The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plate

The article considers the problem of embedding a rigid body into an isotropic elastic-elastic half-space through a deformable plate having properties characteristic of thin plates – elastic bodies with a thickness much smaller than other geometric dimensions and studied according to the theories of Kirchhoff and Poisson. The presence of a thin plate changes the characteristics of the embedding process, since the methods applicable to solving direct indentation into the half-space cannot be used to determine the dependence of the load on deformation. The integral differential equations determining the embedding of a rigid body of finite dimensions are solved using the discretization approach. The integral transformation method made it possible to determine the loading operator, an integral part of which is the parameter of the relative stiffness of a system consisting of a plate and an elastic half-space. The relative stiffness depends on the elastic modulus and geometric parameters of the contact area and the elastic plate. The influence of the stiffness of an elastic plate on the relative stiffness of the entire system is analyzed and the results demonstrating the effect of plate stiffness on the Boussinesq problem of deformation of a half-space are presented. The solution of this problem is applicable to the practical field of scientific research on the compaction of asphalt concrete mixtures with various types of sealing working bodies, since the nature of the formation of defects in asphalt concrete coating retains scientific interest in the creation of alternative sealing equipment.