关于一阶剪切板的Kármán型精化理论

On the Refined First-Order Shear Deformation Plate Theory of Kármán Type

依据Mindlin_Reissner理论 ,着重研究一阶剪切板的K rm n型精化理论 ,并推导出仅以挠度和应力函数为未知变量的广义K rm n型大挠度方程 ,适用于复合材料上复合构造剪切板的非线性分析· 在当前板的精化理论中 ,消去的两个转角以隐含形式作用于板的整体变形· 这一工程理论适用于各种计及横向剪切复合材料板、正交各向异性中厚板和夹层板等的线性和非线性分析· 容易发现 ,针对具体的工程应用 ,由该方程可直接获得相应的退化形式 。

A new refined first_order shear_deformation plate theory of the Karman type is presented for engineering applications and a new version of the generalized Karman large deflection equations with deflection and stress functions as two unknown variables is formulated for nonlinear analysis of shear_deformable plates of composite material and construction, based on the Mindlin/Reissner theory. In this refined plate theory two rotations that are constrained out in the formulation are imposed upon overall displacements of the plates in an implicit role. Linear and nonlinear investigations may be made by the engineering theory to a class of shear_deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates, and laminated shear_deformable plates. Reduced forms of the generalized Karman equations are derived consequently, which are found identical to those existing in the literature.