基于各向异性亥姆霍兹方程的空腔连通性约束拓扑优化设计方法

Structural Topology Optimization with Connectivity Constraints Based on Anisotropic Helmholtz Equation

针对增材制造加工拓扑优化结构存在的内部空腔难以加工和支撑材料无法去除的问题,提出一种基于各向异性亥姆霍兹方程的拓扑优化方法,能够简单有效地实现考虑空腔连通性约束的结构拓扑优化。首先,根据封闭空腔结构特点,定义了结构连续性作为结构连通性的等效描述,便于在拓扑优化框架内添加连通性约束;然后,采用各向异性亥姆霍兹方程,通过设置各向异性参数保证实体结构在特定方向上的连续性,构建了包含空腔连通性限制的拓扑优化模型;最后,采用MMA算法求解拓扑优化模型,实现了考虑空腔连通性约束的结构拓扑优化。多个优化算例结果表明,相比于传统方法,该方法能够在不添加新的约束条件和中间变量的基础上,即可抑制拓扑优化设计中封闭空腔结构的产生,构成面向增材制造的拓扑优化结构。同时,该方法很容易拓展到考虑传统制造约束的拓扑优化模型中,避免设计中出现封闭空腔结构。

With the framework for topology optimization via Solid Isotropic Material with Penalization method(SIMP),a novel and simple method for topology optimization based on Helmholtz equation is constructed to solve the problem of cavity connectivity in the topology optimization design for additive manufacturing.First,the structure continuity is defined as a new equivalent description of structural connectivity according to the characteristics of enclosed void in order to encapsulate connectivity constraints into the framework of topology optimization.Then,the anisotropic Helmholtz equation is used to ensure the continuity of the entity structure in a specific direction by setting different parameters,and the topology optimization model considering the cavity connectivity constraint is constructed.Finally,the MMA algorithm is used to solve the topology optimization model,and the limit of cavity connectivity is realized.Several optimization examples prove the performance of the proposed method for topology optimization of continuum structure with connectivity constraints for additive manufacturing without adding new constraints and intermediate variables compared with conventional methods.This method can also be easily extended to the topology optimization of continuum structure with conventional manufacturing methods to avoid enclosed void.