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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01 Jan 2014
4 citations
Cites methods from "Layerwise partial mixed finite elem..."
...Finite element method (FEM) was used by Lage et al (2004), Liu et al (2004), and Bhangale and Ganesan (2006) to study the static and vibration problems of magneto-electro-elastic layered plates....
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TL;DR: In this paper, the influence of volume fraction of Barium Titanate (BaTiO3) and Cobalt-Ferric oxide (CoFe2O4) and its corresponding coupled material properties on the static response of multiphase magneto-electro-elastic (MEE) cantilever beam was analyzed.
4 citations
01 Jan 2018
TL;DR: In this paper, the authors proposed a transient Newton-Raphson strategy for the treatment of acoustomagneto-mechanical coupling that arises in low-frequency electro-magneto -mechanics, such as MRI scanners.
Abstract: Magnetic Resonance Imaging (MRI) scanners are becoming increasingly popular with many clinical experts for use in both medical research and clinical imaging of patients, due to their ability to perform high-resolution non-intrusive imaging examinations. Recently, however, there has been an increasing demand for higherresolution scanners that are capable of performing quicker scans with increased patient comfort. With this demand for more advanced MRI systems, there also follows a number of challenges facing designers. Understanding the physical phenomena behind MRI is crucial in the development of scanners that are capable of producing accurate images of the patient with maximum comfort and minimal noise signatures. MRI scanners utilise strong static magnetic fields coupled with rapidly time varying gradient magnetic fields to generate images of the patient. In the presence of these time varying fields, the conducting components of MRI scanners generate eddy currents, which give rise to Lorentz forces and cause the conductors to vibrate. These vibrations cause acoustic waves to form that propagate through the air and result in audible noise which can cause significant discomfort for the patient. They also generate Lorentz currents which feedback into the electromagnetic field and this process results in a fully coupled non-linear acousto-magneto-mechanical system. The determination of the coupling mechanisms involved in such a system is a nontrivial task and so, in order to understand the behaviour of MRI systems during operation, advanced computational tools and techniques are required. Moreover, there exists certain small scale physical phenomena that arise in the coupled system which require high resolutions to obtain accurate results. In this thesis, a new computational framework for the treatment of acoustomagneto-mechanical coupling that arises in low-frequency electro-magneto-mechanical systems, such as MRI scanners, is proposed. The transient Newton-Raphson strategy involves the solution of a monolithic system, obtained from the linearisation of the coupled system of equations and two approaches are considered: (i) the linearised approach and (ii) the non-linear approach. In (i), physically motivated by the excitation from static and time varying current sources of MRI scanners, the fields may be split into a dominant static component and a much smaller dynamic component. The resulting linearised system is obtained by performing the linearisation of the fields about this dominant static component. This approach permits solutions in the frequency domain, for understanding the response of MRI systems under various excitations, and provides a computationally efficient way to solve this challenging problem, as it allows the tangent stiffness
4 citations
Cites background from "Layerwise partial mixed finite elem..."
...This problem can be overcome through the use of mixed formulations [109, 55, 207, 144]....
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TL;DR: In this paper, a new layer by layer/discrete layer model for the linearly elastic and thermoelastic responses of multilayered composite plates is presented for the transverse variation of the displacement field is defined in terms of a one-dimensional finite element representation, using quadratic Lagrangian interpolations.
Abstract: 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...
4 citations
TL;DR: In this paper, an analysis of two collinear antiplane cracks in inhomogeneous (functionally graded) anisotropic magnetoelectroelastic materials is presented.
Abstract: An analysis of two collinear antiplane cracks in inhomogeneous (functionally graded) anisotropic magnetoelectroelastic materials is presented. In designing components involving functionally graded materials, an important aspect of the problem is the fracture failure. The problem is formulated for transversely isotropic functionally graded magnetoelectroelastic materials. An integral transform is employed to reduce the problem to a singular integral equation that can be solved.
4 citations
References
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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