矩形悬臂板对称弯曲问题的解

The Solution of the Symmetrical Bending Problem of Rctangular Cantilever Plates

矩形悬臂板弯曲问题是Ｋｉｒｃｈｈｏｆｆ板理论中的难题．利用广义方法讨论了矩形悬臂板的对称弯曲．选择了三角函数和多项式的挠度函数．满足全部位移边界条件．自由角点条件和一部分力的边界条件．所得结果．同一些“精确解”是一致的．文中给出了挠度及弯矩的计算公式．

The bending Of a rectangular cantilever plate is a very complicated problem in the theory of Kirchhoff plate. This peper discusses the problem of the symmetrical bending of a rectangular cantilever plate by the generalized Galerkin mrthod. In this paper, the fie-cural function which consisls of trigonometrical function and POlynomial expression is selected. The fie-cural function satisfies all boundary conditions of displacememt, the conditions at free corner points and part of boundary foundation of force. On this account a very good solution is oblained. Our results are the same as some exact solutions. In this Paper, some simple calculation formulas of the flection and bending moment are given.