轴力二次效应对梁单元的耦合影响

在6个自由度有限梁元基础上,采用单一系数将轴力二次效应对梁单元的影响引入到梁的分析刚度矩阵中,并考虑到梁单元约束扭转时不可避免发生翘曲作用,增加了翘曲角自由度,建立了即能用于通常梁,更能适用于薄壁梁单元的7个自由度的单元分析统一模型,同时将轴向力、弯矩和双力矩的贡献引入到几何刚度矩阵中,得出了综合考虑轴向拉压、弯曲、扭转以及轴力二次效应和翘曲及其耦合影响的变形状态刚度矩阵.线性和非线性算例均表明轴力二次效应对细长构件结构内力和位移的影响不能忽视.

Coupling Influence of the Second Effect of the Axial Force on Beam Element

On the basis of the 6 degrees of freedom beam elements,the paper used the single coefficient to introduce the second effect of the axial force on the stiffness matrix of the beam element,and by adding the freedom of warping angle to consider the beam elements' warping deformation during the restrained torsion,the 7 degrees of freedom united model established is not only applied on the common beam structure but also on the thin-walled beam structure.At the same time,by considering the contribution of the axial force,bend moment and bio-moment in the geometric stiffness matrix,the tangent stiffness matrix under the deforming state is received which can analyze all the factors,such as the axial pulling and pushing,bending,twisting,warping and second effect of axial force as well as their coupling influence.The linear and nonlinear examples indicate that the second effect of the axial force on the analysis of the inner force and displacement of the slightness members' structure can not be neglected.