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 sine–cosine 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.

中文翻译：

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一种基于离散正弦-余弦的任意边界条件下非均质材料弹性的方法


本文的目的是将 Moulinec 和 Suquet （1998） 基于 FFT 的异质弹性方法扩展到非周期性狄利克雷/诺依曼边界条件。该方法基于将位移分解为验证边界条件的已知项和波动项，对边界没有贡献，并由适当的正弦-余弦级数描述。在基于 Galerkin 的方法中，使用跨越正弦-余弦级数的近似空间求解涉及极化张量的修正辅助问题。从平衡的弱公式中出现的基本积分由离散正弦-余弦变换近似，这使得该方法依赖于傅里叶变换的数值复杂度。最后，在运动学均匀性、静态均匀性和任意 Dirichlet/Neumann 边界条件等几个问题中对该方法进行了评估。