计入初始应变项的平面梁单元非线性刚度矩阵

开展平面结构几何非线性分析时经常会遇到杆件含有初始应力力或初始应变的情况。由于非线性刚度矩阵中含有节点位移,矩阵运算量大,给刚度矩阵的推导带来很大困难。根据平面梁单元几何非线性方程,采用计入初始应力和初始应变项的一般性线弹性应力应变关系,导出了相应的切线刚度矩阵,利用MATLAB数学工具箱,给出了含有初始应力和初始应变的所有刚度矩阵的显式表达式,为程序编制奠定了基础。

Nonlinear Stiffness Matrices of Plane Beam Element Including Initial Stress and Strain Item

There were often happened cases for beam elements with initial stress or initial strain while the geometrically nonlinear analysis was performed for the plane structure.The deduction of stiffness matrices was awfully difficult because the nonlinear stiffness matrices included node displacement vectors and extensive matrix operations.Based on the nonlinear geometric equation of plane beam element and general elastic relationship of stress-strain including initial stress and initial strain,the tangent stiffness matrix was derived.All explicit formula of stiffness matrices including initial stress and strain item have been developed by use of the MATLAB Mathematical Tools.The results are of great significance to the nonlinear finite element programming for plane beam elements.