МАТЕМАТИЧНЕ ТА КОМП’ЮТЕРНЕ МОДЕЛЮВАННЯ КОНТАКТНОЇ ВЗАЄМОДІЇ ТРАНСВЕРСАЛЬНО-ІЗОТРОПНИХ ПРУЖНИХ ПІВПРОСТОРІВ ЗА ПРИСУТНОСТІ МІЖ НИМИ ЖОРСТКОГО ПЛОСКОГО ВКЛЮЧЕННЯ ДОВІЛЬНОЇ ФОРМИ

Abstract

Mathematical and computer modeling of the contact interaction of two transversely isotropic elastic half-spaces with different properties in the presence of a rigid flat inclusion between them under compression is carried out. Based on the representation of the general solution of the system of equilibrium equations for a transversally isotropic body in terms of harmonic functions, a correspondence is established between the contact interaction parameters for two transversely isotropic and two elastic isotropic half-spaces (in the presence of a rigid planar inclusion of an arbitrary shape between them), which generalizes Gladwell's result to the case interactions of transversely isotropic half-spaces. By means of the mathematical and computer modeling, the contact interaction of transversely isotropic half-spaces with a disk-like inclusion is studied. The analysis of the numerical results is carried out, the influence of the elastic properties of the half-space, the geometric dimensions of the inclusion on the parameters of the contact interaction is studied.