考虑惯性载荷的多材料结构拓扑优化

Topology Optimization of Multi-material Structures Considering Inertial Loads

基于导重法构建了惯性载荷作用下的多材料结构拓扑优化数学模型,在体积约束下使得其结构柔度最小.将多材料拓扑优化问题分解为一系列单材料拓扑优化问题,采用材料属性有理近似模型(Rational Approximation of Material Properties,RAMP)来表达密度与弹性模量间假定的非线性函数关系,利用导重法建立惯性载荷下设计变量的迭代表达式并通过数值算例验证导重法在考虑惯性载荷作用下多材料结构拓扑优化的有效性.算例结果表明:RAMP插值方法相比其他常用插值模型得到的拓扑构型更清晰,灰度单元更少,在算例1的对比中结构柔度最高降低了35.2%.受惯性载荷影响越大的设计区域其分布的材料弹性模量越大,且高模量密度比能够显著提升结构刚度.

This paper presents a mathematical model for the topological optimization of multi-material structures under inertial load based on the guide-weight method,which aims to minimize structural compliance while adhering to volume constraints.The topological optimization problem of multi-material structures is decomposed into topological optimization problems of single-material structures.Rational approximation of material properties(RAMP) was used to express the nonlinear relationship between density and elastic modulus.The guideweight method was employed to develop iterative expressions for design variables under inertial loads.Numerical examples demonstrate the effectiveness of this approach in optimizing multi-material structures under inertial loads.The results show that the RAMP interpolation method produces clearer topology configurations with fewer gray units and reduces structural compliance(up to 35.2% in example 1) compared with other general interpolation models.The greater the influence of inertial load on the design area,the higher the elastic modulus of distributed material.A high ratio of modulus to density can significantly increase the stiffness of a structure.