Winkler弹性地基上自由矩形板问题

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。

Problem of Rectangular Plates with Four Free Edges on Winkler Elastic Foundations

In the classical thin - plate theory, the exact solution of bending problem of rectangularplates with four free edges on elastic foundations has been considered as a difficult problem for a long time.On the basis of the studies of the exact solution for rectangular places, in this paper the flexual func-tion which consists of trigonometrical function and po1ynomial expression is selected. It satisfies all theboundary conditions on free edges and the conditions at four free corner points. Solutions for bending, freevibrations and stability of the rectangular plates with four free edges on elastic foundations by method ofGalerkin are obtained. In this paper, the results of numerical example are given.