Asymptotic expansion of the solution of a system of elasticity equations in an inhomogeneous thin layer

Abstract

An asymptotic analysis is conducted (in the absence of simplifying hypotheses) for a three-dimensional problem in the theory of elasticity for a plate of thickness ε ≪ s with characteristic dimension of inhomogeneity also equal to ε and a scale of mass forces T ∼ s. A theorem is given for estimating the difference of the exact an asymptotic solutions.