非均匀半平面问题的弹性力学解
An Elasticity Solution of a Nonhomogeneous Half-Plane Problem
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摘要: 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)=Eoexp[βx]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。Abstract: We employ fundamental equations of non-homogeneous elasticity and Fourier integral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the boundary are arbityary for non-homogeneous half-plane problems with the Young's modulus E(x)-E0exp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.
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Key words:
- non-homogeneous half-plane problem /
- accurate solution /
- elasticity
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[1] 徐芝纶,《弹性力学》(上册),高等教育出版社(1984). [2] I.N,史奈登,《富利叶变换》,科学出版社(1958). [3] 中山大学数学力学系,《常微分方程》,人民教育出版社(1979). [4] Прудников А.П.Инmeipaлы u Рябы,Моcква,Наука(1981). -
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