Reference Work Entry

Encyclopedia of Thermal Stresses

pp 2899-2907

Mathematical Models of Reissner-Mindlin Thermoviscoelastic Plates

  • Claudio GiorgiAffiliated withUniversità degli Studi di Brescia Email author 
  • , Maria Grazia NasoAffiliated withUniversità degli Studi di Brescia

Synonyms

Modeling of a Reissner-Mindlin viscoelastic plate with thermal memory

Overview

We here investigate mathematical models describing deformations and thermal variations of a thin homogeneous thermoviscoelastic plate. First, a hereditary non-Fourier constitutive law for the heat flux and some heat power constitutive equation with linear memory are considered. Then, we adapt to hereditary relations some approximation procedures previously established for thermoelastic plates and due to Lagnese and Lions [5, 6]. The resulting models are derived in the framework of the well-established theory of heat conduction, thanks to Gurtin and Pipkin, and according to the standard approximation procedure for the Reissner-Mindlin plate model.

Basic Methodology

We consider a homogeneous, (thermally and elastically) isotropic plate of the Mindlin type, subject to thermal deformations and hereditary heat conduction law. We assume that the plate is of uniform thickness ...

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