Axisymmetrical Problem on Interaction of a Stamp and a Poroelastic Layer Lying on a Winkler Base.

Axisymmetric contact problems on the interaction of a rigid stamp and a poroelastic layer, the bottom boundary of which is located on a Winkler base, were considered based on the equations of the Cowin–Nunziato theory of poroelastic bodies. It was assumed that the base of the cylindrical stamp has the flat or parabolic shape and there is no friction in the contact area. With the help of the Hankel integral transformation, the problems posed were reduced to the integral equations for an unknown contact stresses, which were solved with the use of the collocation methods, while the transformants of the kernels of the integral equations were obtained in explicit form. The values of contact stresses and size of the contact area in the case of the parabolic stamp were determined. The relationship, which is one of the main characteristics, when determining the mechanical parameters of a material by the indentation method, between the force acting on the stamp and its displacement, was studied. A comparative analysis of the studied quantities for various values of the poroelastic parameters and the coefficient of subgrade resistance of the Winkler base was carried out. The model of contact interaction considered and the solution obtained can be used in calculation of the structures foundations located on ground bases. [ABSTRACT FROM AUTHOR]