A discrete sine–cosine based method for the elasticity of heterogeneous materials with arbitrary boundary conditions
Résumé
The aim of this article is to extend Moulinec and Suquet (1998)'s FFT-based method for heterogeneous elasticity to non-periodic Dirichlet/Neumann boundary conditions. The method is based on a decomposition of the displacement into a known term verifying the boundary conditions and a fluctuation term, with no contribution on the boundary, and described by appropriate sine-cosine series. A modified auxiliary problem involving a polarization tensor is solved within a Galerkin-based method, using an approximation space spanned by sinecosine series. The elementary integrals emerging from the weak formulation of the equilibrium are approximated by discrete sine-cosine transforms, which makes the method relying on the numerical complexity of Fourier transforms. The method is finally assessed in several problems including kinematic uniform, static uniform and arbitrary Dirichlet/Neumann boundary conditions.
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