A new combined asymptotic-tolerance model of thermoelasticity problems for thin uniperiodic cylindrical shells

Abstract

AbstractThe objects of consideration are thin linearly thermoelastic Kirchhoff–Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential direction (uniperiodic shells). The aim of this contribution is to formulate and discuss a new averaged mathematical model for the analysis of selecteddynamic thermoelasticity problemsfor the shells under consideration. This so-called combined asymptotic-tolerance model is derived by applying the combined modelling including the consistent asymptotic and the tolerance non-asymptotic modelling techniques, which are conjugated with themselves into a newprocedure. The starting equations are the well-known governing equations of linear Kirchhoff–Love theory of thin elastic cylindrical shells combined with Duhamel–Neumann thermoelastic constitutive relations and coupled with the known linearized Fourier heat conduction equation. For the periodic shells, the starting equations have highly oscillating, non-continuous and periodic coefficients, whereas equations of the proposed model have constant coefficients dependent also on a cell size.