On the issue of variational formulation of problems of generalized GN-thermoelasticity

A. V. Zemskov^ab, D. V. Tarlakovskii<sup>ab

a</sup> Research Institute of Mechanics Lomonosov Moscow State University
^b Moscow Aviation Institute (National Research University)

Abstract: Issues related to the formulation of the variational principles of generalized thermoelasticity based on the Green-Naghdi theory are investigated. Variants of the Green-Naghdi theory are considered: classical coupled thermoelasticity and hyperbolic thermoelasticity. To construct functionals of the linear theory of thermoelasticity the variational principle is used which is a generalization of Hamilton's principle in the linear theory of elasticity. Conditions for the stationarity of the constructed functionals are formulated leading to differential formulations of thermoelasticity problems.

Keywords: thermoelasticity, unsteady problem, dynamic problems, variational principle, Hamilton's principle, Green–Naghdi model.

Received: 01.04.2024
Revised: 03.05.2024
Accepted: 13.05.2024

DOI: 10.20948/mm-2024-05-02