基于遗传算法的离散型结构拓扑优化设计

TOPOLOGY OPTIMIZATION DESIGN FOR DISCRETE STRUCTURES USING GENETIC ALGORITHM

采用遗传算法求解包括桁架结构和框架结构的离散型结构拓扑优化问题。在遗传算法的基础上,通过引入拓扑变量并修改被删除杆件的材料弹性模量,提出了一个受多工况荷载作用,能同时考虑应力、稳定及位移等约束的离散型结构拓扑优化问题统一数学模型。该模型不但能同时适用于桁架结构和框架结构等离散型结构拓扑优化问题,而且还能解决奇异最优解问题。结合上述统一数学模型和遗传算法,给出了求解离散型结构拓扑优化问题的优化方法。算例结果表明,采用该文提出的拓扑优化方法可有效、方便地对桁架结构、框架结构等离散型结构进行拓扑优化设计。

Genetic Algorithm （GA） is applied to solve the topological design optimization problems of discrete structures including truss structures and frame structures. On the basis of GA, a uniform mathematical model for topology optimization design of discrete structures subject to strength, stability, and displacement constraints under multiple loading conditions is presented by introducing topological design variables and modifying material elastic moduli of those inexistent bars. The given mathematical model is applicable to truss structures as well as frame structures, and singular optimization problems of discrete structures can also be resolved by using this model. A GA-based optimization method for the topological design of discrete structures with the uniform mathematical model is proposed. Several examples are given to demonstrate the effectiveness and the convenience of the proposed optimization method for the topological design of discrete structures including truss structures and frame structures.