Encyclopedia of Thermal Stresses

2014 Edition
| Editors: Richard B. Hetnarski

Mathematical Models of Reissner-Mindlin Thermoviscoelastic Plates

  • Claudio Giorgi
  • Maria Grazia Naso
Reference work entry
DOI: https://doi.org/10.1007/978-94-007-2739-7_912



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 \(d\)

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Università degli Studi di BresciaBresciaItaly