Re: [Getfem-users] boundary problem with elastostatic

[Yves Renard]

Dear Radames,

Neumann conditions are taken into account by the source term brick. In weak 
formulation, a Neumann condition is a source term on the corresponding 
boundary. See examples and 
http://download.gna.org/getfem/html/homepage/userdoc/model_source_term.html


Yves. 


On mardi 22 novembre 2011, address@hidden wrote:
> 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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-- 

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard

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