Thermoelastic response of multilayer cylinders: The direct integration and single-solid approach

Abstract

An approach for solving the plane nonaxisymmetric thermoelasticity problems in multilayer cylinders is suggested from the single-solid standpoint, which implies considering a multilayer structure as a single unity with a step-wise variation of material properties. The direct integration method was used to the advantage of our approach by applying toward the compatibility equation in terms of strains instead of the one in terms of stresses. As a result, the governing equation is derived without involving generalized derivatives by the radial coordinate and then reduced to an integral equation of the second kind. Using the resolvent-kernel for solving the latter equation, the thermal stresses are computed as the Fourier series whose constituents are explicitly determined by the corresponding constituents of the thermal loading.