On thermal effects in the theory of shells

Abstract

This paper is concerned with thermomechanics of thin shells by a direct approach based on the theory of a Cosserat surface comprising a two-dimensional surface and a single director attached to every point of the surface. In almost all previous developments of the thermo-mechanical theory of shells by direct approach, only one temperature field has been admitted. This allows for the characterization of temperature changes along some reference surface, such as the middle surface, of the (three-dimensional) shell-like body, but not for temperature changes along the shell thickness. A main purpose of the present study is to incorporate the latter effect into the theory; and, in the context of the theory of a Cosserat surface, this is achieved by a recent approach to thermomechanics (Green & Naghdi 1977) which provides a natural way of introducing two (or more) temperature fields at each material point of the surface. Apart from full discussion of thermomechanics of shells and thermodynamical restrictions arising from the second law of thermodynamics for shells, attention is given to a discussion of symmetries (including material symmetries) and thermal effects in the nonlinear theory of elastic shells with detailed discussion of the linear theory of elastic plates.