Abstract
An energy approach is proposed to derive the physical constitutive equations of nonlinear thermomechanics for inertial elastic systems. A potential of local inertial thermodynamic state and a potential of thermoelastic energy dissipation are introduced. The variational formulation of nonlinear boundary problems of thermoelasticity is implemented on the basis of the Hamiltonian energy functional. Sufficient conditions for the convexity of the functional are formulated
Similar content being viewed by others
REFERENCES
Ya. I. Burak, “Mathematical model for potential description of nonlinear elastic systems,” Dop. NAN Ukrainy, No. 2, 41–49 (1995).
Ya. I. Burak and G. I. Moroz, “Variational formulation and solution of boundary problems in the nonlinear theory of plates using the energy approach,” RAN, Prikl. Mat. Mekh., 67, No.6, 977–985 (2003).
Ya. I. Burak and G. I. Moroz, “Mathematical problems in the nonlinear mechanics of elastic systems,” Mat. Met. Fiz.-Mekh. Polya, 45, No.4, 40–46 (2002).
J. W. Gibbs, Thermodynamics. Statistical Mechanics [Russian translation], Nauka, Moscow (1982).
E. I. Grigolyuk, Ya. S. Podstrigach, and Ya. I. Burak, Optimal Heating of Shells and Plates [in Russian], Naukova Dumka, Kiev (1979).
I. Gyarmati, Nonequilibrium Thermodynamics: Field Theory and Variational Principles, Springer Verlag, Berlin (1970).
A. D. Kovalenko, An Introduction to Thermoelasticity [in Russian], Naukova Dumka, Kiev (1965).
A. D. Kovalenko, Selected Works [in Russian], Naukova Dumka, Kiev (1976).
A. D. Kovalenko, “The current theory of thermoelasticity,” Int. Appl. Mech., 6, No.4, 355–360 (1970).
A. I. Lur'e, Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow (1980).
W. Nowacki, Theory of Elasticity [in Polish], PWN, Warsaw (1970).
Ya. S. Podstrigach and Yu. M. Kolyano, Generalized Thermomechanics [in Russian], Naukova Dumka, Kiev (1976).
Ya. S. Podstrigach and R. N. Shvets, Thermoelasticity of Thin Shells [in Russian], Naukova Dumka, Kiev (1978).
A. Baltov, “Materials sensitive to the type of process,” Int. Appl. Mech., 40, No.4, 361–369 (2004).
Gy. Beda, “Constitutive equations in continuum mechanics,” Int. Appl. Mech., 39, No.2, 123–131 (2003).
I. K. Senchenkov, Ya. A. Zhuk, and V. G. Karnaukhov, “Modeling the thermomechanical behavior of physically nonlinear materials under monoharmonic loading,” Int. Appl. Mech., 40, No.9, 943–969 (2004).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 52–59, September 2005.
Rights and permissions
About this article
Cite this article
Burak, Y.I., Moroz, G.I. Energy Approach to the Formulation of Boundary Problems of Nonlinear Thermomechanics for Elastic Systems. Int Appl Mech 41, 1000–1006 (2005). https://doi.org/10.1007/s10778-006-0007-1
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-006-0007-1