Spatial estimates for transient and steady-state solutions in transversely isotropic plates of Mindlin-type

This paper concerns with a state of bending for a linear transversely isotropic plate model based on the Mindlin assumption on the displacement. By using appropriate families of line-integral measures, we are able to establish results about the spatial behaviour of transient and steady-state solutions. All the results are obtained under relaxed hypotheses on the positive definiteness of the elasticity tensor.     

On representations of a general solution in the theory of micropolar thermoelasticity without energy dissipation

In the present paper, the linear theory of micropolar thermoelasticity without energy dissipation is considered. This work is organized as follows: Section 2 is devoted to basic equations for micropolar thermoelastic materials, supposed to be isotropic and homogeneous, and to assumptions on constitutive constants. In Section 3, some theorems related to representations of a general solution are studied. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1391–1398, October, 2007.     

On the strong ellipticity for orthotropic micropolar elastic bodies in a plane strain state

In the present paper we consider an orthotropic micropolar elastic material subject to a state of plane strain. In this context, we establish necessary and sufficient conditions for the strong ellipticity of constitutive coefficients. Furthermore, we study existence of progressive plane waves under the strong ellipticity conditions previously determined. Finally, we detail the results obtained for a specific class of materials related to tetragonal systems.     

Some results on the spatial behaviour for elastic mixtures

This article studies the spatial behaviour of solutions for some classes of homogeneous and isotropic simple elastic mixtures, for which the internal energy density is not always a positive definite quadratic form. By introducing some appropriate measures, we obtain the domain of influence theorem and the spatial decay estimates with time-independent decay rate inside the domain of influence.     

A uniqueness result for the Cattaneo-Christov heat conduction model applied to incompressible fluids

In the context of heat conduction governed by the celebrated Cattaneo equation, Christov has recently proposed a modification of the time derivative term in order to satisfy the objectivity principle. For such a model applied to an incompressible fluid, the uniqueness of the solution is here proved.     

Some results concerning the state of bending for transversely isotropic plates

In this paper, we present a series of basic theorems for transversely isotropic plates characterized by a state of bending. More precisely, we show a reciprocal theorem and a uniqueness result without positive definiteness assumptions on the elastic coefficients. Moreover, we establish some variational and minimum principles. Finally, we give a Galerkin representation of the solution. Copyright © 2009 John Wiley & Sons, Ltd.