基于应力约束的多相材料结构拓扑优化设计

Topology optimization of multiple materials continuum structure with stress constraints

传统的固体各向同性材料惩罚模型(SIMP)难以准确描述多相材料结构应力约束拓扑优化问题,鉴于此,提出一种基于可分离应力插值模型的多相材料结构应力约束拓扑优化设计方法。利用可分离应力插值模型计算多相材料结构的刚度和应力,以结构的体积最小化作为目标函数,采用改进的P范数求解各相材料结构的最大应力,以各相材料结构的最大应力作为约束,建立多相材料的结构全局应力约束拓扑优化模型,利用设计变量过滤技术避免数值不稳定性现象,采用移动渐近线优化算法求解多相材料结构应力约束拓扑优化问题。数值算例结果表明,采用多相材料结构全局应力约束拓扑优化获得的结构更加合理,能够有效地避免应力集中现象。

The standard Solid Isotropic Material with Penalization(SIMP)model is impossible to accurately describe the problem for topology optimization of multiple materials continuum structure with stress constraints.A method for topology optimization of multiple materials continuum structure with stress constraints using the separable stress interpolation model was proposed.The element stiffness and element stress for multiple materials structure was calculated with the separable stress interpolation scheme.The minimum volume of the structure was developed as the objective function,and the modified P norm was applied to solve the maximum stress for each phase material structure.The maximum stress for each material was used as the constraint,and the model for topology optimization of multiple materials continuum structure with global stress constraints was established.The filtering techniques of design variables were used to avoid the phenomenon of numerical instability.The moving asymptotic optimization algorithm was applied to solve the optimization problem.Numerical results showed that the structures obtained by topology optimization of multiple materials continuum structure with global stress constraints were more reasonable and the stress concentration could be avoided effectively.