Lagrangian–Eulerian multidensity topology optimization with the material point method
Lagrangian–Eulerian multidensity topology optimization with the material point method
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DOI：
10.1002/nme.6668
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发表时间：
2020-03
影响因子：
2.9
通讯作者：
Yue Li;Xuan Li;Minchen Li;Yixin Zhu;Bo Zhu;Chenfanfu Jiang
中科院分区：
文献类型：
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作者：
Yue Li;Xuan Li;Minchen Li;Yixin Zhu;Bo Zhu;Chenfanfu Jiang
在本文中，提出了一种混合拉格朗日 - 欧拉拓扑优化（LETO）方法，用于结合物质点法（MPM）求解弹性力平衡问题。LETO将密度信息从可自由移动的拉格朗日载体粒子传递到一组固定的欧拉积分点。这种传递基于柔顺性目标中涉及的平滑径向核，以避免人为的棋盘格图案。积分点充当嵌入在较低分辨率网格中的MPM粒子，并能够以降低的计算成本实现复杂结构的子单元多密度分辨率。采用了一种基于积分级连通图的方法来避免多分辨率拓扑优化方法中普遍存在的人为棋盘格问题。提供了数值实验以证明所提出方法的有效性。
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 subcell multidensity 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 multiresolution topology optimization methods. Numerical experiments are provided to demonstrate the efficacy of the proposed approach.