Hamilton's principle and associated variational principles in polar thermopiezoelectricity


Dokmeci M. C.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, cilt.389, sa.15, ss.2966-2974, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 389 Konu: 15
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.physa.2010.01.002
  • Dergi Adı: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
  • Sayfa Sayıları: ss.2966-2974

Özet

We express Hamilton's principle for a regular region of thermopiezoelectric polar materials. First, we obtain a four-field variational principle which leads, as its Euler-Lagrange equations, to the divergence equations and the associated natural boundary conditions only. Next, we adjoin the rest of the fundamental equations into the variational principle through an involutory transformation. Thus, we formulate a differential type of unified variational principles operating on all the field variables. The unified variational principle is extended for the region with a fixed internal surface of discontinuity and for a curvilinear laminated region as well. The principles derived in invariant form are expressible in a system of particular coordinate system most appropriate to the geometry of the regions. They are indicated to recover some of earlier principles as special cases. (C) 2010 Elsevier B.V. All rights reserved.