Green tensor and regular solutions of equations of rods thermodynamics and their properties

• Autorzy: Alexeyeva Lyudmila , Dadayeva Assyat , Ainakeyeva Nursaule

Identyfikatory

DOI

10.15632/jtam-pl/133233

• Języki publikacji: EN

Abstrakty

EN

In the present paper, solutions of the equations of uncoupled thermoelastodynamics of ther- moelastic rods are constructed for power and thermal effects. Based on the Fourier transform, the Green tensor and generalized solutions of the thermoelasticity equations are constructed in the original space-time using the apparatus of generalized functions theory. Analytical formulas for definitions of the thermal stress-strain state of the rods taking into account its thermoelastic parameters are obtained. Shock thermoelastic waves are considered and con- ditions on their fronts are obtained. The results of numerical calculations of Green tensor are presented.

Słowa kluczowe

EN

thermoelastic rod; Green tensor; thermoelastic wave; stress; temperature

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2021
• Tom: Vol. 59 nr 2
• Strony: 227--238
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Alexeyeva Lyudmila

• Institute of Mathematics and Mathematical Modelling, Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan

• https://orcid.org//0000-0002-7131-4635

autor

Dadayeva Assyat

• Institute of Mathematics and Mathematical Modelling, Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan

• https://orcid.org/0000-0001-8954-6007

autor

Ainakeyeva Nursaule

• Institute of Mathematics and Mathematical Modelling, Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan

• https://orcid.org/0000-0003-4643-6072

Bibliografia

• 1. Alekseyeva L.A., Dadayeva A.N., Zhanbyrbaev N.B., 1999, The method of boundary integral equations in boundary value problems of unconnected thermoelastodynamics, Applied Mathematics and Mechanics, 63, 5, 803-808.
• 2. Alexeyeva L.A., Ahmetzhanova M.M., 2018, Stationary oscillations of thermoelastic rod under action of external disturbances, Global Journal of Engineering Science and Research Management, 5, 2, 33-43.
• 3. Alipova B.N., Alexeyeva L.A., Dadayeva A.N., 2017, Shock waves as generalized solutions of thermoelastodynamics equations. On the uniquiness of boundary value problems solutions, American Institute of Physics Conference Proceeding, 1798, 020003-1-020003-8.
• 4. Kupradze V.D., Hegelia T.G., Basheleishvili M.O., Burchuladze T.V., 1976, Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, Moscow, 664.
• 5. Novatskiy V., 1970, Dynamic Problems of Thermoelasticity, Moscow, Mir, 256.
• 6. Predeleanu M., 1987, Analysis of thermomechanical coupling by boundary element method, [In:] Thermomechanical Couplings Solids. Jean Mandel Memory Symposium, Amsterdam, 305-318.
• 7. Sah J., Tasaka N., 1988, Boundary element analysis of linear coupled thermoelasticity problems by using Laplace transformation, Proceeding 1st Joint Japan, US Symposium. Boundary Element Methods, Tokyo, 335-544.
• 8. Sharp S., Crouch S.L., 1986, Boundary integral methods for thermoelasticity problems, American Society of Mechanical Engineers (ASME): Journal Applied Mechanics, 53, 2, 298-302.
• 9. Vladimirov V.S., 1988, Equations of Mathematical Physics, Moscow, Nauka, 511.
• 10. Yoshihiro O., Ryohi I., 1988, Three-dimensional unsteady thermal stress analyses by means of the thermoelastic displacement potential and boundary element method, Japan Society of Mechanical Engineers Series A, 54, 506, 1847-1850.