The problem of constructing an exact solution of singular integro-differential equations related to problems of adhesive interaction between elastic thin semi-infinite homogeneous patch and elastic plate is investigated. For the patch loaded with horizontal forces the usual model of the uniaxial stress state is valid. Using the methods of the theory of analytic functions and integral transformation, the singular integro-differential equation is reduced to the Riemann boundary value problem of the theory of analytic functions. The exact solution of this problem and asymptotic estimates of tangential contact stresses are obtained.

中文翻译：

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与弹性理论的粘合剂接触问题有关的一些奇异积分-微分方程的精确解

研究了构造奇异积分微分方程精确解的问题，该奇异积分微分方程与弹性薄半无限均质斑块与弹性板之间的胶粘作用有关。对于受水平力作用的贴片，单轴应力状态的常用模型是有效的。利用解析函数理论和积分变换的方法，将奇异积分微分方程简化为解析函数理论的黎曼边值问题。获得了该问题的精确解，并得到了切向接触应力的渐近估计。