结构非线性分析的变步长增量迭代法研究

A Study of Variable Step-length Incremental/Iterative Method for Nonlinear Structural Analysis

本文深入研究了结构非线性分析的变步长增量迭代法。对目前常用的不变步长增量迭代法、控制位移增量法和控制弧长法作了简单的几何解释。从力学概念出发,建立了零位移增量范数、零残余力范数和零增量功等三种新的迭代控制约束方程。讨论了初始荷载增量步长的自动选择方法。通过对二圆柱壳Snap through和Snap back响应的分析,研究了上述各种变步长增量迭代法的有效性和可靠性。

In this paper we make a deep study on variable step-length incremental/iterative method for nonlinear structural analysis. Simple explanations are given for constant step-length incremental/iterative method, single displacement controlling method and arc length controlling method from their geometric characteristics in load-deformation responses. Based on the mechanical concept, three new constraint.equations (i. e. zero incremental displacement norm, zero residual force norm and zero incremental work) are established for controlling iteration path. The automatic selection method of initial load increment is discussed. The reliability and efficiency of the afore-mentioned methods are studied through tracing snap through and snap back responses of two cylindrical shells.