Abstract
This paper presents the problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity, and the surface is assumed initially quiescent. The governing equations are taken in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. Due attention has been paid to the finite time of rise of temperature, stress, displacement, and strain. The problem has been solved analytically using a direct approach. The derived analytical expressions have been computed for a specific situation. Numerical results for the temperature distribution, thermal stress, displacement, and strain are represented graphically. A comparison is made with the results predicted by the three theories.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Biot, M.: J Appl Phys 27 240 (1956)
Ackerman, C.C., Overtone, W.C.: Phys Rev Lett 22, 764 (1969)
Ackerman, C.C., Ber'cman, B., Fairbank, H.A., Guyer, R.A.: Phys Rev Lett 16, 789, (1966).
Bargmann, H.: Nucl. Eng Des 27, 372 (1974)
Boley, B.A.: In: Hasselman, D.P.H., Heller, R.A. (eds.).: Thermal Stresses: A Survey in Thermal Stresses in Severe Environments, pp. 1–ll. Plenum, New York (1980)
Chandrasekhariah, D.S.: Appl Mech Rev 39, 355 (1986)
Lord, H., Shulman, Y.: J Mech Phys Solids 15, 299 (1967)
Green, A.E., Lindsay, K.A.: J Elasticity 2, 1 (1972)
Bahar, L.Y., Hetnarski, R.B.: J Therm Stresses 1, 135 (1978)
Bahar, L.Y., Hetnarski, R.B.: State space approach to thermoelasticity. In: Proceedings of 6th Canadian Congress on Applied Mechanics, University of British Columbia, Vancouver, pp. 17–18 (1977)
Bahar, L.Y., Hetnarski, R.B.: Transfer matrix approach to thermoelasticity. In: Proceedings of the 15th Midwest Mechanic Conference, University of Illinois, Chicago, pp. 161–163 (1977)
Erbay, S., Suhubi, E.S.: J Therm Stresses 9, 279 (1986)
Furukawa, T., Noda, N., Ashida, F.: JSME Int J 31, 26 (1990)
Furukawa, T., Noda, N., Ashida, F.: JSME Int J 34, 281 (1991)
Sherief, H.: J Therm Stresses 16, 163 (1993)
Chandrasekaraiah, D.S., Murthy, H.N.: J Therm Streses 16, 55 (1993)
Misra, J.C., Kar, S.B., Samanta, S.C.: Trans CSME 11, 151 (1987)
Maugin, G.A.: Continuum mechanics of electromagnetic solids. North-Holland, Amsterdam (1988)
Eringen, A.C., Maugin, G.A.: Electrodynamics of Continua, vol. 2. Springer, Berlin Heidelberg New York (1989)
Abd-Alla, A.N., Maugin, G.A.: Int J Eng Sci 28, 589 (1990)
El-Maghraby, N.M., Youssef, H.M.: Appl Math Comput 156, 577 (2004)
Sherief, H., Youssef, H.M.: J Therm Stresses 27(6), 537 (2004)
Youssef, H.M.: Appl Math Mech 26(4), 4827 (2005)
Misra, J.C., Samanta, S.C., Chakrabarti, A.K.: Comput Struct 43, 951 (1992)
Misra, J.C., Samanta, S.C., Chakrabarti, A.K., Misra, S.C.: Int J Eng Sci 29, 1505 (1991)
Misra, J.C., Samanta, S.C., Chakrabarti, A.K.: Int J Eng Sci 29, 1065 (1991)
Hanig, G., Hirdes, U.: A method for the numerical inversion of Laplace transform. J Comput Appl Math 10, 113–132 (1984)
Chu, H., Chen, C., Weng, C.: Applications of Fourier series technique to transient heat transfer. Chem Eng Commun 16, 215–227 (1982)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Youssef, H. Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading. Arch Appl Mech 75, 553–565 (2006). https://doi.org/10.1007/s00419-005-0440-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-005-0440-3