基于OpenSees的双层柱面网壳结构的非线性有限元可靠性分析

Nonlinear finite element reliability analysis of double-layer cylindrical shell based on opensees

在非线性有限元可靠度分析当中,经常会遇到两个障碍:对于特定的材料模型,约束函数会有不连续的梯度,导致搜索方法的不收敛;试算点离失效域太远,使得结果不能数值收敛[1]。针对这两个障碍,将OpenSees提供的光滑材料模型、改进和新的算法引入大跨度空间网格结构的非线性可靠度分析当中。通过应用光滑的Bouc-Wen材料模型解决了第一个障碍;通过修正已有的算法和引进新的算法解决了第二个障碍,除了已有的改进HL-RF算法、梯度映射法和SQP算法外,又首次将Polak-He算法引入到大跨度空间结构的非线性可靠度分析当中,并且对影响其收敛和计算速度的因素做了详细地阐述;结果发现SQP法和Polak-He算法计算效率较高,iHLRF法和梯度映射法效果较差。表明Polak-He算法是一种高效的计算方法,SQP法对功能函数的调用次数少,计算工作量少。通过引入光滑材料模型及几种算法,给大跨度空间结构的非线性可靠度分析带来方便,值得进一步推广。

In nonlinear finite element reliability analysis, two serious impediments are encountered： for certain material models, the constraint function may have a discontinuous gradient, leading to failure of the search algorithm to converge; The search algorithm may generate trial points too far in the failure domain, where the finite element code fails to produce a result due to lack of numerical convergence r^j Smoothed material, improved and new algorithms are introduced to address two impediments. Boue-Wen model addresses the first, and the second one is addressed by improved and new algorithms. Not only the iHL-RF, the Gradient Projection, and the SQP algorithms, but also the Polak-He algorithm is ap- plied in nonlinear reliability analysis of large-span spatial structure. The results show the SQP and the Polak-He algorithms are more efficient than the iHL-RF and the Gradient Projecton algorithms. The Po- lak-He algorithm is an efficient algorithm. Smoothed material model and algorithms makes nonlinear reliability more convenient, and should be extensively applied.