杆系结构的几何非线性分析──Ⅱ．三维问题

Geometric non-linear analysis of frame structures──Ⅱ.3 dimensional problem

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，导出了空间Ｔｉｍｏｓｈｅｎｋｏ梁大位移、大转动问题内力分析的ＵＬ法（ＵｐｄａｔｅｄＬａｇｒａｎｇｉａｉ１Ｆｏｒｍｕｌａｔｉｏｎ）。本文考虑了轴向、剪切、弯曲和扭转效应，提出了新的几何刚度矩阵，并建立了描述大转动规律的坐标转换矩阵。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 the virtual work increment equation for the three-dimensional continuum,in-terpolating the translations and rotations respectively,the Updated Lagrangian formulation for large displacements and rotations internal force analysis of space Timoshenko beam struc-tures is developed.Considering the effect of axial,shearing,flecxural and torsional deforma-tions,a new type of geometric stiffness matrix is presented.The transformation rnatrix of co-ordinate was given for commutative law of large rotations.Numerical solution showed that the program devoloped by the proposed method 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 arbitrarily large rotations is able to be solved.