Lagrangian–Eulerian multidensity topology optimization with the material point method

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