Construction of mathematical and computer models for calculating contact characteristics of interaction between a rigid punch and an elastic half-space

Abstract

The subject of this study is a punch-elastic half-space system under compressive force. The paper solves the problem of determining contact stresses and displacements. The content of results is the constructed models and the assessment of their adequacy. This work considers the problem of pressing a rigid plane double-connected punch on a homogeneous and isotropic elastic half-space. To obtain an analytical solution, a variant of the perturbation method based on the expansion of the potential of a simple layer distributed over a double-connected region by a small parameter was applied. The problem of pressing a flat punch in the form of a non-circular ring is reduced to a sequence of problems for a punch in the form of a circular ring. This allows us to use a known solution for a circular ring. Finite element models were built using ANSYS. A group of models was constructed to take into account possible damage in the event that the punch-elastic half-space system is exposed to difficult natural conditions or an aggressive environment during a certain time of modeling. A database was formed for the purpose of further transferring it to CLIPS. Sets of rules and knowledge were compiled. A generalizing algorithm was developed for the problems of constructing and analyzing mathematical and computer models of contact interaction between a rigid cylindrical punch with a flat double-connected base with an elastic half-space under the action of a compressive force. The problem of determining the geometric shape of the cross-section of an annular punch in the plan for the punch-elastic half-space system was solved for the case when the contact zone is not known in advance. The devised approach could be employed in engineering calculations for strength and durability