【摘要】 应用Fourier变换法,求解位移满足的Laplace方程,获得位移的一般性解.然后利用位移解与应力之间的关系式和边界条件,导出一组对偶积分方程组.引入积分变换,使对偶积分方程组退耦正则化为含对数核的第一类Fredholm积分方程,并严格证明了两者的等价性;给出对偶积分方程组的封闭解,并严格证明了解的存在性和唯一性.最后给出弹性层纵向剪切问题的应力场.更多还原

【Abstract】 By applying Fourier transformation to solve the Laplace equation about displacement,the general solutions of displacement are obtained. And according to the relation between displacement and stress for longitudinal shear and boundary conditions,the dual integral equations are deduced. The dual integral equations are decoupled and regularized into the first kind of Fredholm canocinal integral equations with logarithmic kernel by using integral transformation,and the equivalence of them are proved exactly. Then the enclosed solutions of dual integral equations are given,and the existence and uniqueness of solutions are proved. Simultaneously,the stress fields for the problem of longitudinal shear of elastic layer are given.更多还原