An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates

Sheikh, Abdul Hamid; Topdar, Pijush; Halder, Sourav

doi:10.1016/s0263-8223(00)00156-2

Cited by 65 publications

(49 citation statements)

References 7 publications

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“…Over the last few years, interest has been emerging for mixed formulations also involving stresses and dielectric displacements as primary variables, see for example the recent works of Lammering et al [26] and of Benjeddou et al [27]. Some of the most recent contributions to the FE analysis of piezoelectric plates that includes an FSDT description of displacements and a LW form of the electric potential have been developed by Sheik et al [28]. The numerical, membrane, and bending behavior of FEs that are based on FSDTs were analyzed by Auricchio et al [29] in the framework of a suitable variational formulation.…”

Section: Introductionmentioning

confidence: 99%

A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches

Cinefra

Valvano

Carrera

2015

International Journal of Smart and Nano Materials

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The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic. The refined models used are derived from Carrera's Unified Formulation (CUF) and they permit the vibration modes along the thickness to be accurately described. The finite-element method is employed and the plate element implemented has nine nodes, and the mixed interpolation of tensorial component (MITC) method is used to contrast the membrane and shear locking phenomenon. The related governing equations are derived from the principle of virtual displacement, extended to the analysis of electromechanical problems. An isotropic plate with piezoelectric patches is analyzed, with clamped-free boundary conditions and subjected to open-and short-circuit configurations. The results, obtained with different theories, are compared with the higher-order type solutions given in the literature. The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches.

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Section: Introductionmentioning

confidence: 99%

A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches

Cinefra

Valvano

Carrera

2015

International Journal of Smart and Nano Materials

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“…Unfortunately, this layerwise approximation is not efficient for all situations as it will be seen later. In a second family, a linear variation is assumed in each layer with respect to the thickness and two quadrilateral finite elements (FE) can be cited: a 9 nodes FE proposed by Sheikh et al [13] and a 4 nodes FE by Cen et al [14]. For the in-plane variation, they use one electric potential dof at each node.…”

Section: Introductionmentioning

confidence: 99%

Electric potential approximations for an eight node plate finite element

Polit¹,

Bruant²

2006

Computers & Structures

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The aim of this work is to develop a computational tool for multilayered piezoelectric plates: a low cost tool, simple to use and very efficient for both convergence velocity and accuracy, without any classical numerical pathologies. In the field of finite elements, two approaches were previously used for the mechanical part, taking into account the transverse shear stress effects and using only five unknown generalized displacements: C 0 finite element approximation based on first-order shear deformation theories (FSDT) [Polit O, Touratier M, Lory P. A new eight-node quadrilateral shear-bending plate finite element. Int J Numer Meth Eng 1994;37:387-411] and C 1 finite element approximations using a high order shear deformation theory (HSDT) [Polit O, Touratier M. High order triangular sandwich plate finite element for linear and nonlinear analyses. Comput Meth Appl Mech Eng 2000;185:305-24].In this article, we present the piezoelectric extension of the FSDT eight node plate finite element. The electric potential is approximated using the layerwise approach and an evaluation is proposed in order to assess the best compromise between minimum number of degrees of freedom and maximum efficiency. On one side, two kinds of finite element approximations for the electric potential with respect to the thickness coordinate are presented: a linear variation and a quadratic variation in each layer. On the other side, the in-plane variation can be quadratic or constant on the elementary domain at each interface layer. The use of a constant value reduces the number of unknown electric potentials. Furthermore, at the post-processing level, the transverse shear stresses are deduced using the equilibrium equations.Numerous tests are presented in order to evaluate the capability of these electric potential approximations to give accurate results with respect to piezoelasticity or finite element reference solutions. Finally, an adaptative composite plate is evaluated using the best compromise finite element.

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“…The initiation and propagation mechanisms have been investigated in [Ingraffea 1983;Mortazavi and Katsabanis 2001;Cho et al 2004]. Generally, two forms of radial crack analysis have been used: dynamic crack analysis (considering stress wave and/or gas pressurization theories) and quasistatic crack analysis (considering only gas pressurization theory); see [Kutter and Fairhurst 1971;Courtesen 1979;Ash 1985;Donzé et al 1997;Cho et al 2004]. Dynamic crack analysis is far beyond our scope; instead we briefly consider quasistatic radial crack analysis due to gas pressurization, to show the effectiveness of the present model for solving some crack problems occurring in rock fracture mechanics.…”

Section: Numerical Analysis Of Radial Cracks In Blastingmentioning

confidence: 99%

“…Recently linear elastic fracture mechanics (LEFM) principles have been widely used in rock fracture mechanics (RFM) [Rossmanith 1983;Whittaker et al 1992;Aliabadi 1998]. Based on LEFM principles, a superposition of the three fracture modes describes the general case of loading called mixed mode loading.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2007

JOMMS

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See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $500 a year. In this paper the dynamic behavior of a fatigue cracked beam is investigated. The purpose is to reveal the nonlinear behavior of the structure with fatigue damage by using wavelet transform. A cracked cantilever beam is modeled by the finite element (FE) method using ALGOR™ software. A breathing crack is described in the FE method as a surface to surface contact of the two edges of the crack during vibration. Strain time history in the area adjacent to the crack has been analyzed using data processing techniques. Nonlinear effects in signals are usually difficult to detect by conventional data processing methods such as fast Fourier transform. However wavelet transform has recently been shown to be an effective method of detecting such nonlinear effects in signals. Modulus maxima, an important property of wavelet transform, have been used as an indicator of the crack size. Numerical results obtained from the FE analysis are presented in this paper, as well as some experimental results. It is shown that detection of fatigue cracks using breathing behavior and wavelet transform can be used to develop a vibration-based crack detection technique.

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An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates

Cited by 65 publications

References 7 publications

A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches

A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches

Electric potential approximations for an eight node plate finite element

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