Presentation of the General Solution of Three-Dimensional Dynamic Equations of a Transversely Isotropic Thermoelastic Medium

B. D. Annin, N. I. Ostrosablin

Research output: Contribution to journalArticlepeer-review

Abstract

A presentation of the general solution of the equations of dynamics of a transversely isotropic thermoelastic medium is obtained in the case where the Carrier–Gassmann condition is satisfied with due allowance for the additional expression relating the temperature stress coefficients to the elasticity moduli. The displacements are expressed via three resolving potentials satisfying three inhomogeneous quasi-wave equations. The potentials are related by the heat conduction equation. A presentation of the solution with the use of the stress and displacement functions is provided. Two displacement functions are determined by solving the system of two homogeneous equations, which do not involve the temperature. After these displacement functions are determined, the temperature can be found from the third equation. The resultant presentation of the solution also yields the solution of the static equations of thermoelasticity.

Original languageEnglish
Pages (from-to)224-233
Number of pages10
JournalJournal of Applied Mechanics and Technical Physics
Volume60
Issue number2
DOIs
Publication statusPublished - 1 Mar 2019

Keywords

  • Carrier–Gassmann condition
  • general solutions
  • plane waves
  • thermal conductivity
  • thermoelasticity
  • transverse isotropy

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