Journal ArticleDOI
Variational Principles for Piezoelectric, Thermopiezoelectric, and Hygrothermopiezoelectric Continua Revisited
Gülay Altay,M. Cengiz Dökmeci +1 more
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TLDR
In this paper, Cimento revisited some variational principles for the fundamental equations of a regular region of piezoelectric, thermopiez-olectric and hygrothermopiezoellectric materials in the elastic range.Abstract:
In this paper some variational principles are revisited for the fundamental equations of a regular region of piezoelectric, thermopiezoelectric, and hygrothermopiezoelectric (but non-stochastic, non-local, and non-relativistic) materials in the elastic range. Certain oversights, and especially, those involving the so-called Hu-Washizu variational principle of piezoelectricity that was first formulated in a paper (“Variational Principles in Piezoelectricity,” Lettere Al Nuovo Cimento, vol. 7, 449–454, 1973) are clarified within the “ISI-Web of Science” publications in the open literature. Similar variational principles of piezoelectricity are cited.read more
Citations
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Book ChapterDOI
Variational Principles in Mechanics
TL;DR: In this article, the authors define the principle of virtual work, which is a departure from other minimizing principles in that it incorporated stationarity and local stationarity in its formulation, and it is used to characterize static equilibrium through requiring that the work done by the external forces during a small displacement from equilibrium should vanish.
Journal ArticleDOI
Review: A review of active structural control: challenges for engineering informatics
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Piezoelectricity An Introduction to the Theory and Applications of Electromechanical Phenomena in Crystals
TL;DR: This online pronouncement piezoelectricity an introduction to the theory and applications of electromechanical phenomena in crystals can be one of the options to choose the book as mentioned in this paper.
Journal ArticleDOI
The elastic dielectric.
TL;DR: Slepian used an operational "definition" of stress and concluded that the compensating mechanical forces which must be introduced operationally are not derivable from a tensor.
References
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Journal ArticleDOI
Variational principles for nonlinear piezoelectric materials
Reinaldo Rodríguez-Ramos,Boris E. Pobedria,Pablo Padilla,Julián Bravo-Castillero,Raúl Guinovart-Díaz,Gérard A. Maugin +5 more
TL;DR: In this article, the behavior of nonlinear piezoelectric materials by generalization for this case of the Hashin-Shtrikman variational principles is considered.
A dynamic analysis of piezoelectric strained elements
TL;DR: In this article, the fundamental equations of piezoelectric media are expressed in variational form as the Euler-Lagrange equations of certain integral and differential types of variational principles.
Journal ArticleDOI
On variational techniques for piezoelectric device analysis
TL;DR: In this paper, the authors pointed out that variational principles are not necessarily unique in the case of piezoelectric media problems and pointed out the importance of variational principle in formulating approximation techniques for complicated boundary conditions.
Journal ArticleDOI
Dynamic variational principles for discontinuous elastic fields
TL;DR: In this paper, generalized variational principles were derived for the three-dimensional theory of elastodynamics, where the continuity requirements on the fields of stresses or strains and/or displacements are relaxed through Friedrichs's transformation.