基于应变能的预应力平面实体结构拓扑优化设计

研究了预应力平面实体钢结构拓扑优化设计问题。建立了以索力值和结构拓扑为设计变量,以结构储存应变能为约束条件,以结构重量最小为目标函数的数学优化模型。在求解方法上,首先以结构储存应变能最小(刚度最大)确定施加在结构上的索力值,然后采用渐进结构优化法(ESO方法)删除低应变能的单元实现结构的拓扑优化并减轻结构重量。算例结果与相应体系受力性能的结论相吻合,表明本文所提出的优化方法是可行的。

TOPILOGY OPTIMIZATION DESIGN OF PRESTRESSED PLANE ENTITY STRUCTURES BASED ON STRAIN ENERGY

A topology optimization design method for prestressed plane entity steel structrues is proposed. The optimization mathematical model is established in such a form that the cables' pretension force and the structural topology are design variables, the structural total strain energy is constrain condition, and the minimum structural weight is the objective function. Then, the cables' pretension force can be determined by minimizing structural strain energy (maximizing structural stiffness). After that, the method of evolutionary structure optimization (ESO) is applied to achieve structural topology optimization by deleting elements with low strain energy, and the structural weight is also reduced. The example result coincides with the corresponding structural performance, which indicates the proposed optimization design method is feasible.