On the theory of chiral plates and associated system of Timoshenko–Ehrenfest type

Abstract

The chiral effects cannot be described by means of the classical theory of elasticity. In this paper we study the thermoelastic deformation of chiral plates in the context of the strain gradient theory of thermoelasticity. The work is motivated by the interest in using chiral continuum as model for some carbon nanotubes, auxetic materials and bones. First, we derive the basic equations which govern the deformation of thin thermoelastic plates. In contrast with the theory of achiral plates, the stretching and flexure cannot be treated independently of each other. A system of Timoshenko–Ehrenfest type is presented and an existence result is established. Then, we consider the dynamic theory of plates and present a uniqueness result with no definiteness assumption on the elastic constitutive coefficients. The effects of a concentrated heat source are investigated.