双曲率壳的力学研究进展

Advances in Mechanics of Doubly-Curved Shells

双曲率壳是飞机、汽车以及船舶上常见的薄壁结构,其中性面可看作是一条动曲线沿着另一条曲线扫掠所形成的曲面.双曲率壳的非线性理论不断更新推动着双曲率壳力学行为的研究.随着工程实际应用的不断改进,如功能梯度材料(FGM),加筋壳,弹性地基模型等的引入,双曲率壳在强度、变形和稳定性等方面的研究得到了进一步促进.本文首先回顾了双曲率壳结构非线性力学基本理论发展过程,主要阐述了经典的二维板壳理论,如Donnell薄壳理论,一阶剪切变形壳理论,高阶剪切变形壳理论,和三维板壳理论的理论体系及基本公式,并对几种理论之间的联系和应用进行了总结和讨论,简述了近几十年来国内外学者在双曲率壳非线性弯曲、稳定性和振动等方面的最新研究成果,最后对双曲率壳体研究目前的局限性和未来的研究方向进行了探讨.

Doubly-curved shells are common thin-walled structural components in airplanes, automobiles and ships, in which their neutral plane can be regarded as a curved surface formed by sweeping one moving curve along another curve. The development of the nonlinear shell theory promotes the study of mechanical behavior of doubly-curved shells. With the continuous progress of practical engineering applications, such as the introduction of functionally-graded materials(FGM), stiffener shell, elastic foundation model, the research on strength, deformation and stability of doubly-curved shells is further promoted. This paper reviews the development of nonlinear theories for doubly-curved shells. In particularly, theoretical background and basic formulations in the Donnell thin shell theory, the first order shear deformation shell theory, the higher order shear deformation theory, and 3D shell model are reviewed, and the relevance and differences among these theories are stated. Then, the latest research achievements on the nonlinear bending, the stability and the dynamics of doubly-curved shells are introduced. Finally,current limitations and needs in the area of mechanics of doubly-curved shells are discussed.