考虑剪切变形的变截面构件的变形计算  

Deformation calculation of variable cross section member considering shear deformation

作　　者：滑硕 周东华[1] 王鹏[1] 苏骁 刘阳杰 何颖成[1] HUA Shuo;ZHOU Donghua;WANG Peng;SU Xiao;LIU Yangjie;HE Yingcheng(Construction Engineering College,Kunming University of Science and Technology,Kuming 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》2022年第3期94-99,共6页Journal of Transport Science and Engineering

基　　金：国家自然科学基金(51668027)。

摘　　要：变截面构件在工程中应用较为广泛,但变形计算则较为复杂。本研究采用拉格朗日插值函数表示单元内的惯性矩和面积的变化,再分别用埃尔米特和拉格朗日插值函数计算单元内的弯曲变形和剪切变形,并根据势能驻值原理得到适用于多种变截面构件的变截面弯曲单元刚度矩阵,最后通过分析力的平衡条件和构件挠度的几何关系,得到考虑剪切变形的变截面弯曲单元刚度矩阵。采用自编的有限元程序与ANSYS分别对算例进行计算分析,讨论圆形构件和环形抵抗剪切变形的影响程度。研究结果表明:算例验证了单元刚度矩阵的正确性,对比发现由变截面构件组成的结构受力性能优于等截面构件组成的结构。Variable cross-section member are widely used in engineering. However,the deformation calculation is complicated. In this paper,the Lagrange interpolation function was used to reflect the change of inertia moment and area in the element. The Hermite and Lagrange interpolation functions were then used to calculate the bending deformation and shear deformation.Consequently,the stiffness matrix of variable cross-section bending element,suitable for different variable cross-section member,could be obtained according to the principle of potential energy standing value. Finally,the stiffness matrix of variable cross-section bending element could be obtained considering shear deformation,while the balance condition of force and the geometric relationship of member deflection were analyzed.The self-made finite element program and the ANSYS were used to calculate the example,verifying the correctness of the element stiffness. It was found that the meachcanical performance of structure composed of variable cross-section is better than that of the structure composed of equal cross-section.

关 键 词：变截面 插值函数 剪切变形 单元刚度矩阵 

分 类 号：TU318[建筑科学—结构工程]