Контактная задача о взаимодействии штампа в форме параболоида вращения и пороупругого слоя, закрепленного на упругом основании

Abstract

The contact problem of the introduction of a rigid punch in the form of a paraboloid of rotation into a poroelastic layer fixed on an elastic half-space is considered on the basis of the equations of the theory of poroelastic bodies of Cowin-Nunziato. It is assumed that there is no friction in the contact zone. With the help of the Hankel integral transformation, the problem posed is reduced to solving the integral equation for an unknown contact stress. The collocation method is used to solve the integral equation. The area of contact, the values of contact stresses are found, and the deformation of the surface outside the punch is investigated. The relationship between the force acting on the punch and its displacement has also been investigated. A comparative analysis of the studied quantities for different values of the parameters of the poroelastic layer and the elastic foundation has been carried out. Numerical results are presented in the form of graphs.