几何非线性问题求解的改进算法

Newton-Raphson法和荷载增量法是求解几何非线性问题的两种常用方法。作为对这两种方法的补充,提出了将不平衡力向量在一个荷载步内逐级施加的改进算法,同时通过设置前后迭代循环单元轴向力的收敛精度改进了CR列式平面梁单元的多次循环迭代法。计算表明,这种方法对某些场合,如悬索桥的施工过程分析等,可取得很好的收敛效果,并能与已有的各种方法有机地结合起来。

Improved Method for Geometrically Nonlinear Analysis

Newton-Raphson Method and load increment method are two main methods for geometrically nonlinear analysis.As a complement for those methods,an improved method,which divides the unbalanced force vector into prescribed parts and makes them act gradually in one load step,was proposed.The n-cycle iteration scheme for 2-D beam element based on CR formulation was also improved by controlling the difference between the element axial force of current cycle and that of previous cycle.This method is proved to be able to improve convergence properties of the equilibrium iteration in some cases,for example in the construction process analysis of suspension bridge,and can be easily used in combination with other methods.