用拓扑优化设计多体分比蜂窝状结构

摘要

提出用拓扑优化及增材制造法设计同一材料制作的蜂窝状结构，并把设计可归结为在不同的设计域内使用不同的体分比的拓扑优化问题。首先推导了多体分比约束条件下的蜂窝状结构拓扑优化问题；然后提出了基于多阈值的等值面法及与商用有限元分析软件对接的算法。给出了有三个体积约束的最小柔顺性问题的数值算例。计算结果表明，对于具有三个体积约束的拓扑优化设计问题，存在一个最佳的体积约束组合；使用等量的材料，与两个体积约束的最佳拓扑设计相比，用最佳体积约束组合所得到的优化结构的柔顺性还要小10%。%This study presents a method for finding optimum topology of cellular structure made from one material using an appropriate addition manufacturing process and tailored with different volume fractions in different struc-tural domains.The topology optimization problem is firstly formulated allowing multi-volume fractions in cellular structures.An algorithm based on MIS T with multi-thresholds is presented and interfaced with commercial finite element analysis software.Numerical examples for the minimum mean compliance problem with three volume frac-tions are presented to illustrate the present algorithm.The present numerical results show that,for the optimum topology design with three volume fractions,there exists an optimum combination that yields an additional 10% re-duction in the minimum mean compliance when compared to the design with two volume fractions.