| 张文福,吴宇,黄斌,杭昭明.T形截面悬臂柱自重下弯扭屈曲无穷级数解与FEM验证[J].安徽建筑大学学报,2022,30(): |
| T形截面悬臂柱自重下弯扭屈曲无穷级数解与FEM验证 |
| Infinite series solution and FEM verification of lateral-torsional buckling of a T-section cantilever column under its own weight |
| 投稿时间：2021-06-01 修订日期：2021-07-22 |
| DOI： |
| 中文关键词: 悬臂柱 弯扭屈曲 能量变分原理 有限元分析 |
| 英文关键词: cantilever column lateral-torsional buckling variational principle of energy finite element analysis |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 以自重作用下的T形截面悬臂柱为研究对象，研究其屈曲模态及屈曲荷载。基于板—梁理论和能量变分原理，建立了位移和转角的变形曲线为三角函数无穷级数形式的T形截面弯扭屈曲总势能方程。根据悬臂柱的边界条件并依据势能驻值原理，在引入无量纲参数后，获得了T形截面悬臂柱在自重作用下的弯扭屈曲无量纲无穷级数解。借助大型通用有限元分析软件ANSYS计算了长细比大于等于50的6组T形截面悬臂柱在自重荷载下的特征值屈曲解，并与位移函数取50项的精确理论解进行了对比，最大误差为1.45%，且随着长细比增大误差越来越小。 |
| 英文摘要: |
| Taking the T-section cantilever column under its own weight as the research object, the buckling mode and buckling load are studied. Based on the Plate-beam theory and the principle of energy variation, the total potential energy equation of T-section lateral-torsional buckling is established in which the deformation curves of displacement and rotation angle are in the form of infinite series of trigonometric functions. According to the boundary conditions of the cantilever column and the principle of stationary potential energy, after introducing the dimensionless parameters, the dimensionless infinite series solution of the lateral-torsional buckling of the cantilever column with T-section under the action of its own weight is obtained. With the help of the large-scale general finite element analysis software ANSYS, the eigenvalue buckling solutions of 6 groups of T-section cantilever columns with a slenderness ratio greater than or equal to 50 under self-weight load were calculated, and compared with the accurate theoretical solution of the displacement function taking 50 terms, the maximum The error is 1.45%, and the error becomes smaller and smaller as the slenderness ratio increases. |
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