热力耦合结构的弹性支撑分析与拓扑优化设计

弹性支撑是保证热力耦合载荷作用下结构有效承载的一种支撑设计方案, 可以在满足结构刚度设计要求的同时有效降低结构内的应力集中, 保证结构的热变形协调. 从理论分析与数值计算两个方面, 研究了热力耦合载荷作用下结构的弹性支撑优化设计. 首先以弹性支撑梁模型为例, 通过给出热力耦合载荷下应力计算的解析表达式, 从理论上说明弹性支撑对结构应力峰值的影响, 阐述了弹性支撑的承载与热变形协调的双重效果. 在此基础上, 提出了解决该类问题的弹性支撑通用优化数学模型和拓扑构型优化方法, 通过数值算例与优化结果展示了方法的有效性.

ANALYSIS AND TOPOLOGY OPTIMIZATION OF ELASTIC SUPPORTS FOR STRUCTURES UNDER THERMO-MECHANICAL LOADS

Elastic supports are recognized as an efficient means for structural designs under thermo-mechanical loads.Their introduction is beneficial not only for the achievement of the specific structure stiffness but also for the reduction of stress intensities to match the thermal deformation of the structure.In this paper,both theoretical and numerical studies are carried out to optimize the elastic support under thermo-mechanical loads. First,the analytical expression of the maximal thermo-mechanical stress is derived for a beam model with elastic support to illustrate the effects of the load-bearing and thermal deformation coordination of the elastic support. On this basis,a general topology optimization model and related topology optimization methods are proposed. Numerical examples and results are presented to demonstrate the validity of the proposed approach.