Axiomatic/Asymptotic Technique Applied to Refined Theories for Piezoelectric Plates

Abstract

This article is devoted to the evaluation of refined theories for static response analysis of piezoelectric plate. The Carrera Unified Formulation (CUF) is employed to generate the refined plate models. The CUF allows the hierarchical implementation of refined models based on any-order expressions of the unknown variables. Equivalent single layer (ESL) and layerwise (LW) approaches are used to generate the refined models. The governing equations are obtained considering Navier-type, closed-form solutions. The axiomatic/asymptotic technique is employed in order to evaluate the relevance of each model term. This technique computes the relevance of a model term by measuring the error introduced with its deactivation with respect to a reference solution. The axiomatic/asymptotic technique is applied considering the sensor and actuator configurations for piezoelectric plates. Moreover, the analyses are performed taking into account the influence of the length-to-thickness ratio (a/ h) and the use of isotropic or orthotropic materials. "Best" models are proposed and the stress/displacement components and electric potential distributions are evaluated by means of these reduced models.

The Ritz – Sublaminate Generalized Unified Formulation approach for piezoelectric composite plates

“…The effect of model assumptions on the accuracy can be quantified in a systematic manner with respect to the associated computational cost by referring to the so-called mixed axiomatic/asymptotic approach [37][38][39]: Best Theory Diagrams have been derived in the framework of analytical Navier-type and FEM solutions for sample problems involving homogeneous metallic plates as well as laminated and sandwich plates. This technique has been applied to analytical Navier-type solutions for piezoelectric plates in [40]. The implementation of this methodology on the basis of the Ritz-SGUF approach could be an interesting subject for a further study.…”

Best Theory Diagrams for cross-ply composite plates using polynomial, trigonometric and exponential thickness expansions

“…This leads to the development of reduced models whose accuracies are equivalent to those of full higher-order models. The AAM has been applied to several problems, including: static and free vibration of beams [38,40], metallic and composite plates [39,41], shells [42,43], LW models [44,45], advanced models based on the Reissner Mixed Variational Theorem [46], and piezoelectric plates [47].…”

Electro-magneto-thermo-elastic response of infinite functionally graded cylinders without energy dissipation

“…The development of the interactions of an electromagnetic field, the thermal field, and the elastic field is available in many studies. Recently, Zenkour and his colleagues [6][7][8][9][10] have presented the analysis of functionally graded piezoelectric cylinders and plates in a hygrothermal environment.…”