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

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Presentation of the General Solution of Three-Dimensional Dynamic Equations of a Transversely Isotropic Thermoelastic Medium. / Annin, B. D.; Ostrosablin, N. I.

In: Journal of Applied Mechanics and Technical Physics, Vol. 60, No. 2, 01.03.2019, p. 224-233.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{b9f18df6989e4900bffb360c62f16ffa,

title = "Presentation of the General Solution of Three-Dimensional Dynamic Equations of a Transversely Isotropic Thermoelastic Medium",

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.",

keywords = "Carrier–Gassmann condition, general solutions, plane waves, thermal conductivity, thermoelasticity, transverse isotropy",

author = "Annin, {B. D.} and Ostrosablin, {N. I.}",

note = "Publisher Copyright: {\textcopyright} 2019, Pleiades Publishing, Ltd.",

year = "2019",

month = mar,

day = "1",

doi = "10.1134/S0021894419020044",

language = "English",

volume = "60",

pages = "224--233",

journal = "Journal of Applied Mechanics and Technical Physics",

issn = "0021-8944",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Presentation of the General Solution of Three-Dimensional Dynamic Equations of a Transversely Isotropic Thermoelastic Medium

AU - Annin, B. D.

AU - Ostrosablin, N. I.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - 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.

AB - 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.

KW - Carrier–Gassmann condition

KW - general solutions

KW - plane waves

KW - thermal conductivity

KW - thermoelasticity

KW - transverse isotropy

UR - http://www.scopus.com/inward/record.url?scp=85066477996&partnerID=8YFLogxK

U2 - 10.1134/S0021894419020044

DO - 10.1134/S0021894419020044

M3 - Article

AN - SCOPUS:85066477996

VL - 60

SP - 224

EP - 233

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 2

ER -

ID: 20347218