On elastostatics of multilayered solids subjected to general surface traction

Extensive studies have been done on the elastostatic responses of multilayered solids subjected to surface traction using integral-transform techniques during the past several decades. Due to the complexity of the problems, a number of methodologies have been proposed to solve problems associated with multilayered elastic solids. However, there has been no general mathematical proof that the solution obtained using these methodologies is the solution of the boundary-value problem in the sense of the theory of elasticity. This paper presents a rigorous mathematical study on the solution for the elastostatic response of a bonded multilayered solid subjected to surface traction, where the total number of the dissimilar layers is an arbitrary integer. The classical integral transforms and a backward transfer-matrix technique are adopted to uniquely formulate the solution of the boundary-value problem in the multilayered solid. It is shown analytically that the solution presented in this study satisfies all the required constraints of elasticity including the governing equations and the interfacial and boundary conditions. Furthermore, the solution is formulated in a unique way such that there is no difficulty in the numerical evaluation of the solution with high accuracy and efficiency.