Abstract
A variational principle for coupled piezoelectric heat conduction is derived. The bilinear convolution due to Gurtin is used to formulate a general variational function. An extended function is presented that is suitable for finite element analysis.
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Chang, M.F. et al. (1984): Role of the piezoelectric effect in device uniformity of GaAs integrated circuits. Appl. Phys. Lett. 45, 279–281
Girrens, S.P.; Bennett, J.G.; Buchanan, G.R. (1986): Finite element modeling of piezoelectric effects in semiconductor devices. First World Congress on Computational Mechanics, Univ. of Texas
Gurtin, M.E. (1964): Variational principles for linear initial-value problems. Quart. Appl. Math. 22, 252–256
Gurtin M.E. (1964): Variational principles for linear elastodynamics. Arch. Rat. Mech. Anal. 16, 234–250
Mason, W.P. (1950): Piezoelectric crystals and their application to ultrasonics. Princeton: Van Nostrand
Mindlin R.D. (1961): On the equations of motion of piezoelectric crystals. In: Problems of continuum mechanics, pp. 282–290. Philadelphia; SIAM
Nowacki (1975): Dynamic problems of thermoelasticity, Chap. 5. Amsterdam: Noordhoff
Nowinski, J.L. (1978): Theory of thermoelasticity with applications, chap. 24. Amsterdam: Sijthoff and Noordhoff
Nye, J.F. (1957): Physical properties of crystals. London: Oxford University Press
Oden, J.T.; Reddy, J.N. (1976): Variational methods in theoretical mechanics. Berlin, Heidelberg, New York: Springer
Onodera, T. et al. (1985): Improvement in GaAs MESFET performance due to piezoelectricity. IEEE Trans Elect. Devices, ED-32, 2314–2318
Sandhu, R.S.; Pister, K.S. (1971): Variational principles for boundary value and initial boundary value problems in continuum mechanics. Int. J. Solids Struct. 7, 639–654
Sandhu, R.S.; Pister K.S. (1971): A variational principle for linear coupled problems in continuum mechanics. Int. J. Engr. Sci. 8, 989–999
Sandhu, R.S.; Pister, K.S. (1972): Variational methods in continuum mechanics. In: Variational methods in engineering. Brebbia and Tottenham (eds). Proc. Int. Conf., Univ. of Southampton, 1/3–1/25
Sandhu, R.S.; Salaam, U. (1975): Variational formulation of linear problems with nonhomogeneous boundary conditions and internal discontinuities. Comp. Meth. Appl. Mech. Engrg. 7, 75–91
Tiersten, H.F. (1969): Vibrations of piezoelastic plates. New York: Plenum Press
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Communicated by S.N. Atluri, August 4, 1986
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Buchanan, G.R. A note on a variational principle for crystal physics. Computational Mechanics 2, 163–166 (1987). https://doi.org/10.1007/BF00282137
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DOI: https://doi.org/10.1007/BF00282137