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: In this paper, a new finite element based upon an elastic equivalent single-layer model for shear deformable and straight magneto-electro-elastic generally laminated beam is presented.
29 citations
TL;DR: In this article, a meshless local Petrov-Galerkin (MLPG) method is presented for the analysis of functionally graded material (FGM) plates with a sensor/actuator magnetoelectroelastic layer localized on the top surface of the plate.
Abstract: A meshless local Petrov–Galerkin (MLPG) method is presented for the analysis of functionally graded material (FGM) plates with a sensor/actuator magnetoelectroelastic layer localized on the top surface of the plate. The Reissner–Mindlin shear deformation theory is applied to describe the plate bending problem. The expressions for the bending moment, shear force and normal force are obtained by integration through the FGM plate and magnetoelectric layer for the corresponding constitutive equations. Then, the original three-dimensional (3D) thick-plate problem is reduced to a two-dimensional (2D) problem. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding the node. The weak-form on small subdomains with a Heaviside step function as the test function is applied to derive local integral equations. After performing the spatial MLS approximation, a system of ordinary differential equations of the second order for certain nodal unknowns is obtained. The derived ordinary differential equations are solved by the Houbolt finite-difference scheme. Pure mechanical loads or electromagnetic potentials are prescribed on the top of the layered plate. Both stationary and transient dynamic loads are analyzed.
28 citations
Cites methods from "Layerwise partial mixed finite elem..."
...Lage et al [18] applied the layerwise partial mixed finite element analysis for MEE plates....
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TL;DR: To overcome the overstiffness and the imprecise magneto-electro-elastic coupling effects of finite element model, the authors presented a cell-based smoothed FME model to more accurately simulat...
Abstract: To overcome the over-stiffness and the imprecise magneto-electro-elastic coupling effects of finite element model, we presented a cell-based smoothed finite element model to more accurately simulat...
28 citations
TL;DR: In this article, various forms of the Reissner mixed variational theorem are considered to a priori fulfill the interlaminar continuity of transverse electromechanical variables, and a classical formulation based on the principle of virtual displacements are implemented for comparison purposes.
Abstract: Mixed plate elements for accurate evaluation of transverse mechanical stresses and electrical displacement are developed and compared in this work. Various forms of the Reissner mixed variational theorem are considered to a priori fulfill the interlaminar continuity of transverse electromechanical variables. Classical formulation based on the principle of virtual displacements are implemented for comparison purposes. 2D assumptions are introduced by means of the Carrera unified formulation (CUF). Layer-wise theories are developed by using Legendre type polynomials of various order in the plate-thickness expansion. The evaluation of the interlaminar continuity of transverse electric displacement and/or transverse stresses on the static response of piezoelectric actuated/sensing plate is provided and compared. Orthotropic and anisotropic simply supported plates are considered. Results are assessed by comparison with available 3D piezoelasticity solutions. The mixed formulations that a priori evaluate the tr...
27 citations
TL;DR: In this paper, the scaled boundary finite element method (SBFEM) with the precise integration technique (PIT) is further extended to present the semi-analytical analysis of static bending and free vibration behaviors of laminated magneto-electro-elastic composite plates.
27 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