Re: [Getfem-users] Stiffness matrix for linear elasticity

[Renard Yves]

Dear Roman,

This formula implements in fact a weak term. This represents

lambda div(u).div(v) + mu grad(u):grad(v) + mu grad(u)^T:grad(v)

where A:B is the Frobenius (scalar) product of matrices.

Yves.


Roman Putanowicz <address@hidden> a écrit :

> Dear All,
>
> I am looking at function asm_stiffness_matrix_for_linear_elasticity.
> There is code like this:
> generic_assembly assem("lambda=data$1(#2); mu=data$2(#2);"
>          "t=comp(vGrad(#1).vGrad(#1).Base(#2));"
>          "M(#1,#1)+=sym(t(:,i,j,:,i,j,k).mu(k)"
>                      "+ t(:,j,i,:,i,j,k).mu(k)"
>                      "+ t(:,i,i,:,j,j,k).lambda(k))");
> I cannot figure why this is written as above.
> In the Navier's equation we have terms
>
>      mu * u_i,jj + (mu+lambda)*u_j,ji
>
> so I would expect
> the second and third components at mu and lambda, respectively, be the same.
>
> I would really appreciate a hint on this as I have serious doubts in my
> ability to juggle the tensor indices :-).
>
> Best regards
>
> Roman
> --
> Roman Putanowicz, PhD  < address@hidden  >
> Institute for Computational Civil Engng (L-5)
> Dept. of Civil Engng, Cracow Univ. of Technology
> www.l5.pk.edu.pl, tel. +48 12 628 2569, fax 2034
>
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