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在经典薄板理论中，弹性地基上自由矩形板弯曲问题的精确解，长期以来被认为是一个相当困难的课题。根据对矩形板精确解的研究，构造了一个包括三角函数和多项式组成的近似挠度函数。它满足四个自由边上的全部边界条件和自由角点条件，利用伽辽金方法得到Winkler弹性地基上自由边矩形板弯曲、自由振动和稳定问题的解。还给出了数值算例。
In the classical thin plate theory, the exact solution of the bending problem of free rectangular plates on elastic foundations has long been considered as a very difficult topic. According to the study of the exact solution of the rectangular plate, an approximate deflection function consisting of a trigonometric function and a polynomial is constructed. It satisfies all the boundary conditions and free-corner conditions on the four free edges. The Galerkin method is used to obtain the solution to the bending, free vibration and stability problems of the free-edge rectangular plate on the Winkler elastic foundation. Numerical examples are also given.