纵向剪切问题中一类对偶积分方程组的封闭解及其应力场  

The enclosed solutions of a kind of dual integral equations and stress field of elastic layer in the problem of longitudinal shear

作　　者：王文友[1] 

机构地区：[1]徐州师范大学数学科学学院,江苏徐州221116

出　　处：《徐州师范大学学报（自然科学版）》2010年第3期30-34,共5页Journal of Xuzhou Normal University(Natural Science Edition)

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.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.

关 键 词：纵向剪切 对偶积分方程组 积分变换 应力场 

分 类 号：O175.5[理学—数学]