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

From: Renard Yves
Subject: Re: [Getfem-users] Stiffness matrix for linear elasticity
Date: Tue, 28 Dec 2010 21:19:41 +0100
User-agent: Dynamic Internet Messaging Program (DIMP) H3 (1.1.2)

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.


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(:,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 Putanowicz, PhD  < address@hidden  >
Institute for Computational Civil Engng (L-5)
Dept. of Civil Engng, Cracow Univ. of Technology, tel. +48 12 628 2569, fax 2034

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