High-order plate finite elements for smart structure analysis

Abstract

This paper presents new finite elements for plate analysis of smart composite structures. Based on the sinus model, Murakami's ZigZag functions are introduced in the three directions, improving the accuracy for multilayered modeling. The transverse normal stress is included allowing use of the three-dimensional constitutive law. Three different eight-node finite elements are developed using C 0 approximations, each with a different number of unknown functions: 9, 11 or 12. For the piezoelectric approximation, a layer wise description is used with a cubic variation in the thickness of each layer while the potential is assumed to be constant on each elementary domain for the in-plane variation. These finite elements aims at modeling both thin and thick plates without any pathologies of the classical plate finite elements (shear and Poisson or thickness locking, spurious modes, etc.). This family is evaluated on classical piezoelectric problems of the literature and special emphasis is pointed towards the introduction of equipotential conditions.

Elastic Wave Characteristics of Graphene Reinforced Polymer Nanocomposite Curved Beams Including Thickness Stretching Effect

“…The current work utilized a higher-order shear deformation beam theory that accounts for the thickness stretching effect. The displacement field which has been used in analyzing the different mechanics of beams are given below [ 26 , 58 , 59 ]: where ; t is the time; u 0 and w 0 are, respectively, the curvilinear axial displacement and transverse displacement of a mid-line point of the beam; w 1,2 represents the stretching contributions of the displacement in the transverse direction; θ is a measure for the rotation of the section. The definition of the function f ( z ) is defined as follows: …”

“…The current work utilized a higher-order shear deformation beam theory that accounts for the thickness stretching effect. The displacement field which has been used in analyzing the different mechanics of beams are given below [26,58,59]: Furthermore, by using the above relations, the variation of weight fraction in the GNPs for a variety of layers number is illustrated in Figure 2b.…”

“…The current work utilized a higher-order shear deformation beam theory that accounts for the thickness stretching effect. The displacement field which has been used in analyzing the different mechanics of beams are given below [26,58,59]:…”

A review on modeling techniques of piezoelectric integrated plates and shells

“…Ray and Reddy (2005) and Vasques and Rodrigues (2005) applied a first-order zigzag shear deformation (or layerwise FOSD) theory, and Kapuria (2001) and Kapuria et al (2003) applied a third-order zigzag shear deformation theory, for piezolaminated structures. In addition, Polit et al (2016) applied Murakami’s zigzag functions for accurately modeling of multilayered piezo structures, while Carrera and Demasi (2002) applied for composite structures.…”

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

“…On the other hand, a computationally efficient procedure is necessary, for instance in the framework of optimization procedures [3] or in the control algorithm for allowing a real-time adaptation [4]. The threedimensional (solid) elements with piezoelectric coupling currently available in commercial finite element software provide an excessively cumbersome computational framework, therefore much effort has been dedicated to the formulation of accurate reduced-order models, as witnessed by the early review papers [5,6] and by the more recent developments [7][8][9][10][11][12].…”