非线性有限元分析与分叉问题数值方法

Nonlinear Finite Element Analysis and Numerical Methods for Bifurcation Problems

非线性有限元分析和分叉问题的数值方法研究是当今计算力学领域中受重视的研究方向之一。虽然在单元构造、非线性分析与分叉数值方法方面已有长足进展，但迄今为止，可以用于实际复杂结构分叉问题的方案还存在不少困难。本文对有限元的发展作了简要回顾，并介绍了一种有效的用于分叉计算的数值方法。文末以实际上常见的平面杆系结构为对象。

Research on nonlinear finite element analysis and numerical methods for bifurcation problems is one of the noticed directions in the field of computational mechanics at present.There have been a lot of advances in element construction,nonlinear analysis and numerical methods for bifurcation problems,but up to now,there are few of the programmes which can be used in numerical analysis for bifurcation problems of complicated structures.In this paper,firstly,the history of finite element method and numerical methods for nonlinear analysis and bifurcation problems are reviewec.Then the pseudo-arc-length continuation method,as one of the important methods for nonlinear problems,is introduced.Finally,a practical scheme for solving large deflection of structures of planar bar systems including bifurcation problems,is given.