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arXiv · 2003.01215

Lagrangian-Eulerian Multi-Density Topology Optimization with the Material Point Method

Yue Li·Xuan Li·Minchen Li·Yixin Zhu·Bo Zhu·Chenfanfu Jiang
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Abstract

In this paper, a hybrid Lagrangian-Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with the Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian carrier particles to a fixed set of Eulerian quadrature points. This transfer is based on a smooth radial kernel involved in the compliance objective to avoid the artificial checkerboard pattern. The quadrature points act as MPM particles embedded in a lower-resolution grid and enable a sub-cell multi-density resolution of intricate structures with a reduced computational cost. A quadrature-level connectivity graph-based method is adopted to avoid the artificial checkerboard issues commonly existing in multi-resolution topology optimization methods. Numerical experiments are provided to demonstrate the efficacy of the proposed approach.

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Yue Li, Xuan Li, Minchen Li, Yixin Zhu, Bo Zhu, Chenfanfu Jiang. 2020-03-02. Lagrangian-Eulerian Multi-Density Topology Optimization with the Material Point Method. https://doi.org/10.1002/nme.6668

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