具有动应力、位移和稳定性约束的离散变量桁架结构布局优化设计算法

Approach for Layout Optimization of Truss Structures With Discrete Variables Under Dynamic Stress,Displacement and Stability Constraints

给出了在动应力、动位移和动稳定约束下离散变量结构布局优化设计问题的数学模型,用“拟静力”算法,将具有动应力约束、动位移约束和动稳定约束的离散变量结构布局优化设计问题化为静应力、静位移和静稳定约束的优化问题,然后利用两级优化算法求解该模型.优化过程由两级组成,拓扑级优化和形状级优化.在每一级,都使用了综合算法,并且在搜索过程中都根据两类设计变量的相对差商值进行搜索.对包含稳定约束和不包含稳定约束的优化结果做了比较,结果显示稳定性约束对优化结果产生较大的影响.

A mathematical model was developed for layout optimization of truss strucinres with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization trader the dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures included two parts, i.e. the topology optimization and the shape optimization. In each procedure, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.