应力约束全局化策略下的连续体结构拓扑优化

TOPOLOGICAL OPTIMIZATION OF CONTINUUM STRUCTURE UNDER THE STRATEGY OF GLOBALIZATION OF STRESS CONSTRAINTS

利用Mises强度理论,提出了应力约束全局化策略,将局部的应力约束问题转化为结构整体的应变能约束问题．基于ICM(独立、连续、映射)方法,引入了独立、连续的拓扑变量,对单元重量、单元刚度和单元许用应力的过滤函数进行了选择,建立了以重量为目标,以结构应变能代替应力约束的多工况下连续体结构拓扑优化模型,寻找到了多工况下的最佳传力路径．运用对偶二次规划方法对上述优化模型进行了求解．另外,利用PCL语言,在MSC／PATRAN的开发平台上,实现了应用应力约束全局化策略进行连续体结构拓扑优化的模块化处理．数值算例表明了该方法的可行性和有效性．

Since the stress is a local quantity, a large number of constraints must be considered in the topology optimization of continuum structure. This increases the computational complexity of both the optimization algorithm and sensitivity analysis. A strategy with globalization of stress constraints is proposed based on yon Mises＇ yield criterion. The local stress constraints of element are transformed into the global strain energy constraints of structure. Based on ICM （Independent, Continuous, Mapping） method, independent continuous topological variables are introduced; a suitable set of Filter functions of element with respect to weight, allowable stress and stiffness is selected. The optimal topology model of continuum structure is established with weight as objective and subjected to strain energy constraints with multiple load cases. The best path transmitted force in the multiple load cases is selected successfully. Furthermore, the dual quadratic programming is applied to solve the optimal model of continuum. In addition, the present optimal model and its algorithm have been implemented by means of the MSC/Patran software platform using PCL （Patran Command Language）. Numerical examples indicate that the method is efficient.