弹性地基上四边自由正交各向异性矩形板的一般精确解

General Exact Solution of Orthotropic Rectangular Plate with Four Free Edges Rested on Elastic Foundation

本文利用Ｆｏｕｒｉｅｒ双三角余弦级数和单三角余弦级数，讨论和分析了弹性地基上四边自由正交各向异性矩形板的弯曲问题。挠度函数ｗ（ｘ，ｙ）ｍ足自由边总剪力、弯矩边界条件和自由角点条件，从而得到问题的精确解。文中给出了数值算例。

The flexural problems of orthotropic rectangular plate with four free edges rested on elastic foundation have been discussed in this paper and analyzed by the Fourier trigonometrical cosine series and double trigonometrical cosine series. As the deflection function w(x, g) satisties the boundary conditions of total shearing force and bending moment on free edges as well as the conditions at four free corners, an exact solution is thus obtained. A numerical example is worked out by the proposed method for comparison of its accuracy with the solution of other methods.