杆系结构的几何非线性分析──Ⅰ．平面问题

Geometric non-linear analysis of frame structures Ⅰ. 2 dimensional problem

本文以三维连续体的虚功增量方程为基础，采用平动、转角位移分别插值的方法，导出了梁结构大位移、大转动问题内力分析的ＵＬ法。本文考虑了轴向、剪切和弯曲效应，提出了新的几何刚度矩阵。算例表明，依本文方法编制的程序具有分析结构强几何非线性行为的能力；在满足本文位移假定（即每次加载增量中转角增量是小量）的条件下，可以描述任意大角度的刚体转动。

Based on thevirtual workincrement equation for thethree-dimensional continuum,in-terpolating the translations and rotations respectively,the Updated Lagrangian forrnulationfor large displacements and rotations analysis of beam structures is developed .Consideredthe effect of axial.shearing and flexural deformations,a new type of geometric stiffness ma-trix is presented.Numerical solution showed that the program developed by the proposedmethod in this paper is available for the analysis of strong non-linear behavior of structures.Under the assumption of rotational increment in every step is small,problem of arbitrarilylarge rotions is able to be solved.