An elastic half-space under the action of one-dimensional time-dependent diffusion perturbations

Abstract

A one-dimensional problem of elastic diffusion for a one-component half-space is considered. A locally static geometrically linear model of elastic diffusion is used, which contains mass transfer equations and a coupled system of the motion equations of an elastic body. To construct the solution, the integral Fourier transform with respect to the spatial coordinate and the integral Laplace transform with respect to time are applied. The problem of inverting Laplace transformants is reduced to inverting a rational function, while the inverse Fourier transform is implemented numerically. A fundamental solution of the problem is constructed. An example for the case where the diffusion flux on the boundary is constant is considered. The obtained results are a theoretical basis for an analysis of the stress-strain state in aeronautical and space constructions operating in conditions of multifactorial external influences.