2002
DOI: 10.2514/2.1618
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Higher-Order Piezoelectric Plate Theory Derived from a Three-Dimensional Variational Principle

Abstract: A three-dimensional mixed variational principle is used to derive a Kth-order two-dimensional linear theory for an anisotropic homogeneous piezoelectric (PZT) plate. The mechanical displacements, the electric potential, the inplane components of the stress tensor, and the in-plane components of the electric displacement are expressed as a nite series of order K in the thickness coordinate by taking Legendre polynomials as the basis functions. However, the transverse shear stress, the transverse normal stress, … Show more

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Cited by 170 publications
(50 citation statements)
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“…As observed by other authors, such as Batra et al [28,29], enforcing the equilibrium equations in the variational statement is a powerful technique for predicting accurate 3D stress fields in multilayered structures in a variationally consistent manner. However, the present contracted HR functional results in a structural model with fewer degree of freedom than the generalised model by Batra et al as the in-plane and transverse shear stresses are based on the same degrees of freedom and fewer displacement Lagrange multipliers are needed.…”
Section: Governing Equations From the Hellingerreissner Mixed-variatimentioning
confidence: 84%
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“…As observed by other authors, such as Batra et al [28,29], enforcing the equilibrium equations in the variational statement is a powerful technique for predicting accurate 3D stress fields in multilayered structures in a variationally consistent manner. However, the present contracted HR functional results in a structural model with fewer degree of freedom than the generalised model by Batra et al as the in-plane and transverse shear stresses are based on the same degrees of freedom and fewer displacement Lagrange multipliers are needed.…”
Section: Governing Equations From the Hellingerreissner Mixed-variatimentioning
confidence: 84%
“…Nevertheless, we would like to suggest two possible ways of incorporating the effects of transverse normal deformation if these effects are deemed to be significant. The first is to use the generalised approach presented by Batra and co-workers [28,29] of assuming independent Taylor or Legendre series expansions for the six stress and three displacement fields. The drawback of this approach is that the number of variables increases significantly.…”
Section: Discussionmentioning
confidence: 99%
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“…Vidoli and Batra [37] and Batra and Vidoli [38] deduced a variable order plate theory for piezoelectric and orthotropic linear elastic plates in which the order K up to which terms in the thickness coordinate, z, are kept is a variable. They called the plate theory "mixed" ("compatible") when the constitutive relations for the plate are derived from the Hellinger-PrangeReissner principle (from the plate theory displacement field and the constitutive relation of the 3D linear elasticity theory [LET]).…”
Section: Introductionmentioning
confidence: 99%