应力约束下桁架结构拓扑优化的静定基法

Method of Statically Determinate Base for the Topology Optimization of the Truss Structure under Multiple Loading Conditions with Stress Constraints

对于从基结构出发的单工况应力约束下使桁架结构重量最轻的最优拓扑,必定是静定结构;对于多工况应力约束下桁架结构的最优拓扑大多数是静定结构。而对于超静定结构的求解,目前的方法多是转化为静定的基本结构来求解。由此,本文提出一种求解桁架拓扑优化问题的新分析方法——静定基法,给出了静定基法的基本思想和求解策略,用解析方法求解了单工况应力约束下的桁架拓扑优化问题,研究了多工况应力约束下最优拓扑为静定结构的桁架结构,给出了优化问题的精确解。算例表明了该方法的有效性和可行性。

The topology optimization for truss structures with stress constraints under a single load condition, with minimum weight as the design objective, requires the structure to be statically determinate. And most of trusse structures to be topology optimized with stress constraints under multiple loading conditions are also statically determinate. To analyze the statically indeterminate structures, usually, they are transformed to statically determinate basic structures. In this paper, a new method based on statically determinate bases is proposed, which can be applied for topology optimization of truss structures with stress constraints under multiple loading conditions. The basic idea and the strategy of solution are given. In addition, an exact solution of the optimization is given by analytical method. Examples show that this method is efficient and reliable.