基于鲁棒性优化的桁架结构失效-安全设计

FAIL-SAFE OPTIMAL DESIGN OF TRUSS STRUCTURES BASED ON ROBUST OPTIMIZATION

基于鲁棒优化思想,提出了桁架结构失效-安全优化设计问题的双层规划算法.其中上层规划用来寻找杆件的最优尺寸,而下层规划的目标是确定结构最不利的失效模式.为了获得下层优化的全局最优解,以保证所得到的最优结构真正安全可靠,特别地还发展了相关问题求解的混合0-1规划算法.与以往研究工作相比,该方法不需要预先假定破坏模式,因此更容易获得理论上最优的结果.数值算例表明了所提出方法的有效性.

Traditional fail-safe optimal design was always performed based on a prior assumed failure mode. However,the assumed failure mode may not necessarily be the most dangerous one,and if this is the case,then the reliability of the obtained optimal solution cannot be guaranteed.To circumvent this difficulty,in the present paper,fail-safe optimal design is carried out in a robust optimization framewok.The problem is formulated in a Bi-level form.The upper level program aims at finding the optimal design variables while the lower level program is solved to find the worst case failure mode.In order to find the global optimal solution of the lower level program,a mixed 0-1 programming is proposed and solved with the branch-and-bound algorithm.The effectiveness of the proposed approach for fail-safe design and optimization are illustrated by some numerical examples.