# Message Boards

0
|
3607 Views
|
0 Replies
|
0 Total Likes
View groups...
Share
 Hello, I want to simulate a the deformation of a circular excavation. So I defined the displacement vector (u=ur(r)), and then the deformation and the stress tensor, and I wrote the equation I want to solve : div [Sigma] = D[u,{t,2}] Then I wrote the initial conditions : at t=0, the field is charged normally, and at t=1, we excavate a part. Here is the code : Excavation circulaire, dynamique lambda = 1; mu = 1; ro = 1; ur =.; u[r_, teta_, t_] = {ur[r, t], 0}; gradientu[r_, teta_, t_] = Grad[u[r, teta, t], {r, teta}, "Polar"]; epsilon[r_, teta_, t_] = 0.5*(gradientu[r, teta, t] + Transpose[gradientu[r, teta, t]]); \[Sigma][r_, teta_, t_] = 2*mu*epsilon[r, teta, t] + lambda*Tr[epsilon[r, teta, t]]*IdentityMatrix; eq1 = Div[\[Sigma][r, teta, t], {r, teta}, "Polar"][]; eq2 = ro*D[ur[r, t], {t, 2}]; ursol = NDSolveValue[{eq1 == -eq2, \[Sigma][r, teta, 0][[1, 1]] == 1, \[Sigma][r, teta, 0][[2, 2]] == 1, DirichletCondition[\[Sigma][r, teta, t][[1, 1]] == 1, r == 5], DirichletCondition[\[Sigma][r, teta, t][[1, 1]] == 0, r == 1 and t >= 1]}, ur, {r, 1, 5}, {t, 0, 2}];  But when I run the code, Mathematica stops, and return nothing. Can you help me please ? Thank you