Analysis of laminated adaptive plate structures using layerwise finite element models

Garção, J.; Soares, Carlos A. Mota; Reddy, J. N.

doi:10.1016/j.compstruc.2003.10.024

Cited by 36 publications

(8 citation statements)

References 25 publications

(80 reference statements)

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“…Saravanos (1997) introduced a mixed laminated theory combining equivalent single layer assumptions for the mechanical displacements with layerwise representation for the electric potential. Many formulations have also been proposed in recent times (Balamurugan and Narayanan, 2001;Narayanan and Balamurugan, 2003;Kulkarni and Bajoria, 2003;Topdar et al, 2004;Semedo Garc et al, 2004;Correia et al, 2004;Simoes Moita et al, 2005;Marinkovic´et al, 2006) where the electric potential over thickness is assumed to vary linearly over the thickness, which would not accurately include the induced electric field due to deformation. This limits the applicability of these elements, since the electric potential induced by deformation is important in many applications.…”

Section: Introductionmentioning

confidence: 99%

Multilayer Higher Order Piezolaminated Smart Composite Shell Finite Element and its Application to Active Vibration Control

Balamurugan

Narayanan

2008

Journal of Intelligent Material Systems and Structures

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This paper deals with the formulation of a higher order shear-flexible piezolaminated 8-node C1 continuous multilayer smart composite shell finite element with higher order modeling of electric potential. The potential induced due to bending deformation is more accurately modeled assuming quadratic variation of electric potential through the thickness of each piezoelectric layer. This is achieved by interpolating using nodal mid-plane electric potentials and one electric degree of freedom representing the potential difference between the top and bottom surfaces of the piezoelectric layer, resulting in nine electric degrees of freedom per piezoelectric layer in the element. The higher order shell theory used satisfies the stress and displacement continuity at the interface of the composite laminates and has zero shear stress on the top and bottom surfaces. The transverse shear deformation is of a higher order represented by the trigonometric functions, allowing us to avoid the shear correction factors. In order to maintain the field consistency, the inplane displacements, u and v, and rotations θx and θ y, are interpolated using quadratic interpolation functions while the transverse displacement w is interpolated using Hermite cubic interpolation function, resulting in 48 elastic degrees of freedom per element. The active vibration control performances of the piezolaminated smart composite plates/shells have been studied by modeling them with the above element and applying LQR optimal control.

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Section: Introductionmentioning

confidence: 99%

Multilayer Higher Order Piezolaminated Smart Composite Shell Finite Element and its Application to Active Vibration Control

Balamurugan

Narayanan

2008

Journal of Intelligent Material Systems and Structures

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“…(12) by Fourier's law available for heat conduction, and inserting it in interface and top and bottom conditions for normal heat flux similarly to Eqs. (10) and (11), we deduce the final temperature field in the following form:…”

Section: Extension To the Thermoelastic Response Of Laminatesmentioning

confidence: 99%

“…Pioneer work in layer by layer approximations such as one-dimensional finite element representation along the thickness of the laminate was published by Reddy [7], and it is termed the "layerwise" theory. Applications of the layerwise theory to piezoelectric laminates can be found in Saravanos et al [8], Garcia Lage et al [9], and Semedo Garção et al [10], and for heat conduction see Blanc and Touratier [11]. Several different layer by layer approaches, not using one-dimensional finite element representation through thickness of laminates, are of course available in the literature (see Carrera [3]).…”

Section: Introductionmentioning

confidence: 99%

Modelling Elastic and Thermoelastic Thick Multilayered Composites by a New Constrained Discrete Layer Approach

Blanc

Touratier

2006

Mechanics of Advanced Materials and Structures

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A new layer by layer/discrete layer model is presented for the linearly elastic and thermoelastic responses of multilayered composite plates. The transverse variation of the displacement field is defined in terms of a one-dimensional finite element representation, using quadratic Lagrangian interpolations. The laminate thickness is subdivided into a series of one-dimensional finite elements (i.e., thickness subdivisions) whose nodes correspond to planes of constant transverse normal coordinates in the undeformed configuration of the laminate. Each of the displacements and loads is expanded in a double Fourier series in the cartesian surface coordinates. Interface and boundary conditions are exactly verified and exploited to reduce the number of independent generalized displacements, before solving the boundary value problem from the standard variational principle for displacements. This leads to a new model, whose size 3N in 3D, is less than the classic layer by layer approach requiring 3(2N + 1), also in 3D. In addition, this model allows satisfying exactly all the interface and boundary conditions. Numerical evaluations and comparisons with exact 3D elasticity solutions confirm the efficacy of the proposed approach. Finally, the proposed modelling has been extended to the thermoelastic response of laminates and the results are compared with the exact 3D solutions. Temperature distributions required for the thermoelastic analysis are determined from the constrained discrete layer approach previously applied to heat conduction.

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“…The FEM was first used to investigate the behavior of piezoelectric ultrasonic transducers by Allik and Hughes (1970). Many articles have since been published on the topic (Benjeddou, 2000; Lerch, 1990; Saravanos et al, 1997) and also on the analysis of piezoelectric laminated plates (Garcia Lage et al, 2004; Semedo Garcao et al, 2004). The BEM is an efficient and popular alternative to FEM.…”

Section: Introductionmentioning

confidence: 99%

Meshless analysis of piezoelectric sensor embedded in composite floor panel

Tadeu

Sládek

2014

Journal of Intelligent Material Systems and Structures

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Piezoelectric materials are the key element in various sensors and sensory devices used in industry and research. In this article, we use the meshless local Petrov–Galerkin method to analyze a three-dimensional piezoelectric sensor that is embedded in a composite floor panel. Temporal variation of panel deformation is determined analytically and then prescribed as a boundary condition for the sensor. In the proposed formulation, quasi-static governing equations for the electric field and elastodynamic equations for mechanical fields are coupled together. Local integral equations are derived from the local weak form of the governing equations, using a Heaviside step function as the test function. Nodal points are distributed in the analyzed domain, and each node is the center of a small subdomain of spherical shape. The spatial variations of the displacement and electric potential are approximated by the moving least squares scheme. A system of ordinary differential equations is obtained after evaluation of all spatial integrals. The Houbolt finite-difference scheme is applied to solve this system of ordinary differential equations as a time-stepping method. The temporal variation of the induced electric field is finally obtained. It is shown that significant peak amplitudes of the electric field are detected at the top of the sensor.

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Analysis of laminated adaptive plate structures using layerwise finite element models

Cited by 36 publications

References 25 publications

Multilayer Higher Order Piezolaminated Smart Composite Shell Finite Element and its Application to Active Vibration Control

Multilayer Higher Order Piezolaminated Smart Composite Shell Finite Element and its Application to Active Vibration Control

Modelling Elastic and Thermoelastic Thick Multilayered Composites by a New Constrained Discrete Layer Approach

Meshless analysis of piezoelectric sensor embedded in composite floor panel

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