T形截面轴压短柱畸变屈曲的无穷级数解与FEM验证  

Infinite Series Solution and Finite Element Verification for Distorted Buckling of T-shaped Short Columns under Axial Compression

作　　者：张文福 郭雪妞[1] 黄斌 杭昭明 ZHANG Wenfu;GUO Xueniu;HUANG Bin;HANG Zhaoming(School of Civil Engineering,Anhui Jianzhu University,Hefei Anhui 230601;School of Architectural Engineering,Nanjing Institute of Technology,Nanjing Jiangsu 211167;School of Civil Engineering and Architecture,Northeast Petroleum University,Daqing Heilongjiang 163318)

机构地区：[1]安徽建筑大学土木工程学院,安徽合肥230601 [2]南京工程学院建筑工程学院,江苏南京211167 [3]东北石油大学土木建筑工程学院,黑龙江大庆163318

出　　处：《湖北理工学院学报》2023年第1期36-40,共5页Journal of Hubei Polytechnic University

基　　金：国家自然科学基金面上项目(项目编号:51578120,51178087,52178143)。

摘　　要：为研究T形截面短柱的畸变屈曲力学性能,采取理论计算和有限元验证的方法,根据“板-梁”理论和传统能量法理论,求出在两端恒载作用下简支T形截面短柱发生畸变屈曲的应变能。通过假定截面的横向位移和截面转角以及待定系数的纵向位移来表示构件的应变能和初应力的势能,得到构件的总势能方程。根据最小势能原理,获得总势能函数的偏导数以及畸变屈曲的能量矩阵,以最小特征值法求得屈曲临界荷载。同时,借助ANSYS有限元软件建立T形截面短柱端部轴压有限元模型,并对其屈曲性能进行分析研究。结果表明:T形截面短柱的跨高比在6.67左右时,结构处于弯扭屈曲和畸变屈曲的临界状态。所得屈曲临界荷载模拟数值与理论计算值较吻合,误差均控制在10%以内,可以验证理论方法的正确性和计算公式的准确性。In order to study the deformation buckling mechanical properties of short T-shaped section columns,theoretical calculations and finite element verification are adopted to find out the strain energy of deformation buckling of simply supported short T-shaped section columns under constant load at both ends according to the plate-beam theory and traditional energy method theory.The total potential energy equation of the member is then obtained by assuming the transverse displacement and section turning angle of the section and the longitudinal displacement with a coefficient to be determined to represent the strain energy and the potential energy of the initial stress of the member.Finally,according to the principle of minimum potential energy,the partial derivatives of the total potential energy function and the energy matrix of distortional buckling are obtained to find the buckling critical load by the minimum eigenvalue method.Meanwhile,the axial compression finite element model of T-shaped section short column end is established with the help of ANSYS finite element software,and its flexural performance is analyzed and studied.The results show that the structure is in the critical state of bending torsional buckling and distortional buckling when the span-to-height ratio of short T-section columns is around 6.67.The simulated values of buckling critical load obtained are in good agreement with the theoretical calculated values,and the errors are controlled within 10%,which can verify the correctness of the theoretical method and the accuracy of the calculation formula.

关 键 词：T形截面柱 临界荷载 畸变屈曲 有限元分析 轴压 

分 类 号：TU391[建筑科学—结构工程]