Extension of the Body Force Analogy to Generalized Thermoelasticity
Abstract
The classical body force analogy for static problems of thermoelasticity is extended towards generalized thermoelastic problems including Lord-Shulman’s and Green-Lindsay’s theories. We consider two dynamic problems, namely a thermal problem without body forces, but with a given distribution of transient sources of heat, and a force problem without sources of heat, but with body forces. Both problems are treated within the two different theories of generalized thermoelasticity. We show that, given suitable boundary and initial conditions, a distribution of body forces can be constructed, such that the dynamic displacements in both problems become equal. This analogy is checked by means of illustrative analytical examples. We also discuss the relations between the stresses and the temperature in both problems.
References
- 1.Furukawa, T., Irschik, H.: Body-force analogy for one-dimensional coupled dynamic problems of thermoelasticity. J. Therm. Stress. 28, 455–464 (2005)CrossRefGoogle Scholar
- 2.Furukawa, T., Irschik, H.: Extension of body force analogy to generalized thermoelasticity. In: Proceedings of 4th European Conference on Structural Control, St. Petersburg, vol. 1, pp. 250–257 (2008)Google Scholar
- 3.Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2, 1–7 (1972)CrossRefMATHGoogle Scholar
- 4.Irschik, H., Pichler, U.: Dynamic shape control of solids and structures by thermal expansion strains. J. Therm. Stress. 24, 565–576 (2001)CrossRefGoogle Scholar
- 5.Irschik, H., Pichler, U.: An extension of Neumann’s method for shape control of force-induced elastic vibrations by eigenstrains. Int. J. Solids Struct. 41, 871–884 (2004)CrossRefMATHGoogle Scholar
- 6.Lord, H., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967)CrossRefMATHGoogle Scholar
- 7.Noda, N., Hetnarski, R.B., Tanigawa, Y.: Thermal Stresses, 2nd edn. Taylor and Francis, New York (2003)Google Scholar