双参数地基上Reisner板弯曲问题的边界积分方程

Boundary Integral Equations for Bending Problem of Reissner's Plates on Two_Parameter Foundation

本文应用广义函数的Ｆｏｕｒｉｅｒ积分变换，导出了双参数地基上Ｒｅｉｓｓｎｅｒ板弯曲问题的两个基本解·在此基础上，从虚功原理出发，依据胡海昌导出的Ｒｅｉｓｓｎｅｒ板弯曲理论，推导出适用于任意形状、任意荷载、任意边界条件情形的三个边界积分方程，为边界元法在这一问题中的应用提供了理论基础·文中给出了固支、简支、自由三类边界的算例，并与解析解比较，均得到满意的结果·

Two fundamental solutions for bending problem of Reissner's plates on two_parameter foundation are derived by means of Fourier integral transformation of generalized function in this paper. On the basis of virtual work principles,three boundary integral equations which fit for arbitrary shapes,loads and boundary conditions of thick plates are presented according to Hu Haichang's theory about Reissner's plates.It provides the fundamental theories for the application of BEM.A numerical example is given for clamped,simply supported and free boundary conditions.The results obtained are satisfactory as compared with the analytical methods.