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.
@article{arxiv.2003.01215,
title = {Lagrangian-Eulerian Multi-Density Topology Optimization with the Material Point Method},
author = {Yue Li and Xuan Li and Minchen Li and Yixin Zhu and Bo Zhu and Chenfanfu Jiang},
journal= {arXiv preprint arXiv:2003.01215},
year = {2021}
}