The present work is a pioneering study on the contact mechanics including Pasternak foundation model. The context of this research is frictionless plane contact problem between a rigid punch and a functionally graded orthotropic layer lying on a Pasternak foundation in the limits of the linear elasticity theory. The layer is pressed by rigid cylindrical or flat punches that apply a concentrated force in the normal direction. The orthotropic material parameters are assumed to vary exponentially in the in-depth direction. Applying the Fourier integral transform technique and the boundary conditions of the problem, a singular integral equation is obtained, in which the contact stress and the contact width are unknowns. Using the Gauss–Chebyshev integration formula the singular integral equation is solved numerically. Effects of the Pasternak foundation parameters, material inhomogeneity, external load, punch radius or punch length on the contact stress, the contact width, the vertical displacements on the top and bottom surfaces of the layer, the subsurface and in-plane stresses are given.

目前的工作是对包括 Pasternak 基础模型在内的接触力学的开创性研究。本研究的背景是在线性弹性理论的限制下，刚性冲头和位于 Pasternak 基础上的功能梯度正交各向异性层之间的无摩擦平面接触问题。该层由刚性圆柱形或扁平冲头压制，在法线方向施加集中力。假设正交各向异性材料参数在深度方向上呈指数变化。应用傅里叶积分变换技术和问题的边界条件，得到奇异积分方程，其中接触应力和接触宽度是未知的。使用高斯-切比雪夫积分公式对奇异积分方程进行数值求解。