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基于板梁理论的轴心受压T形截面柱弯扭屈曲无穷级数解 被引量:3

Infinite Series Solution of Flexural Torsional Buckling of T-section Columns under Axial Compression Based on Plate-beam Theory
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摘要 为了从理论上探究T形等截面简支柱在轴心压力下的弯扭屈曲问题,基于板梁理论,首先给出简支柱弯扭屈曲的总势能方程,根据边界条件,通过假设T形截面变形时侧向位移和转角模态势函数为无穷三角级数,得到总势能方程的无穷级数表达式;然后引入无量纲参数,得到T形截面简支柱在轴心压力作用下弯扭屈曲的无量纲无穷级数解;最后借助有限元分析软件ANSYS模拟相同条件下的T形截面简支柱,求解得到屈曲荷载,与理论公式进行对比,验证了理论公式的正确性. In order to theoretically explore the flexural torsional buckling of T-shaped constant section simple supported columns under axial pressure,based on the plate-beam theory,the total potential energy equation of flexural torsional buckling of simple supported columns is given.According to the boundary conditions,the infinite series expression of the total potential energy equation is obtained by assuming that the modal potential functions of lateral displacement and rotation angle during T-shaped section deformation are infinite triangular series.Then,by introducing dimensionless parameters,the dimensionless infinite series solution of flexural torsional buckling of T-section simple supported columns under axial pressure is obtained.Finally,the T-section simple supported columns under the same conditions is simulated with the help of finite element analysis software ANSYS,and the buckling load is obtained.Compared with the theoretical formula,the correctness of the theoretical formula is verified.
作者 张文福 闫学森 杭昭明 ZHANG Wen-fu;YAN Xue-sen;HANG Zhao-ming(College of Civil Engineering,Anhui Jianzhu University,Hefei,230601,China;School of Architectural Engineering,Nanjing Institute of Technology,Nanjing,211167,China;School of Civil Engineering and Architecture,Northeast Petroleum University,Daqing,163318,China)
出处 《南京工程学院学报(自然科学版)》 2022年第2期56-61,共6页 Journal of Nanjing Institute of Technology(Natural Science Edition)
基金 国家自然科学基金项目(51178087、51578120)。
关键词 弯扭屈曲 板梁理论 能量变分法 轴心受压 flexural-torsional bucking plate-beam theory energy variational method axial compression
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