Modelling of Piezolaminated Plates using Layerwise Mixed Finite Elements

Lage, R. Garcia; Soares, Carlos A. Mota; Reddy, J. N.

doi:10.4203/ccp.75.128

Cited by 6 publications

(6 citation statements)

References 14 publications

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“…Further comparisons are given with the results in [Garcia Lage et al 2004b] and with three dimensional solutions in [Heyliger 1994]. To compare the analysis with closed-form exact solutions, attention has been restricted to simply supported square plates.…”

Section: Numerical Resultsmentioning

confidence: 99%

Mixed piezoelectric plate elements with continuous transverse electric displacements

Carrera

Fagiano

2007

JOMMS

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This paper proposes mixed finite elements, FEs, with an a priori continuous transverse electric displacement component Ᏸ z . The Reissner Mixed Variational Theorem (RMVT) and the Unified Formulation (UF) are applied to the analysis of multilayered anisotropic plates with embedded piezoelectric layers. Two forms of RMVT are compared. In a first, partial, form (P-RMVT), the field variables are displacements u, electric potential Φ and transverse stresses σ n . The second, full, form (F-RMVT) adds Ᏸ z as an independent variable. F-RMVT allows the a priori and complete fulfillment of interlaminar continuity of both mechanical and electrical variables.We treat both equivalent single-layer models (ESLM), where the number of variables is kept independent of the number of layers, an layerwise models (LWM), in which the number of variables depends in each layer. According to the UF the order N of the expansions assumed for the u, φ, σ n and Ᏸ z fields in the plate thickness direction z as well as the number of the element nodes N n have been taken as free parameters.In most cases the results of the classical formulation which are based on Principle of Virtual Displacements (PVD) are given for comparison purposes. The superiority of the F-RMVT results, with respect to the P-RMVT and to PVD ones, is shown by few examples for which three-dimensional solution is available. In particular, the F-RMVT results to be very effective for the evaluation of interlaminar continuous Ᏸ z fields.

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Section: Numerical Resultsmentioning

confidence: 99%

Mixed piezoelectric plate elements with continuous transverse electric displacements

Carrera

Fagiano

2007

JOMMS

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“…(10) and it contains the same information of the system in Eq. (16). See the Appendix A for the explicit form of H k .…”

Section: Constitutive Relationsmentioning

confidence: 99%

“…Many works have been devoted to the extension of the CUF: PVD and RMVT variational statements where extended to piezolaminated plates. 15 The modeling of piezolaminated plates using layerwise mixed finite elements was then proposed 16 and subsequently an extension of the RMVT to piezoelectric laminates with analytical results was published. 17 Mixed finite elements for static and dynamics analysis of piezoelectric plates have been provided, 18 where only transverse stresses were modeled by RMVT.…”

Section: Introductionmentioning

confidence: 99%

Hierarchic Plate and Shell Theories with Direct Evaluation of Transverse Electric Displacement

Carrera

Nali

Brischetto

et al. 2009

50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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A mixed variational statement for the analysis of layered structures under the effect of mechanical and electrical fields is proposed in this paper to develop finite plate elements what permits direct evaluation (that is "a priori") of transverse electrical displacement D z. The original Reissner Mixed Variational Theorem RMVT is modified to account "only" for interlaminar continuous Dz. Continuity of mechanical variables, such as transverse shear and normal stress components, is discarded to provide a simple "Electrical" modified RMVT, here denoted RMVT-Dz. Implementation are made via Carrera Unified Formulation. The applications of the proposed approach is demonstrated by comparison with classical formulations based on the Principle of Virtual Displacements as well as to available 3D and analytical solutions.

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“…As far as piezoelectric adaptive plate is concerned, mixed formulation has also proved to be efficient. Although primal models exist [9], and some of them fulfill interlaminar continuity implementation [16], the use of mixed Layerwise theory for piezoelectric adaptive structure has also proved to be of a high interest in static and modal analysis [39,40], thermodynamic analysis [10]. Carrera and Boscolo's article [20] shows an extension to electro-mechanical piezoelectric plate problems of a previously cited article by Carrera [21,22] on both primal and mixed FEM for multilayered plate elements using both ESL and LWM theories.…”

Section: Introductionmentioning

confidence: 99%

A new component mode synthesis for dynamic mixed thin plate finite element models

2015

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International audienceThis paper presents a methodology for the reduction in dynamic mixed finite element models (DM-FEMs) based on the use of a sub-structuring primal methods adapted to such models. We implement a DM-FEM for Kirchhoff–Love thin plates using the Hellinger–Reissner variational mixed formulation adapted to dynamic, and give a quick insight of its convergence. This model uses both displacement and generalized stress fields within the plate, obtained as a primary result, but the numerical size of the model is bigger than with a primal displacement model. Thus, we choose to offset this complication by reducing the model with a totally new sub-structuring reduction method, especially adapted to DM-FEMs. The aim of our method is to adapt sub-structuring reduction methods commonly used for primal displacement FEM only (such as Craig and Bampton method) and split the reduction in the two fields. With these displacement methods, the whole structure is splitted into few smaller ones, and each of them is condensed with eigenmodes of the substructure and static connections between them. The principle of our method is to build, for each substructure, a reduced basis for the displacements according to the existing method, and a projection of the primal basis for the stresses. A new reduced basis for the whole mixed model is then built up exclusively with modes taken from the primal model. That method reduces significantly the number of degrees of freedom and keeps the properties and advantages of the mixed formulation

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Modelling of Piezolaminated Plates using Layerwise Mixed Finite Elements

Cited by 6 publications

References 14 publications

Mixed piezoelectric plate elements with continuous transverse electric displacements

Mixed piezoelectric plate elements with continuous transverse electric displacements

Hierarchic Plate and Shell Theories with Direct Evaluation of Transverse Electric Displacement

A new component mode synthesis for dynamic mixed thin plate finite element models

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