Hello Wolfgang, thanks for your reply.
I will follow your point to see if I could find the solution. One moire question,how could I get ∂A(θ)/∂θx,because I did not find any information about density vector like θ=[θ1,θ2,...,θm],may I know if I have to set density vector value in this finite element? Code Link:https://www.dealii.org/current/doxygen/code-gallery/Quasi_static_Finite_strain_Compressible_Elasticity/cook_membrane.cc mu is invoked from prm file at the position of line 252 Best regards Lance On Monday, July 24, 2023 at 6:49:12 PM UTC+2 Wolfgang Bangerth wrote: > > The given conditions are stiffness matrix,destination function and x > from > > Ax=b,x is movement ,b is force,A is global stiffness matrix. > > J(x)=||x||norm-1 > > This is a questionable choice because dJ/dx is not defined at x=0. > > > There is one equation: > > > > dJ(x,θ)/dθ=∂J(x,θ)/∂θ+∂J(x,θ)/∂x > > *∂x/∂θ=∂J(x,θ)/∂θ+∂J(x,θ)/∂x*[A^-1(θ))(-∂A(θ)/∂θ)x],because b has no > relation > > with density. > > > > I don't know how to get [A^-1(θ))(-∂A(θ)/∂θ)x],A is matrix with nxn,if θ > is > > mx1 vector,∂A(θ)/∂θ is nxnxm matrix. > > ∂A(θ)/∂θ)x is an nxm matrix. You want to apply A^{-1} to it. The way you > do > that is to call the result > Y = A^{-1} [∂A(θ)/∂θ)x] > and then each column of Y, call it y_k (k=1...m) is computed as > y_k = A^{-1} {[∂A(θ)/∂θ)x]_k} > which requires solving a linear system > A y_k = {[∂A(θ)/∂θ)x]_k} > > You never need A^{-1} explicitly. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > www: http://www.math.colostate.edu/~bangerth/ > > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/0a3ade68-cbed-4551-8cba-67e49970217en%40googlegroups.com.
