一种密度约束的拓扑优化方法

A Density-constrained Topological Optimization Method

拓扑优化方法是改善结构性能、实现结构创新设计的有效手段。本文采用浮动映射技术,提出了一种密度约束的拓扑优化(Density-constrained topology optimization,DCTO)方法。该方法不同于SIMP方法,采用线性无惩罚材料插值模型,通过准则优化,首先找到结构的最优“厚度”(材料相对密度)分布,然后通过浮动映射函数不断对材料相对密度施加约束,使其逐渐趋于0/1分布。所提出拓扑优化方法的材料相对密度直接代表了材料在结构中的“厚度”分布,其求解原理与SIMP方法有着本质区别。数值算例表明,该方法得到的拓扑结构边界更清晰、光滑,且可避免材料插值模型选取问题。

Topological optimization is an effective means to improve structural performance and achieve totally novel designs.With the Heaviside projection function,this article presents a topological optimization method based on constraining the density design variables.The method adopts a linear material interpolation model without penalization,which is quite different from the solid isotropic material with penalization(SIMP)method.Its basic idea is,firstly,to find the optimal structural″thickness″(material density)distribution with the optimality criterion method.Secondly,sequential constraints are applied to the material density distribution through a floating projection function to push it towards a 0/1 distribution step by step.In this topological optimization method,the material density directly represents the material″thickness″distribution in the structure.Therefore the solutions of the proposed topological optimization method are fundamentally different from the SIMP method.Numerical examples demonstrate that the proposed method can obtain clearer and smoother structural topologies and avoid the difficulties in selecting artificial material interpolation schemes.