狭长矩形薄板自由扭转和约束扭转的统一理论
首发时间:2014-04-10
摘要:薄壁构件受扭是工程中极为常见的一种现象。理论上,可将等截面开口薄壁构件看作是矩形薄板的组合体,比如工字型和十字型薄壁构件。本文基于Kirchhoff的薄板理论和Volasov刚周边假设,分别建立了狭长矩形薄板的能量表变分模型和微分方程模型,文中还给出了悬臂狭长矩形薄板在端扭矩作用下的解析解答,并通过数值算例初步证明了本文薄板扭转理论的正确性。
关键词: 矩形薄板 自由扭转 约束扭转 能量表变分模型 微分方程模型
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Unified Theory of Free and Restricted Torsion for Narrow Rectangular Plate
Abstract:It is very common phenomenon for thin-walled member to sustain torque. Theoretically, thin-walled member of open section with constant-section, e.g. I-shape and cross-shape member, can be taken as the combination of rectangular plate. In this paper, on the basis of Kirchhoff's thin plate theory and Volasov's rigid perimeter assumption, energy variational model and differential equation model for the narrow rectangular plate are established, respectively. The analytical solution to the cantilever case of narrow rectangular plate under toque applied at the free end is presented. The correctness of the torsion theory for the thin plate presented in this paper is preliminary verified by the numerical example problems.
Keywords: Rectangular Plate Free Torsion Restricted Torsion Energy Variational Model Differential Equation Model
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No.4592261967110139****
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