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

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、势能驻值原理,并引入无量纲参数,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。运用ANSYS有限元分析软件计算了长细比≥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项的精确理论解对比,最大误差为1.45%;且随着长细比增大,误差越来越小。

Taking a T-section cantilever column under its own weight as the object to study its buckling mode and buckling load.Based on the Beam and Plate Theories and the variational principle,the total potential energy equation of T-section lateral-torsional buckling is established and the deformation curves of displacement and rotation angle are in the form of trigonometric infinite series.Considering the boundary conditions of the cantilever column and the principle of stationary potential energy,the non-dimensional parameters are introduced to obtain the non-dimensional infinite series solution of the lateral-torsional buckling of the column under its own weight.The buckling solutions of six groups of T-section cantilever columns with slenderness ratio≥50 were obtained with software ANSYS and compared with the exact solution of the displacement function taking 50 terms.The maximum error reaches 1.45%,and the error becomes smaller as the slenderness ratio increases.