Computer modeling of the boundary value problem solution for a layer weakened by two through holes under sliding faces clamping

Abstract

This paper presents a new mathematical model for solving the static skew-symmetric boundary value problem for a layer weakened by two through-holes under sliding clamping of its end faces. A new method based on a system of six singular integral equations has been developed and numerically validated. A high-precision numerical study demonstrates that the proposed mathematical model is both accurate and efficient. The algorithm exhibits good scalability and enables efficient resource management by providing an optimal balance between the number of computational processes and solution accuracy. A new spline-function-based technique was developed for the numerical analysis of stress–strain state parameters, significantly improving the computational efficiency of the algorithm. The influence of the material’s elastic properties, characterized by Poisson’s ratio, on the sought parameters was investigated. Materials with high shear stiffness (e.g., ceramics and concrete with a Poisson’s ratio of approximately 0.15) were compared with easily deformable materials (e.g., rubber-like materials and soft polymers with a Poisson’s ratio of approximately 0.40). The results show that decreasing both Poisson's ratio and the distance between the hole centers leads to an increase in the relative circumferential stress. As Poisson's ratio increases, the location of the maximum relative circumferential stress shifts from the surface of the layer toward its interior. It is also shown that, for certain combinations of parameters, the influence of one hole on the stress distribution around the other becomes negligible. The corres-ponding numerical results are presented, and the relevant dependencies are illustrated graphically.