几何非线性新梁柱单元及结构程序设计

基于更新拉格朗日构形的增量虚位移原理,在其势能项中引入了全部6个应力分量,采用可计入单元剪切变形影响的三次多项式插值函数,详细推导了考虑剪切变形及翘曲的空间梁—柱单元几何非线性切线刚度矩阵。根据面向对象的程序设计思想,将整个有限元域划分为8个基本类,在单元基类的基础上派生了新的单元类,采用C++语言编制了面向对象的空间钢结构分析程序。几何非线性算例分析结果表明,本文提出的理论分析方法和计算程序是正确的和高效的。

A geometric nonlinear new beam-column element and structure program design

According to the increment virtual displacement principle based on the updated Lagrange configuration,the potential energy associated with all six stress components was taken into account.The cubic interpolation function which can be used to consider the shear deformation effects has been applied to derive the geometrical nonlinear stiffness matrix of the space beam-column element considering the shear deformation and warping effects.Based on the object-oriented design conception,the finite element analysis domain is divided into eight classes.A new class is derived from the base element class.Using C++ language,the spatial steel frame advanced analysis program is complied.Numerical examples including both geometric and material nonlinearities are used to demonstrate the accuracy and efficiency of the proposed analytical method and computer program.