考虑有限转角下薄壁构件稳定理论及其应用

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

摘要:

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.

Abstract:

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.