曲梁弯扭屈曲分析

本文基于有限变形理论导出了薄壁曲梁位移和应变的一般表达式。从探讨薄壁曲梁弯扭屈曲的变形模态出发,考虑其弯矩作用平面内变形的影响,利用变分原理导出了曲梁稳定分析的基本微分方程。稳定分析表明,即使绕弱轴弯曲,曲梁也可能发生弯扭屈曲。对于曲率甚小的情况,本文把曲梁看作为具有初曲率的直梁,较精确地分析了初曲率对直梁弯扭屈曲临界弯矩的影响。此外,本文给出的闭合解与Timoshenko,Vlasov及Chai Hong Yoo等人的结果进行了比较,指出了其间差异的根源所在。

ANALYSIS OF LATERAL-TORSIONAL BUCKLING OF CURVED BEAMS

Based on the theory of finite derormation, the general relation ship between deformations and strains of a thin-walled curved beam are derived in this paper. And then inquired in to the configuration of lateral-torsional buckling on thin-walled curved beams,along with taking in plane deformation into accornt, the basic differential equations of stability analysis for curved beams are also derived by the variational principle. The stability analysis shows that lateral-torsional buckling may be possible eventhough a curved beam is loaded in its original curved plane and bending round its weak axis. A curved beam with very small curvature is considered as a straight beam having initial curvature in this paper, so that the effect of the original curvature on lateral-torsional buckling strength can be accurately studied, Finally,the closed solutions given in this paper are compared with the ones obtained by Timoshenko,Vlasov and Yoo,and the sources of discrepancies are traced.