Topology optimization for concurrent design of structures with multi-patch microstructures by level sets

This paper focuses on the novel concurrent design for cellular structures consisting of multiple patches of material microstructures using a level set-based topological shape optimization method. The macro structure is featured with the configuration of a cluster of non-uniformly distributed patches, while each patch hosts a number of identical material microstructures. At macro scale, a discrete element density based approach is presented to generate an overall structural layout involving different groups of discrete element densities. At micro scale, each macro element is regarded as an individual microstructure with a discrete intermediate density. Hence, all the macro elements with the same discrete densities (volume fractions) are represented by a unique microstructure. The representative microstructures corresponding to different density groups are topologically optimized by incorporating the numerical homogenization approach into a parametric level set method. The multiscale concurrent designs are integrated into a uniform optimization procedure, so as to optimize both topologies for the macrostructure and its microstructures, as well as locations of the microstructures in the design space. Numerical examples demonstrate that the proposed method can substantially improve the structural performance with an affordable computation and manufacturing cost. (C) 2017 Elsevier B.V. All rights reserved.

本文聚焦于一种新颖的多孔结构并行设计，该结构由多个材料微观结构斑块组成，采用基于水平集的拓扑形状优化方法。宏观结构的特征是具有一组非均匀分布斑块的构型，而每个斑块包含若干相同的材料微观结构。在宏观尺度上，提出了一种基于离散单元密度的方法来生成涉及不同离散单元密度组的整体结构布局。在微观尺度上，每个宏观单元被视为具有离散中间密度的单个微观结构。因此，所有具有相同离散密度（体积分数）的宏观单元由一种独特的微观结构表示。通过将数值均匀化方法纳入参数化水平集方法，对对应于不同密度组的代表性微观结构进行拓扑优化。多尺度并行设计被集成到一个统一的优化过程中，以便同时优化宏观结构及其微观结构的拓扑以及微观结构在设计空间中的位置。数值算例表明，所提出的方法能够以可承受的计算和制造成本显著提高结构性能。（C）2017爱思唯尔有限公司。保留所有权利。