A finite element model based on coupled refined high-order global-local theory for static analysis of electromechanical embedded shear-mode piezoelectric sandwich composite beams with various widths

Abstract

a b s t r a c tIn this study, a new theory for the accurate simulation of the shear-mode behaviour of thin or thick piezoelectric sandwich composite beams is developed. The effects of transverse normal stress and transverse flexibility of layers are considered in the development of the proposed formulation. In order to increase the computational accuracy, all kinematic and stress continuity conditions are satisfied at layer interfaces. Moreover, for the first time, both the electrically induced strain components and the transverse flexibility are taken into account in the proposed formulation. Despite the fact that the number of unknown mechanical parameters in this theory is only one degree higher than the first order shear deformation theory, the accuracy is surprisingly more pronounced for the thicker beams. (S.B. Beheshti-Aval).[10], Kogl and Bucalem [11,12] Chee et al. [13], Jiang and Li[14], Shu [15], Thornburgh and Chattopadhyay [16], Fukunaga et al. [17] and Mitchell and Reddy [18]used equivalent single layer theories (ESLT) for the analysis of extension-mode piezoelectric beams/plates structures. The idea of layer-wise theory (LWT) or discrete-layer theory was presented and developed by Heyliger and Saravanos [19], Saravanos and Heyliger [20], Saravanos et al.[21], Kusculuoglu et al. [22], Garcia Lage et al. [23,24] Robaldo et al. [25], and Tzou and Ye [26]. Beheshti-Aval and Lezgy-Nazargah[27,28] used a sinus zigzag (ZZ) model for analyzing and controlling of smart laminated piezoelectric beams. Kapuria [29], Kapuria et al. [30], and Kapuria and Alam [31] presented an efficient coupled ZZ theory for static and dynamic analysis of extension-mode piezoelectric laminated/sandwich beams based on third order ZZ approximations. introduced a computationally low cost FE model for the static analysis of extension-mode piezoelectric multilayered/sandwich beams based on global-local theory. For an overview on the modeling of extension-mode piezoelectric laminates, readers can refer to Benjeddou [33].The use of a shear-mode piezoelectric actuator was first proposed by Sun and Zhang [34]. In their work, they employed thickness-shear piezoelectric patches to create transverse deflection in sandwich beams. Moreover, they demonstrated that shear-mode actuators can offer many advantages over the extension-mode actuators. The analysis of this study was carried out using the ANSYS finite-element package. Furthermore, Zhang and Sun [35] developed an analytical model to predict the static, as well as the dynamic behavior of a sandwich beam which comprises of a core layer of shear-mode piezoelectric. The model relies on the assumptions that the face layers obey the Euler-Bernoulli theory, while the core piezoelectric layer follows the Timoshenko theory. Moreover, closed-form solutions of a static cantilever beam with shear-mode actuators were presented. Benjeddou et al. [36] proposed a finite element model of a sandwich beam with extension and shear piezoelectric segments. To verify their model, they compared their finite e...

A three-dimensional Peano series solution for the vibration of functionally graded piezoelectric laminates in cylindrical bending

“…(9) identically satisfy the boundary conditions (5)- (6) on the edges x 1 = 0 and x 1 = L. It is worth to note that no assumption for U (k) (x 3 ), V (k) (x 3 ), W (k) (x 3 ), and (k) (x 3 ) is introduced in Eq. (9). They are unknown functions that must be determined.…”

“…Various studies are available in the open literature which deal with the prediction of static and dynamic behaviors of piezoelectric laminated composite structures as well as their e ective electromechanical properties [1][2][3][4][5][6][7][8][9][10][11][12][13]. The conventional piezoelectric devices are made of several layers of di erent piezoelectric materials.…”

NURBS-based isogeometric analysis of laminated composite beams using refined sinus model

“…These theories are able to reproduce piecewise continuous displacement and transverse stress fields in the thickness direction of the laminated structures [13][14][15][16][17][18][19][20][21][22][23][24][25]. The 2D global-local higher-order plate theories [26][27][28][29][30][31][32][33] are also capable of giving accurate results. For a comprehensive overview on theories and computational models for laminated composite structures, readers can refer to Carrera and Brischetto [34], Zhang and Yang [35], and Hu et al [36].…”

“…The finite element method [27][28][29][30][31][32][33], the finite difference method [43][44], the meshfree methods [45], the differential quadrature methods [46], the Ritz methods [47][48][49][50], the strip element method [51][52], etc. are also some of typical numerical methods which were successfully applied for the analysis of laminated composite structures.…”

An efficient coupled polynomial interpolation scheme for shear mode sandwich beam finite element

“…FSDT based beam finite element was proposed by Rathi and Khan (2012) to study vibration attenuation and shape control of smart beams. Beheshti-Aval et al (2013) developed a coupled refined high-order global-local theory for static analysis of shear mode piezoelectric sandwich composite beams. Kapuria and Hagedorn (2007) proposed a unified layerwise theory for piezoelectric smart beams and validated their formulation with finite element simulations using ABAQUS.…”