python3","display_name":"Python 3","language":"python"}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"code","source":"# -*- coding: utf-8 -*-\n\"\"\"\nBarrage du Ternay (calcul élastique linéaire, HPP)\n\nCreated on Wed Oct 11 12:46:22 2017\n@author: Jeremy Bleyer, Xavier Chateau\nEcole des Ponts ParisTech, Laboratoire Navier (ENPC,IFSTTAR,CNRS UMR 8205)\n@email: jeremy.bleyer@enpc.fr, xavier.chateau@enpc.fr\n\"\"\"\nfrom dolfin import *\nimport subprocess\nimport matplotlib.pyplot as plt\n\n# Unités : longueurs en m\n# efforts en MN, contraintes en MPa\n\n\n# masse volumique béton\nrhob = Constant(2.5e3)\n# masse volumique eau\nrhow = Constant(1e3)\n# accélération de la pesanteur\ng = Constant(9.81e-6)\n# vecteur forces volumiques\nrhoF = rhob*g*Constant((0, -1.))\n\n# Pression de l'eau\nPw = Expression(\"rho*g*(H-x[1])\", rho=rhow, g=g, H=40., degree=1)\n\n# propriétés élastiques du béton\nE = Constant(30e3)\nnu = Constant(0.25)\nlmbda = E*nu/(1+nu)/(1-2*nu)\nmu = E/2./(1+nu)\n\n## MAILLAGE\n# nom du fichier .geo\nfname = \"Ternay\"\n# appel de Gmsh, génération du fichier .msh (ancien format \"msh2\")\nsubprocess.call([\"gmsh\", \"-2\", fname+\".geo\", \"-format\", \"msh2\"])\n# appel de dolfin-convert pour conversion en .xml \n# (on peut aussi passer par meshio cf. https://fenicsproject.discourse.group/t/transitioning-from-mesh-xml-to-mesh-xdmf-from-dolfin-convert-to-meshio/412)\nsubprocess.call([\"dolfin-convert\", fname+\".msh\", fname+\".xml\"])\n\n## Lecture du maillage généré\nmesh = Mesh(fname+\".xml\")\n# On récupère également les physical regions\nsubdomains = MeshFunction(\"size_t\", mesh, fname+\"_physical_region.xml\")\n# ainsi que les facet regions\nboundaries = MeshFunction(\"size_t\", mesh, fname+\"_facet_region.xml\")\n# Et on génère les normales aux facets pour l'application de la pression\nn = FacetNormal(mesh)\n# élément d'intégration sur le volume\ndx = Measure(\"dx\")\n# élément d'intégration sur le bord du domaine\nds = Measure(\"ds\",subdomain_data=boundaries)\n\n# Définition de l'espace d'interpolation pour le déplacement\nV = VectorFunctionSpace(mesh,\"CG\",degree=2)\n# Définition de fonctions tests (champs de vitesse virtuels)\nu_ = TestFunction(V)\nv = TrialFunction(V)\n# fonction où l'on va stocker la solution\nu = Function(V, name=\"Deplacement\")\n\n# Fonction utiles à l'écriture du problème\ndef eps(w):\n return sym(grad(w))\ndef sigma(w):\n # loi de comportement élastique linéaire isotrope (état initial naturel)\n return lmbda*tr(eps(w))*Identity(2) + 2*mu*eps(w)\n\n# Définition du travail virtuel de déformation\nWdef = inner(sigma(v), eps(u_))*dx\n# Définition du travail des efforts extérieurs\nWext = dot(rhoF, u_)*dx + dot(-Pw*n, u_)*ds(1)\n#\n\n# Définition des conditions aux limites sur la surface \"2\" (y=0)\nbc = DirichletBC(V, Constant((0, 0)), boundaries, 2)\n\n# Résolution du problème\nsolve(Wdef == Wext, u, bc)\n\n# Tracé de la déformée\nplot(u, mode = \"displacement\")\nplt.show()\n\n# Evaluation du déplacement en x=0 y=H\nprint(\"Deplacement en (0,40):\", u(0, 40))\n\n# Posttraitement des contraintes (projetées sur un espace continu linéaire/élement)\nVsig = TensorFunctionSpace(mesh, \"CG\", degree=1)\nsig = Function(Vsig, name=\"Contraintes\")\nsig.assign(project(sigma(u), Vsig))\n# tracé de la contrainte sigma_{yy}\nplot(sig[1, 1], mode=\"color\", title=\"sigma_yy\")\nplt.show()\n# tracé de la contrainte sigma_{xy}\nplot(sig[0, 1], mode=\"color\", title=\"sigma_xy\")\nplt.show()\n# évaluation de sigma en x=L,y=0\nprint(\"Contrainte en (-4,0):\", sig(-4, 0))\n\n# Sauvegarde de la solution au format VTK (pour Paraview)\nu_file = File(\"Ternay/xi.pvd\")\nu_file << u\nsig_file = File(\"Ternay/sig.pvd\")\nsig_file << sig\n\n# ou dans un seul fichier au format XDMF (pour Paraview également)\nffile = XDMFFile(\"Ternay/results.xdmf\")\nffile.parameters[\"functions_share_mesh\"]=True\nffile.write(u, 0)\nffile.write(sig, 0)\nffile.close()\n\n## QUELQUES COMPLEMENTS\n# Calcul de l'effort vertical résultant en y=0 via les contraintes\nprint(\"Rx(y=0) via contraintes:\", assemble(-sig[1, 0]*ds(2)))\n# Calcul de l'effort horizontal résultant en y=0\nprint(\"Ry(y=0) via contraintes:\", assemble(-sig[1, 1]*ds(2)))\n# Calcul du moment/O autour de z en y=0\nprint(\"Mz/O(y=0) via contraintes:\", assemble(-Expression(\"x[0]\", degree=1)*sig[1, 1]*ds(2)))\n\n# Calcul de la résultante au pied du barrage via le travail des efforts intérieurs\nbc_pied_x = DirichletBC(V, Constant((1., 0.)), boundaries, 2)\nbc_pied_y = DirichletBC(V, Constant((0., 1.)), boundaries, 2)\nbc_pied_m = DirichletBC(V, Expression((\"0.\", \"x[0]\"), degree=1), boundaries, 2)\nv_x = Function(V)\nbc_pied_x.apply(v_x.vector())\nv_y = Function(V)\nbc_pied_y.apply(v_y.vector())\nv_m = Function(V)\nbc_pied_m.apply(v_m.vector())\nWreac = action(Wdef, u) - Wext\nprint(\"Rx(y=0) via travail:\",assemble(action(Wreac,v_x)))\nprint(\"Ry(y=0) via travail:\",assemble(action(Wreac,v_y)))\nprint(\"Mz/O(y=0) via travail:\",assemble(action(Wreac,v_m)))\n\n# Assemblage de la matrice de rigidité et du vecteur des forces nodales\nK, F = assemble_system(Wdef, Wext, bc)\n# vecteur solution\nU = u.vector()\n# On verifie que KU = F\nres = K*U - F\nprint(\"Norme du résidu:\", res.norm(\"l2\"))\n\n# Calcul de l'énergie mécanique (F^T,U)/2.\n# 1ere solution : méthode \"inner\" de F ou de U\nprint(0.5*F.inner(U))\nprint(0.5*U.inner(F))\n# 2eme solution : on convertit F et U en Numpy array puis\nU_numpy = U.get_local()\nF_numpy = F.get_local()\nprint(0.5*F_numpy.dot(U_numpy))\n# ou encore\nimport numpy as np\nprint(0.5*np.dot(F_numpy.T,U_numpy))\n# 3ème solution : on évalue le travail virtuel des efforts extérieurs pour la solution\nprint(assemble(action(0.5*Wext,u)))\n","metadata":{"trusted":true},"execution_count":2,"outputs":[{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 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\n"},"metadata":{"needs_background":"light"}},{"name":"stdout","text":"Deplacement en (0,40): [0.00309074 0.00022182]\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 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\n"},"metadata":{"needs_background":"light"}},{"output_type":"display_data","data":{"text/plain":"<Figure 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\n"},"metadata":{"needs_background":"light"}},{"name":"stdout","text":"Contrainte en (-4,0): [0.43550639 0.84015827 0.84015827 1.5452058 ]\nRx(y=0) via contraintes: -7.872121063829414\nRy(y=0) via contraintes: 12.48889308588453\nMz/O(y=0) via contraintes: 172.8054660254949\nRx(y=0) via travail: -7.848000000096919\nRy(y=0) via travail: 12.535936298799605\nMz/O(y=0) via travail: 172.69938227720974\nNorme du résidu: 1.1151204272763373e-12\n0.002866757084281998\n0.002866757084281998\n0.002866757084281998\n0.002866757084281998\n0.002866757084281998\n","output_type":"stream"}]},{"cell_type":"code","source":"","metadata":{},"execution_count":null,"outputs":[]}]}
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