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以三维连续体的虚功增量方程为基础,采用平动和转角位移分别插值的方法,导出了三维空间梁结构大位移、大转动问题内力分析的 UL 法(Updated Lagrangian FormuIation)。考虑轴向、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 incremental equation of three-dimensional continuum, and using the methods of interpolation of translation and angular displacement respectively, the UL method for the analysis of the internal forces of the large-displacement and large-rotation problems of three-dimensional space beam structures is derived (Updated Lagrangian Formuation). Considering axial, shear, bending and torsion effects, a new geometric stiffness matrix is proposed and a coordinate transformation matrix describing a large rotation law is established. The example shows that the program compiled by the method of this paper has the ability to analyze the strong geometric nonlinear behavior of the structure. Under the condition that this hypothesis is satisfied (that is, the increment of the increment of the incremental middle rotation is a small amount each time), any large angle can be described. The rigid body rotates.