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Abstract <p>Issues related to the formulation of the variational principles of generalized thermoelasticity based on the Green–Naghdi (GN-thermoelasticity or GN theory) 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, which is a generalization of Hamilton’s principle in the linear theory of elasticity, is used. Conditions for the stationarity of the constructed functionals are formulated leading to differential formulations of thermoelasticity problems.</p>

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On the Issue of Variational Formulation of Problems of Generalized GN-Thermoelasticity

  • 期刊论文

  • 发表日期：

    2025年2月28日

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  • A. V. Zemskov,
  • D. V. Tarlakovskii

摘要

Abstract

Issues related to the formulation of the variational principles of generalized thermoelasticity based on the Green–Naghdi (GN-thermoelasticity or GN theory) 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, which is a generalization of Hamilton’s principle in the linear theory of elasticity, is used. Conditions for the stationarity of the constructed functionals are formulated leading to differential formulations of thermoelasticity problems.