考虑自重影响的拓扑优化方法

A Topology Optimization Method Considering the Effect of Self-Weight

针对在考虑自重影响的连续体结构拓扑优化中常见的问题,本研究提出一种新的拓扑优化方法。首先,为避免寄生效应,提出一种带惩罚的固体各向同性材料(SIMP)改进模型,建立刚度模量、质量密度和体积光滑惩罚函数三者间的合理匹配关系。同时,引入密度过滤、Heaviside映射的三场过滤方案,并提出一种低物理密度单元的体积变化率约束措施,从而极大地提高考虑自重效应的结构拓扑问题的优化计算效率,获得清晰的0-1分布。基于上述方法,建立以结构柔顺度最小为目标,同时考虑变体限约束、位移约束以及低物理密度单元的体积变化率约束等措施的优化模型。最后,采用MMA算法对优化模型进行求解,并通过算例验证本研究所提出的方法是正确有效的。

Aiming at the common problems in topology optimization of continuum structures considering the influence of self-weight,this paper proposes a new topology optimization design method.First,to avoid parasitic effects, an improved Solid Isotropic Material with Penalty(SIMP) model is proposed,which establishes a reasonable matching relationship between stiffness modulus and bulk smoothness penalty function.At the same time,a three-field filtering scheme of density filtering and Heaviside mapping is introduced, and a volume change rate constraint measure for low physical density cells is proposed to greatly improve the optimization calculation efficiency of structural topology problems considering selfweight effects,and obtain clear 0-1 distributionBased on the above method,an optimization model is established,which takes the minimum structural compliance as the goal,and considers the constraints of the variation limit and the volume change rate of the low physical density element.Finally,the MMA algorithm is used to solve the optimization model.And the method proposed in this paper is verified to be correct and effective by an example.