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.

Keywords:

• Explicit solutions
• multilayer elastic cylinders
• plane non-axisymmetric problem
• single-solid concept
• thermal stresses
• thermoelasticity

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors gratefully acknowledge partial support of this research by the Ministry of Education and Science of Ukraine (grant No 0123U103235) and the Slovak Research and Development Agency (grant No SK-UA-21-0010) under the joint research and development project “Effect of nano-, micro-, and meso-nonhomogeneities in the macro-scale thermomechanical performance of composite structure members.”