Uniqueness theorem in the linear theory of piezoelectric micropolar thermoelasticity. (English) Zbl 0899.73449
Summary: The linear theory of piezoelectric micropolar thermoelasticity in the case of quasistatic electric fields, stated by W. Nowacki [Theory of asymmetric elasticity, Chap. 6 PWN-Scientific Publishers, Warszawa (1986; Zbl 0604.73020)] is considered. Basic equations of this theory are given in a tensorial form. The mixed problem is defined and a uniqueness theorem of its solution is proved using some results from I. A. Crăciun [Bull. Pol. Acad. Sci. Techn. sci. 42, 369-379 (1994; Zbl 0821.73057)] a method suggested by D. Ieşan (1990) and a result due to J. Ignaczak.
MSC:
| 74F15 | Electromagnetic effects in solid mechanics |
| 74G30 | Uniqueness of solutions of equilibrium problems in solid mechanics |
| 74H25 | Uniqueness of solutions of dynamical problems in solid mechanics |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
References:
| [1] | Nowacki, W., Theory of Asymmetric Elasticity (1986), PWN-Scientific Publishers: PWN-Scientific Publishers Warszawa, Chap. 6 · Zbl 0604.73020 |
| [2] | Voigt, W., Teoretische Studien über die Elasticitatsverhaltnisse der Krystalle, Abh. Ges. Wiss. Gotingen, 34, 100 (1887) |
| [3] | Crǎciun, I. A., Bull. Acad. Pol. Sci., Techn. Sci., 42, 369 (1994) · Zbl 0821.73057 |
| [4] | Ieşan, D., Int. J. Engng Sci., 28, 1139 (1990) · Zbl 0718.73071 |
| [5] | Brun, L., C. R. Acad. Sci. Paris, 261, 2584 (1965) |
| [6] | Toupin, R. A., Int. J. Engng Sci., 1, 101 (1963) |
| [7] | Carlson, D. E., Linear thermoelasticity, (Flügge, S., Handbuch der Physik VIa/2 (1972), Springer: Springer Berlin) · Zbl 0221.73013 |
| [8] | J. IGNACZAK, private communication.; J. IGNACZAK, private communication. |
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