预应力结构的最小挠度拓扑优化

Topology Optimization of Prestressed Structures for Minimum Deflections

传统的预应力结构设计通常采用分步方式进行,先获得不包含预应力的最优结构,再布置预应力索.这种方法获得的结构未必具有最优性能.为了获得最优的预应力结构,在结构的拓扑设计阶段考虑预应力的影响,建立优化模型.目标函数为结构特定位置的位移响应,拓扑变量为单元的密度,其中位移响应通过叠加法获得.给出了结构最佳预应力值的确定方法,并推导了目标函数的灵敏度计算方法.算例结果表明,所提出的优化模型具有有效性,所得结果明显优于传统方法的结果.

Conventional prestressed structures are usually obtained by two steps. An optimal structure without prestress is firstly designed, then the prestressed cables are distributed in the structure. Hence, the obtained prestressed structure is usually not the optimal one. The purpose of the study is to propose a structural optimization method to obtain really optimal prestressed structures. A topology optimization model is developed to take the prestress into account at the period of topology design of a structure. The objective function is the special displacement response of the structure, and the design variables are the elements densities. The displacement response is obtained by the superposition method. The method for the determination of the optimum prestress value of the structure as well as the sensitivity analysis is derived. The effectiveness of the optimization model is verified by some examples. The results show that the proposed method is superior to the conventional method.