NONSTATIONARY CONTACT PROBLEM FOR SMOOTH RIGID DIE AND ELASTIC HALF PLANE ON SUB-RAYLEIGH INTERVAL OF INTERACTION

Abstract

Within the flat statement non-stationary problem of the contact interaction of an absolutely rigid die bounded by a smooth convex curve, with elastic half-plane is considered. The low of motion of the die assumed to be known. Problem statement includes the equations of the plane theory of elasticity in the potentials of elastic displacements, equations relating the potentials of the displacements and stresses, the initial conditions and the boundary conditions of mixed type. It is assumed that the contact is the contact is frictionless. On the basis of the principle of superposition, the normal movement of the half-plane boundaries are represented by the convolution of the normal stress with the influence function. The influence function is a solution of Lamb's problem. The method of solution is based on the introduction of analytic representations of the unknown functions and applying analytical algorithm of joint inverse of integral transformations of Fourier-Laplace. It is essential to the function that described by the die movement was homogeneous. In the case of movement of the contact region boundaries with speed not exceeding the speed of Rayleigh wave propagation the analytical relations, permitting the task are obtained.

Keywords: nonstationary contact problems of the theory of elasticity, mixed boundary conditions, moving boundary of the contact area, principle of superposition, integral transforms, generalized functions, analytical representations.