Worst case plastic limit analysis of trusses under uncertain loads via mixed 0-1 programming
Worst case plastic limit analysis of trusses under uncertain loads via mixed 0-1 programming
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DOI：
10.2140/jomms.2007.2.245
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发表时间：
2007-04
影响因子：
0.9
通讯作者：
Y. Kanno;I. Takewaki
中科院分区：
文献类型：
--
作者：
Y. Kanno;I. Takewaki
本文提出了一种计算未知但有界荷载作用下桁架最小极限荷载系数的全局优化方法。我们假设外力由与载荷系数成正比的部分和围绕其名义值不确定的部分组成。引入了最坏情况极限载荷系数，作为在某些不确定参数下实现的最小极限载荷系数。为了发现最坏情况，我们必须找到一个非凸优化问题的全局最优解，这是最坏情况极限分析的主要困难。将最坏情况判定问题转化为混合0-1规划问题，提出了一种基于线性规划松弛的分支定界法和基于析取或提升投影割的割平面法相结合的全局优化算法。通过计算最坏情况下的极限载荷以及相应的临界载荷模式，证明了该方法能够成功地收敛到全局最优解。
The paper presents a global optimization method to compute the minimum limit load factor of trusses subjected to unknown but bounded loads. We assume that the external forces consist of a part proportional to a load factor and a part that is uncertain around its nominal value. The worst-case limit load factor is introduced as the smallest limit load factor realized with some uncertain parameters. In order to detect the worst case, we have to find the global optimal solution of a nonconvex optimization problem, which is the major difficulty of the worst-case limit analysis. By reformulating the worstcase determination problem as a mixed 0-1 programming problem, we propose a global optimization algorithm as a combination of a branch-and-bound method based on the linear programming relaxations and a cutting plane method based on the disjunctive or lift-and-project cuts. The worst-case limit loads, as well as the corresponding critical loading patterns, are computed to demonstrate that our method converges to the global optimal solutions successfully.