基于节点变量法的连续体结构拓扑优化设计

Topology Optimization of Continuum Structures Using Node Variable Method

为避免结构拓扑优化设计中的数值不稳定性及考虑制造因素,提出了一种节点变量的连续体结构拓扑优化设计方法。在指定的子区域内,采用不依赖网格的映射函数表示节点设计变量与节点密度变量的关系,实现最小尺寸约束,以满足加工工艺要求。以应变能力最小化为目标函数满足结构刚度要求,以结构体积作为约束,建立最小尺寸约束下的连续体结构拓扑优化模型,将移动近似算法用于拓扑优化问题求解。数值算例结果表明,提出的方法应用于连续体拓扑优化设计中是有效的,能够消除数值不稳定性现象获得清晰的拓扑结果,结构便于制造加工。

A topology optimization design of continuum structures using node variable method was proposed not only to avoid the phenomenon of numerical instabilities but also to consider the manufacturing requirements. Within the defined sub-domain, the projection function independent on element mesh was adopted to represent the relationship of node design variables and node density variables. It could achieve the minimum length scale constraint of the topological solution to meet processing requirements. With the objective function developed by the minimum strain energy to meet stiffness requirement, and the volume used as the constraints, the topology optimization model of continuum structure under minimum length scale constraints was developed. The method of moving asymptotes was adopted to solve the topology optimization problem. The numerical examples indicated that the approach could avoid the phenomenon of numerical instabilities and obtain distinct topological structure which is convenient for manufacturing.