comment recuperer la matrice de raideur lorsque la solution est un champ vectoriel ? voila mon code que je developpe // Définir la forme variationnelle pour la matrice de raideur varf a([u, v], [w, s]) = int2d(th)( lambda * div(w, s) * div(u, v) + 2. * mu * ( epsilon(w, s)’ * epsilon(u, v) ) ) + on(4, u = 0, v = 0); // Définir la forme variationnelle pour le vecteur de charges varf L([uu, vv], [w, s]) = int1d(th, 2)(P * w);

Hello, You have an example here: [image] Traction Forces - BilinearOperator NM error General Discussion The problem is that the space Vh you give in matrix A = avar(Vh, Vh, tgv = -1) has not the right size, since varf avar([ur, uz], [vr, vz]) has two unknowns ur,uz. You have to set fespace Vh2(Th,[P1,P1]); Vh2 [u1,u2]; The space Vh2 has the right size. Then you correct your system resolution by matrix A = avar(Vh2, Vh2, tgv = -1); // System matrix real[int] b = Lrhs(0, Vh2); // Right-hand side vector set(A, solver = sparsesolver); real[int] sol = A^-1 * b; u1[]=sol;// dist…

// Paramètres int n = 100; real rayon = 5; real E = 210; // en GPa real sigma = 0.2; real P = 1.; // traction en MPa // Bords du carré (sens trigonométrique) border a(t = -20, 20){ x = t; y = -20; label = 1; } // bas border b(t = -20, 20){ x = 20; y = t; label = 2; } // droite border c(t = 20, -20){ x = t; y = 20; label = 3; } // haut border d(t = 20, -20){ x = -20; y = t; label = 4; } // gauche // Trou circulaire au centre (sens horaire pour le trou intérieur) border cercle(t = 0, 2*pi){ x = rayon * cos(t); y = rayon * sin(t); label = 5; } mesh th = buildmesh(b(n) + c(n) + d(n) + a(n) + cercle(-n)); // Espace fespace Vh(th, [P1, P1]); // Déformation & divergence real sqrt2 = sqrt(2.); macro epsilon(u1, u2) [dx(u1), dy(u2), (dy(u1)+dx(u2))/sqrt2] // macro div(u,v) (dx(u) + dy(v)) // // Paramètres matériaux real mu = E/(2*(1+sigma)); real lambda = Esigma/((1+sigma)(1-2*sigma)); // Définir la forme variationnelle pour la matrice de raideur varf a([u, v], [w, s]) = int2d(th)( lambda * div(w, s) * div(u, v) mu * ( epsilon(w, s)’ * epsilon(u, v) ) ) on(4, u = 0, v = 0); // Définir la forme variationnelle pour le vecteur de charges varf L([uu, vv], [w, s]) = int1d(th, 2)(P * w); // Assemblage matrix K = avar(Vh2, Vh2, tgv = -1); // Matrice du système real[int] b = Lrhs(0, Vh2); // Vecteur second membre // Export K vers fichier CSV ofstream fk(“kk.csv”); for (int i = 0; i 1e-14) // ignorer les zéros fk << i << " " << j << " " << K(i,j) << endl; // Export rhs vers fichier CSV ofstream fp(“pp.csv”); for (int i = 0; i < rhs.n; ++i) fp << b[i] << endl; // Exporter les coordonnées des sommets ofstream fxy(“xy.csv”); for (int i = 0; i < th.nv; ++i) { fxy << th(i).x << " " << th(i).y << endl; } il me donne une erreur de compilation à la ligne 36 a cause d,un point virgule ! aidez moi s’il vous plais

the error message says “The identifier a exists”. Your varf needs another name instead of “a” because “a” is a border in your code. → call it “avar” “varf avar([u, v], [w, s]) =…” Then the name “Vh2” has to be replaced by “Vh” “Lrhs” has to be replaced by “L” “b” needs also another name that you need to choose, different from the variables you already have in your code (“b” is a border in your code).

Merciiiiiii merciiiiiii beaucoup :folded_hands:t2::white_heart:

Bonjour Mr j’espère que vous allez bien et en bon santé Si je veux récupérer la matrice de raideur, quelle est la différence entre : varf avar([u, v], [w, s]) = int2d(th)( lambda * div(w, s) * div(u, v) mu * (epsilon(w, s)’ * epsilon(u, v)) ) on(1, u = 0, v = -1) on(5, u = 0, v = 0); // Assemblage matrix K = avar(Vh, Vh, tgv = -1); // Matrice du système (((((( et les cas où tgv = 1 et tgv = 0 ? )))))))

The effect of the value of tgv for Dirichlet boundary condition is explained in the documentation Finite element in the “Note” just before the section “Numerical Integration”. tgv=-1 is the most accurate, it replaces the lines of the linear system corresponding to degrees of freedom of the test function on the considered boundary, by the exact equation u=Dirichlet value. tgv=large value (1e30 is the default) uses a penalty term similar to tgv*\int_\Gamma (u-u_D)*w, where w is the test function.

La matrice de raideur lorsque la solution est un champ vectoriel

General Discussion

fb77 (François Bouchut) April 26, 2025, 10:03am 2

Hello,
You have an example here:

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La matrice de raideur lorsque la solution est un champ vectoriel

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