非均匀半平面问题的弹性力学解

本文使用非均匀平面弹性力学的基本方程,通过富氏积分变换,求得了应力函数通解。在此基础上对弹性模量E(x)=E_oexpβx]为指数型的非均匀半平面问题,具体求得了当边界上受任意载荷作用的精确解。最后经退化处理,还得到了有名的Boussnesq解,这说明本文的方法是成功的。

An Elasticity Solution of a Nonhomogeneous Half-Plane Problem

We employ fundamental equations of non-homogeneous elasticity and Fourier integral transformations to obtain the general solutions of the stress function.On the basis of these points of view and when forces on the boundary are arbitrary for non-homogeneous half-plane problems with the Youngs modulus E(x)=accurate solutions are obtained.At last with the degeneracy it is obtained that the famous Boussnesq solution and this method is successful.