Efficient topology optimization using compatibility projection in micromechanical homogenization

2021/07/07 by Jödicke, Indre, Leute, Richard J., Junge, Till +1 · 1 citation
#Computational Engineering #FOS: Computer and information sciences #Finance #and Science (cs.CE)

paper · doi:10.48550/arxiv.2107.04123

Abstract

The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas Fourier-based solvers have recently shown large efficiency gains for homogenization problems. In this paper, we derive the discrete adjoint method for Fourier-based solvers that employ compatibility projection. We demonstrate the method on the optimization of composite materials and auxetic metamaterials, where void regions are modelled with zero stiffness.

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