考虑有限转角下薄壁构件稳定理论及其应用

为了解决传统稳定理论的两个力学缺陷,引入半切线转角矢量作为构件转角的变量,由二阶转动矩阵推导出梁单元的二阶位移表达式,并利用有限变形理论,得出构件位移与应变的非线性关系,通过Bernoulli平截面弯曲假定得出转角与侧移导数.运用薄壁构件稳定理论,推导出构件弯扭屈曲的总势能,证实了传统理论,解决了传统理论中的缺陷,能够适用各种边界条件和荷载条件下的弯扭屈曲分析.

Theory of Thin walled Component Stability Based on Finite Rotation and Its Application

To overcome the default of the classic theory, semitangential rotation was introduced as the spatially rotational parameters. Based on the second order rotation matrix, the expression of the second order displacement of beam element was deduced. According to the finite deformation theory, the strain displacement non linear relationship for the thin walled structures were presented. Based on the Bernoulli plain section assumption, the relation between rotation and transverse displacement derivative was derived. Thin walled component stability theory was adopted to duduce the total potential energy of flexural torsional buckling, which verified the traditional formula and overcame the defects of traditional theory. The analysis results show that the proposed theory is suitable for flexural torsional buckling analysis of beams under any boundary conditions and loadings.