北京大学学报（自然科学版）2017，Vol.53Issue(5)：793-800,8.DOI:10.13209/j.0479-8023.2017.072
非线性有限元方程组的弧长延拓算法
Arc-Length Continuation Algorithm for Nonlinear Finite Element Equations
摘要
Abstract
Stability analysis of engineering structures requires tracing equilibrium path of the structure when member's buckling or material softening occurs. In nonlinear finite element analysis, the traditional Newton method fails at limit point and bifurcation point. The arc-length continuation method can overcome these numerical difficulties. To develop a nonlinear finite element code for stability analysis, the standard iteration formulation of Newton method is presented for the arc-length continuation method. Two practical formulations of the arc-length continuation method and their relationships with the standard form are also discussed. The applicability of the practical formulation is examined by the finite element analysis of stability for a slope.关键词
弧长延拓算法/平衡路径曲线/非线性分析/牛顿迭代法/有限元方法Key words
arc-length continuation algorithm/equilibrium path curve/nonlinear analysis/Newton iteration method/finite element method分类
通用工业技术引用本文复制引用
殷有泉,邸元,姚再兴..非线性有限元方程组的弧长延拓算法[J].北京大学学报（自然科学版）,2017,53(5):793-800,8.基金项目
国家科技重大专项(2016ZX05014)和国家自然科学基金(51674010)资助 （2016ZX05014）
