采用多点逼近遗传算法的屈曲约束下桁架拓扑优化
Truss Topology Optimization with Buckling Constraints Solved by Multi-point Approximation and Genetic Algorithm

基于线弹性屈曲理论，讨论了杆单元建模及欧拉单杆失稳判据在桁架结构稳定性分析中的缺陷。为更精确地获得桁架屈曲响应，建议以梁单元进行有限元建模，并利用特征值屈曲分析来获取结构各阶失稳载荷因子及屈曲模态。分析了从基结构法出发求解特征值屈曲约束下桁架拓扑优化问题所存在的求解困难与奇异性。为有效求解该类问题，采用了多点逼近遗传算法，对离散拓扑变量和连续尺寸变量进行了联合优化。同时，通过屈曲模态识别、删除杆件屈曲模态过滤、局部约束临时删除等措施，特征值约束下的求解困难和删除杆件在优化过程中的不利影响也得到了克服。数值算例验证了本文结构建模及优化方法的有效性，同时也表明了该方法具有较高的效率，能够凭借较少的结构分析次数来获得优化解。
Based on the elastic buckling theory, the paper discussed the insufficiency of rod elements with Euler buckling criterion while conducting the stability analysis for truss structures. In order to obtain relatively more accurate buckling responses, beam elements were supposed to be adopted in truss modeling. After that, buckling load factors as well as buckling modes could be obtained via eigenvalue buckling analysis. Then, from the point of ground structure method, the paper pointed some solving difficulties and the singularity of truss topology optimization problems under eigenvalue buckling constraints. To handle such problems effectively, the multi-point approximation algorithm combined with genetic algorithm was implemented to optimize both the discrete topology variables and the continuous sizing variables coordinately. In the meantime, several techniques, such as recognition of buckling modes, filtration of buckling on removed bars, temporary deletion of local constraints, were proposed and applied to tackle the solving difficulties and the singularity. At last, the effectiveness of the optimization strategy was verified by numerical examples. Besides, the efficiency of the method was also presented as the optimization could be achieved through relatively small number of structural analysis