Розробка і постпроцесінг математичних та комп’ютерних моделей контактних задач

This study investigates the process of contact interaction between a rigid punch and an elastic half-space under the action of a centrally applied clamping load. The task addressed is automating the processing of results for data analysis. This paper considers a problem for a punch with complex geometry. The contact zone has a doubly connected shape bounded by concentric ellipses, which complicates the analytical description of the stressed-strained state. To solve the problem analytically, a perturbation method was applied, using the previously found expansion of the simple layer potential with a small parameter. This makes it possible to reduce the problem to a configuration with a circular ring whose exact solutions are known in the form of a series with recurrent coefficients. The obtained analytical results serve as a reference basis for assessing the accuracy of numerical modeling, for example, when constructing a finite element model. Such mathematical formalization makes it possible to effectively assess the reliability of the results. Consequently, calculation models were built in the Ansys software environment taking into account features of the punch shape. Special software was developed that enables exporting calculation data to the MATLAB software package with subsequent post-processing to automate data processing. The proposed approach reduced the complexity of post-processing by approximately 45–55%. It was found that with an increase in the eccentricity of the ellipse, the pressure under the punch increases. In the central zone, a lower pressure is recorded, which increases along the edges of the contact area. The numerical results correlate well with the analytical ones. The results reported here could be used for strength calculations in engineering practice under conditions of contact interaction between structural elements of mechanical engineering where the contact zone has the shape of an elliptical ring.