薄壁曲梁的稳定性研究进展

曲梁是桥梁、建筑、船舶、航空和航天工程中常见的薄壁构件,根据外载荷与主曲率平面的关系,又被称为拱或水平曲梁.随着工程材料的日益发展,如复合材料、功能梯度材料的引入,曲梁的应用范围更加广泛,进一步推进了薄壁曲梁稳定性问题的研究.本文首先对薄壁梁结构的稳定性行为进行了分类.接着简述了薄壁构件的基本假设,对比了近几十年来薄壁曲梁的基本理论,针对复合材料薄壁曲梁,总结了相应的本构关系,并对各理论间存在的分歧进行了归纳.结合最新的薄壁曲梁研究,根据平衡法、能量法和虚位移(虚功)原理推导出控制微分方程,阐述了相应的求解方法,如解析法、半解析法和数值解法.为验证薄壁曲梁理论的准确性,曲梁承载能力试验验证尤为重要,但目前国内外相关研究还很少,亟待发展.最后讨论了现阶段薄壁曲梁研究的局限性和未来发展的方向.

Advances in Stability Analysis of Thin-Walled Curved Beams

Curved beam are a common thin-walled structure in bridge, building, ship, airplane and aerospace. It is referred to as the arch or the planar curved beam according to the relationship between the external load and the principal curvature plane. The application of the curved beams is expanded by the development of engineering materials, such as the composite material and the functionally-graded material (FGM), which further promotes the research on the stability of curved beams. The buckling mode of thin-walled beam is discussed firstly, with the basic assumptions of thin-walled structures elaborated. The linear and nonlinear theories of isotropic thin-walled curved beams are reviewed, where the relevance and difference among those theories are discussed, and the constitutive behavior is summarized for the composite laminated curved beam. The differential governing equation is derived based on the equilibrium principle, the energy principle and the virtual principle of displacement. Three methods, i.e., the closed-form analytical method, the semi-analytical method and the numerical method, are used to solve the stability behavior of thin-walled curved beams. The importance of the bearing capacity tests on the curved beams for verifying the accuracy of the thin-walled curved beam theory is emphasized. Finally, the current limitations and the future perspectives in the research area of thin-walled curved beams are discussed.