Layerwise partial mixed finite element analysis of magneto-electro-elastic plates
TL;DR: In this paper, a partial mixed layerwise finite element model for adaptive plate structures is presented by considering a Reissner mixed variational principle, and the mixed functional is formulated using transverse stresses, displacement components and electric and magnetic potentials as primary variables.
About: This article is published in Computers & Structures.The article was published on 2004-07-01. It has received 148 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.
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TL;DR: A multi-physics node-based smoothed radial point interpolation method (MNS-RPIM) for the transient responses of two-dimensional magneto-electro-elastic (MEE) structures is presented, the displacement, electrical potential and magnetic potential are obtained by combining the coupling MEE Newmark method as mentioned in this paper.
Abstract: A multi-physics node-based smoothed radial point interpolation method (MNS-RPIM) for the transient responses of two-dimensional magneto-electro-elastic (MEE) structures is presented, the displacement, electrical potential and magnetic potential are obtained by combining the coupling MEE Newmark method. Based on constitutive equation of MEE material and introducing the weakened weak (W2) formulation and the G space theory, the discretized system equations are produced. The method developed here is suitable for arbitrary boundary conditions, which could be the complement to the analytical solution. For two-dimensional structures, triangular element is adopted to discrete models because it could be automatically generated for complex geometries. The generalized displacement is computed for a cantilever beam, a layered MEE sensor and a typical MEE energy harvester. Results shows the following important properties of MNS-RPIM: (1) insensitive to mesh distortion; (2) accurate and convergent; (3) volumetric locking free; (4) high efficiency over FEM at the same accuracy.
10 citations
TL;DR: In this paper, the finite element method was proposed to analyze coated fiber composites with piezoelectric and piezomagnetic phases, and the computational homogenization technique was applied for fiber composite composites.
Abstract: The finite element method is proposed to analyze coated fiber composites with piezoelectric and piezomagnetic phases. The computational homogenization technique is applied for fiber composites with...
9 citations
Cites background from "Layerwise partial mixed finite elem..."
...However, they were mostly for laminated composites (Annigeri et al., 2007; Buchanan, 2004; Carrera et al., 2008; Lage et al., 2004), and that there is nearly no FEM article toward the important subject as investigated in this article, namely, the effect of coating layer on the effective composite material properties of multiferroics....
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...However, they were mostly for laminated composites (Annigeri et al., 2007; Buchanan, 2004; Carrera et al., 2008; Lage et al., 2004), and that there is nearly no FEM article toward the important subject as investigated in this article, namely, the effect of coating layer on the effective composite…...
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TL;DR: In this article, the generalized finite element method (GFEM) was used to numerically analyze the coupled electro-structural response of laminated plates with orthotropic fiber reinforced layers and piezoelectric layers.
Abstract: This paper presents a procedure to numerically analyze the coupled electro-structural response of laminated plates with orthotropic fiber reinforced layers and piezoelectric layers using the generalized finite element method (GFEM). The mechanical unknowns, the displacements, are modeled by a higher order shear deformation theory (HSDT) of the third order, involving seven generalized displacement functions. The electrical unknowns, the potentials, are modeled by a layerwise theory, utilizing piecewise linear functions along the thickness of the piezoelectric layers. All fields are enriched in the in-plane domain of the laminate, according to the GFEM, utilizing polynomial enrichment functions, defined in global coordinates, applied on a bilinear partition of unities defined on each element. The formulation is developed from an extended principle of Hamilton and results in a standard discrete algebraic linear motion equation. Numerical results are obtained for some static cases and are compared with several numerical and experimental results published in the literature. These comparisons show consistent and reliable responses from the formulation. In addition, the results show that GFEM meshes require the least number of elements and nodes possible for the distribution of piezoelectric patches and the enrichment provides more flexibility to reproduce the deformed shapes of adaptive laminated plates.
9 citations
TL;DR: Investigation of the bending response performances of the magneto–electro–elastic (MEE) laminated plates resting on the Winkler foundation or the elastic half-space subjected to a transverse mechanical loading shows excellent agreements with the solutions based on the analytical and numerical approaches.
Abstract: This article investigates the bending response performances of the magneto–electro–elastic (MEE) laminated plates resting on the Winkler foundation or the elastic half-space subjected to a transverse mechanical loading .By assuming that the foundation is not electrically and magnetically conductive, the scaled boundary finite element method (SBFEM) based on the three-dimensional (3D) theory of elasticity is applied for both the simulation of the MEE laminated plate and the elastic half-space. The SBFEM model considers the generalized displacement involving the elastic displacement, electric potential and magnetic potential as the nodal degree of freedom for the MEE laminated plates, and only the in-plane of the MEE laminated plate or the boundary of the elastic half-space needs to be discretized leading to reduce the spatial dimension by one. Furthermore, in the SBFEM, the governing equations can be solved by using an analytical approach in the radial direction of the scaled coordinate system, so that it is particularly suitable for the simulation of the elastic half-space. For the Winkler foundation–plate system, the global stiffness coupling governing equation that includes the interaction between the MEE laminated plate and the Winkler foundation is derived directly from the 3D elasticity equations of the MEE laminated plate by assuming that the foundation reactions are proportional to the transverse displacements of the plate structure. While for the MEE laminated plate-half-space system, the whole domain is divided into three sub-domains including the MEE laminated plate structure, the near and semi-infinite far foundation systems based on the sub-structure method, and then the stiffness matrix of each sub-domain can be determined by means of the SBFEM. As a result, the global stiffness equation of the plate-half-space system can be assembled according to the principle of the degree of freedom matching at the same nodes. The numerical results obtained for limiting cases by using the proposed method were compared with the published works and showed excellent agreements with the solutions based on the analytical and numerical approaches, so that the accuracy and applicability of the proposed formulations for the analysis of the interaction problems between the MEE laminated plate and the Winkler foundation or elastic half-space can be verified. Moreover, several numerical examples with various material properties, geometries, stacking sequences, aspect ratios, and supported boundary conditions were presented to show the effects of which on the responses of the plate–foundation system.
9 citations
TL;DR: A bibliography is given containing 1887 references published during 2004 on piezoelectric and pyroelectric properties of materials and their applications as discussed by the authors, which contains listings of journal articles and patents with complete bibliographic citations.
Abstract: A bibliography is given containing 1887 references published during 2004 on piezoelectric and pyroelectric properties of materials and their applications. It contains listings of journal articles and patents with complete bibliographic citations. Journal and patent references from 2004 in which the first author's name began with letters between A and K were given in Guide 25 (published previously). Journal articles and patents by authors with names beginning with the letters L through Z are published in the present Guide. This bibliography is the continuation of a series published semi-annually.
9 citations
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Book•
19 Nov 1996TL;DR: The use of composite materials in engineering structures continues to increase dramatically, and there have been significant advances in modeling for general and composite materials and structures in particular as discussed by the authors. But the use of composites is not limited to the aerospace domain.
Abstract: The use of composite materials in engineering structures continues to increase dramatically, and there have been equally significant advances in modeling for general and composite materials and structures in particular. To reflect these developments, renowned author, educator, and researcher J.N. Reddy created an enhanced second edit
5,301 citations
Book•
01 Jan 2004
TL;DR: In this article, the authors present an analysis of the properties of composite materials using the classical and first-order theories of Laminated Composite Plates and shells, as well as a detailed analysis of their properties.
Abstract: Equations of Anisotropic Elasticity, Virtual Work Principles, and Variational Methods Fiber-Reinforced Composite Materials Mathematical Preliminaries Equations of Anisotropic Entropy Virtual Work Principles Variational Methods Summary Introduction to Composite Materials Basic Concepts and Terminology Constitutive Equations of a Lamina Transformation of Stresses and Strains Plan Stress Constitutive Relations Classical and First-Order Theories of Laminated Composite Plates Introduction An Overview of Laminated Plate Theories The Classical Laminated Plate Theory The First-Order Laminated Plate Theory Laminate Stiffnesses for Selected Laminates One-Dimensional Analysis of Laminated Composite Plates Introduction Analysis of Laminated Beams Using CLPT Analysis of Laminated Beams Using FSDT Cylindrical Bending Using CLPT Cylindrical Bending Using FSDT Vibration Suppression in Beams Closing Remarks Analysis of Specially Orthotropic Laminates Using CLPT Introduction Bending of Simply Supported Rectangular Plates Bending of Plates with Two Opposite Edges Simply Supported Bending of Rectangular Plates with Various Boundary Conditions Buckling of Simply Supported Plates Under Compressive Loads Buckling of Rectangular Plates Under In-Plane Shear Load Vibration of Simply Supported Plates Buckling and Vibration of Plates with Two Parallel Edges Simply Supported Transient Analysis Closure Analytical Solutions of Rectangular Laminated Plates Using CLPT Governing Equations in Terms of Displacements Admissible Boundary Conditions for the Navier Solutions Navier Solutions of Antisymmetric Cross-Ply Laminates Navier Solutions of Antisymmetric Angle-Ply Laminates The Levy Solutions Analysis of Midplane Symmetric Laminates Transient Analysis Summary Analytical Solutions of Rectangular Laminated Plates Using FSDT Introduction Simply Supported Antisymmetric Cross-Ply Laminated Plates Simply Supported Antisymmetric Angle-Ply Laminated Plates Antisymmetric Cross-Ply Laminates with Two Opposite Edges Simply Supported Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported Transient Solutions Vibration Control of Laminated Plates Summary Theory and Analysis of Laminated Shells Introduction Governing Equations Theory of Doubly-Curved Shell Vibration and Buckling of Cross-Ply Laminated Circular Cylindrical Shells Linear Finite Element Analysis of Composite Plates and Shells Introduction Finite Element Models of the Classical Plate Theory (CLPT) Finite Element Models of Shear Deformation Plate Theory (FSDT) Finite Element Analysis of Shells Summary Nonlinear Analysis of Composite Plates and Shells Introduction Classical Plate Theory First-Order Shear Deformation Plate Theory Time Approximation and the Newton-Raphson Method Numerical Examples of Plates Functionally Graded Plates Finite Element Models of Laminated Shell Theory Continuum Shell Finite Element Postbuckling Response and Progressive Failure of Composite Panels in Compression Closure Third-Order Theory of Laminated Composite Plates and Shells Introduction A Third-Order Plate Theory Higher-Order Laminate Stiffness Characteristics The Navier Solutions Levy Solutions of Cross-Ply Laminates Finite Element Model of Plates Equations of Motion of the Third-Order Theory of Doubly-Curved Shells Layerwise Theory and Variable Kinematic Model Introduction Development of the Theory Finite Element Model Variable Kinematic Formulations Application to Adaptive Structures Layerwise Theory of Cylindrical Shell Closure Subject Index
3,457 citations
TL;DR: In this paper, the advances and trends in the formulations and applications of the finite element modeling of adaptive structural elements are surveyed and discussed in a first attempt to survey and discuss the advances.
639 citations
TL;DR: In this paper, exact solutions for three-dimensional, anisotropic, linearly magneto-electroelastic, simply-supported, and multilayered rectangular plates under static loadings are derived.
Abstract: Exact solutions are derived for three-dimensional, anisotropic, linearly magneto-electroelastic, simply-supported, and multilayered rectangular plates under static loadings. While the homogeneous solutions are obtained in terms of a new and simple formalism that resemble the Stroh formalism, solutions for multilayered plates are expressed in terms of the propagator matrix. The present solutions include all the previous solutions, such as piezoelectric, piezomagnetic, purely elastic solutions, as special cases, and can therefore serve as benchmarks to check various thick plate theories and numerical methods used for the modeling of layered composite structures. Typical numerical examples are presented and discussed for layered piezoelectric/piezomagnetic plates under surface and internal loads.
584 citations
TL;DR: The use of the Reissner Mixed Variational Theorem (RMVT) for multilayered plate and shell analysis has been extensively studied in the literature as mentioned in this paper, with a thorough review of the literature involving the use in the modeling of multi-layered plates and shells using RMVT is presented.
Abstract: This review article is devoted to the use of the Reissner Mixed Variational Theorem ~RMVT! forward two-dimensional modeling of flat and curved, multilayer structures. A thorough review of the literature involving the use in the modeling of multilayered plates and shells using RMVT is also presented. In the first part, the paper overviews relevant key points that should be taken into account for an accurate description of strain and stress fields in multilayered plate and shell analysis. It is then shown that RMVT has been originated in view of the fulfillment of such key points, herein referred to as C-Requirements ~zig-zag form of the displacement fields in the thickness direction and continuity of transverse normal and shear stresses at each layer interface!. Classical variational statements are used to introduce Reissner’s Theorem. In the second part, the paper presents various ways in which RMVT can be used to develop plate and shell theories in a systematic manner. The so called layer-wise and equivalent single layer variable description are considered. Both strong and weak ~finite element! forms of governing equations have been derived. A Weak Form of Hooke’s Law ~WFHL!, is also discussed as an idea to eliminate transverse stress variables leading to standard classical models with only displacement unknowns. Two appendices display details of governing equations related to multilayered doubly curved shells and to finite element matrices of multilayered plates. A third part reviews the works that have appeared in literature which make use of RMVT. Mainly papers on multilayered plate and shell modelings have been addressed. The final part of the paper is devoted to giving an overview with selected results of numerical performance that can be acquired by RMVT applications; extensive comparison to elasticity solutions and to other significant analyses, based on classical and refined approaches, are given. It is concluded that Reissner’s Mixed Theorem should be considered as a natural tool for multilayered structure analyses; it plays a similar role to that of the Principle of Virtual Displacement in the analysis of isotropic single-layer structures. This review article includes 119 references. @DOI: 10.1115/1.1385512#
435 citations