An Algorithm of Generating Consistent Stiffness Matrices for Incremental Analysis of Elastic-plastic structures

在弹塑性结构临界行为的增量分析中，寻找与物质流动规律一致的单元刚度系数集的传统迭代方法往往会导致循环过程的陷阱，即交替或反复选择一致的刚度系数集的倍数。这是组合非线性分析中尚未解决的最严重的难题之一。本研究以简单刚体-弹簧柱模型Shanley模型阐明了这些循环过程的内在机理和特征。在此基础上，提出了一种利用系统刚度矩阵最小负特征值对应的特征向量作为比较体寻找一致集的有效策略。

In the incremental analysis of the critical behavior of an elastic-plastic structure, a conventional iterative procedure for finding the set of element stiffness coefficients consistent with the material flow law may often lead to a pitfall of cyclic process, in which a multiple in consistent sets of stiffness coefficients are to be alternately or recurrently selected. This is one of the most serious difficulties left unsolved in combined nonlinear analysis. In this study, the intrinsic mechanism and characteristics of these cyclic processes are clarified for a simple rigid body-spring column model called Shanley model. On the basis of the results, an effective strategy for finding the consistent set is proposed with the use of the eigenvector associated with the smallest negative eigenvalue of system stiffness matrix as the comparison body.