考虑剪切变形和二阶效应的变截面构件的计算  

Calculation of tapered members considering shear deformation and second order effect

作　　者：苏骁 周东华[1] 王鹏[1] 滑硕 刘阳杰 何颖成[1] SU Xiao;ZHOU Donghua;WANG Peng;HUA Shuo;LIU Yangjie;HE Yingcheng(Faculty of Civil Engineering and Architecture,Kunming University of Science and Technology,Kunming 650500,China)

机构地区：[1]昆明理工大学建筑工程学院,云南昆明650500

出　　处：《交通科学与工程》2023年第1期52-58,共7页Journal of Transport Science and Engineering

基　　金：国家自然科学基金资助项目(51668027)。

摘　　要：同时考虑剪切变形和二阶效应来解析计算杆件的临界力,是求解变系数临界微分方程的难题。本研究采用有限元法推导了变截面单元刚度矩阵。采用三次Hermite插值函数和三次拉格朗日插值函数来计算单元内的弯曲变形和惯性矩变化。采用线性插值函数来计算单元内的剪切变形和截面面积变化。利用最小势能原理对总势能进行变分,系统给出了计入弯曲变形、剪切变形以及轴力二阶效应的变截面构件单元刚度矩阵。最后,用自编的有限元程序对算例进行验证。研究结果表明:本算法的计算精度较高,还可分析二阶位移放大系数以及变截面门式刚架立柱之间的支援作用。Simultaneously considering shear deformation and second-order effects to analytically calculate the critical load of a structural member is a challenging task in solving the variable coefficient critical differential equation.In this study,a finite element method was used to derive the stiffness matrix of a variable cross-section element.Third-order Hermite interpolation functions and third-order Lagrange interpolation functions were used to calculate the bending deformation and inertia moment changes within the element.Linear interpolation functions were used to calculate the shear deformation and cross-sectional area changes within the element.By using the minimum potential energy principle to vary the total potential energy,the stiffness matrix of the variable cross-section component element incorporating bending deformation,shear deformation,and axial force second-order effects was determined.Finally,the self-developed finite element program was used to perform calculations on the case studies.The research results indicate that this algorithm has good computational accuracy and can analyze the second-order displacement amplification factor and the support effects between variable cross-section portal steel frame columns.

关 键 词：变截面单元 有限元 单元刚度矩阵 剪切变形 二阶效应 

分 类 号：TU311[建筑科学—结构工程]