[Getfem-users] boundary problem with elastostatic

[radames42]

Dear all,

I'm a newbie to getfem++.

I want to solve an isotropic homogenous elastostatic problem. The (first) mesh 
is ready but I cannot see how to include my boundary conditions.

Here are the equations of my problem:

e_ij = (u_i,j + u_j,i)/2 in V
sigma_ij =lambda delta_ij epsilon_kk + 2 mu epsilon_ij in V with lambda, mu 
Lamé coefficient
sigma_ij,j + b_j = 0 in V with b data
u_i = w_i on S_D with w data
sigma_ij n_j = p1 n_i on S_N1 with p1 data and n the unit normal of the surface 
(face)
sigma_ij n_j = p2 n_i on S_N2 with p2 data and n the unit normal of the surface 
(face)

p1 and p2 are gas pressures. Therfore there is no tangential traction at the 
surfaces S_Ni, but only normal pressure. S_N1 + S_N2 + S_D = \partial V.


For the first three equations I can use the linear elasticity brick [1] AFAICS. 
For the Dirichlet condition I can use the Dirichlet brick [2]. But with the two 
Neumann boundaries I cannot see how to specify them. The unknown of the FEM is 
the displacement field u. The boundary condition is given in terms of sigma but 
not (directly) in terms of u. I expect that the Neumann brick [3] implements 
u_i,j n_j = v_i, but that's not what I need.
How can I proceed?
At the moment I use the python interface, but I can move to the c++ interface 
if it can solve my problem easier.

[1] 
[2] 
[3] 


Many thanks for any hints.

Kind regards,
Radames




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