基于多因素耦合影响的薄壁梁材料非线性分析

综合分析了薄壁梁受轴向拉压、弯曲、剪切、扭转和翘曲以及轴力二次效应等耦合效应,根据Von Mises屈服准则及Prandtl-Reuss增量关系,推导出理想及强化弹塑性材料薄壁梁单元的增量本构关系.应用虚功原理,建立了薄壁梁单元精确模型的弹塑性增量刚度矩阵,并用高斯(Gauss)积分数值分析方法求得了该刚度矩阵,实现了薄壁梁多因素耦合影响下的材料非线性分析.通过与实体模型的算例比较,进一步验证了模型,说明该模型在薄壁杆系结构计算分析中,具有实体或其他模型无法替代的优点.

Material Nonlinear Analysis of Thin-Walled Beam Based on Diversified Coupling Factors

Based on the Von Mises yield rule and the Prandtl-Reuss increment relation,this article deduces the increment constructive relation of the ideal and intensified material.Through analyzing the various coupling effects such as axial extension or compression,bending,shear,torsion,warping and bio-effect of axial force,the article builds the precision analyzing model and the elasto-plastic increment stiffness matrix of the element under the principle of virtual displacement,solves the matrix by the multi-gauss numerical valve integral way,and realizes the material nonlinear analysis of the thin-walled beam under the multi-factor coupling effects.Finally,compared with the solid element,the numerical examples prove that the suggested model and method have high accuracy and practicability in the thin-walled beam structure,which shows it exceed the solid and other models in many ways.