桁架拓扑优化几何稳定性判定法和约束方案比较

为提高桁架结构几何稳定性的判定准确度和桁架拓扑优化结果的工程实用性，对桁架结构几何稳定性的判定方法和桁架结构拓扑优化问题中3种几何稳定约束方案的有效性进行了比较研究。首先结合简单桁架示例，对比了判定桁架结构几何稳定性的几种方法，给出评估桁架结构几何稳定性的一种简单流程；然后对处理桁架结构几何稳定性的3种常见约束方案，给出了对应拓扑优化问题的一个统一的半定规划（SDP）模型；最后结合算例讨论了3种几何稳定约束方案下的拓扑优化结果，说明了不同方案的有效性。结果表明，考虑附加载荷或全局稳定约束均不能保证优化后桁架结构的几何稳定性，但在约束值合理设置的情况下，考虑基频约束则可以保证。 

Comparison of determining methods and constraint schemes for geometric stability in truss topology optimization

To improve the accuracy of determining truss geometric stability and the practicability of truss topology optimization results, several ways of determining truss geometric stability were compared, and the validity of three schemes for guaranteeing truss geometric stability of topology optimization results were discussed. First, by comparing several ways to identify truss geometric stability through some illustrative tiny trusses, a simple procedure was outlined to evaluate truss geometric stability. Second, a unified semidefinite programming (SDP) formulation of the truss topology optimization problem was established for three kinds of constraints to address the geometric stability issue. Finally, three truss structures were optimized with the SDP formulation, and the geometric stabilities of the resultant trusses were evaluated by the given simple scheme to reveal the validity of the three kinds of constraints to guarantee geometric stability. The results show that considering additional loads or the global stability constraint cannot guarantee the geometric stability of the optimized trusses while the fundamental frequency constraint can do when the constraint values are reasonably chosen.