三维杆系结构的几何非线性有限元分析

为了更准确地描述杆系结构的几何非线性性能,建立了一种基于三维梁单元有限元分析的计算方法。引入了考虑两方向曲率和扭转角变化的坐标转换矩阵来描述任意增量下的单元平移和转动;采用了包括轴向变形和扭转的非线性项的刚度矩阵来考虑高阶非线性项的影响。应用广义位移控制法进行增量迭代,编制了相应的三维梁单元非线性计算程序NL_Beam3D。通过对几个例子进行的分析,验证了该方法可较好地考虑结构几何非线性。

A GEOMETRIC NONLINEAR FINITE ELEMENT ANALYSIS FOR 3D FRAMED STRUCTURES

For further studies on geometric nonlinearity of framed structures, a finite element method based on beam element is developed. To describe the changing status of incremental displacements and rotations, the curvatures in two directions and torsional angle are considered in the orientation matrix. The influence of higher order nonlinearity term is considered by introducing axial and torsional deformation nonlinear items into the stiffness matrix. A corresponding compter program of 3D beam, NL Beam3D, using general displacement control method in iterative analysis, is presented. The accuracy of this method is verified by some examples.