Layer-Wise Mixed Models for Accurate Vibrations Analysis of Multilayered Plates

1998 ◽  
Vol 65 (4) ◽  
pp. 820-828 ◽  
Author(s):  
E. Carrera
Keyword(s):  
Mixed Models ◽  
Dynamic Equilibrium ◽  
Variational Equation ◽  
A Priori ◽  
Three Dimensional ◽  
Single Layer ◽  
Multilayered Plates ◽  
Three Dimensional Elasticity ◽  
Free Vibration Response ◽  
Principle Of Virtual Displacements

This paper presents the dynamic analysis of multilayered plates using layer-wise mixed theories. With respect to existing two-dimensional theories at the displacement formulated, the proposed models a priori fulfill the continuity of transverse shear and normal stress components at each interface between two adjacent layers. A Reissner’s mixed variational equation is employed to derive the differential equations, in terms of the introduced stress and displacement variables, that govern the dynamic equilibrium and compatibility of each layer. The continuity conditions at the interfaces are used to write corresponding equations at multilayered level. Related standard displacement formulations, based on the principle of virtual displacements, are given for comparison purposes. Numerical results are presented for the free-vibration response (fundamental and higher order frequencies are calculated) of symmetrically and unsymmetrically laminated cross-ply plates. Several comparisons to three-dimensional elasticity analysis and to some available results, related to both layer-wise and equivalent single-layer theories, have shown that the presented mixed models: (1) match the exact three-dimensional results very well and (2) lead to a better description in comparison to results related to other available analysis.

A Reissner’s Mixed Variational Theorem Applied to Vibration Analysis of Multilayered Shell

1999 ◽  
Vol 66 (1) ◽  
pp. 69-78 ◽  
Author(s):  
E. Carrera
Keyword(s):  
Normal Stress ◽  
Structural Model ◽  
Dynamic Equilibrium ◽  
A Priori ◽  
Three Dimensional ◽  
Single Layer ◽  
Transverse Normal Stress ◽  
Variational Theorem ◽  
Reissner’S Mixed Variational Theorem ◽  
Static Conditions

A comprehensive model of anisotropic multilayered double curved shells fulfilling a priori the interlaminar continuity requirements for the transverse shear and transverse normal stress as well as the static conditions on the bounding surfaces of the shell is developed in this paper. To this end, Reissner’s mixed variational theorem is employed to derive the equations governing the dynamic equilibrium and compatibility of each layer, while the interlaminar continuity conditions are used to drive the equations at the multilayered level. No assumptions have been made concerning the terms of type thickness to radii shell ratio h/R. Classical displacement formulations and related equivalent single layer equations have been derived for comparison purposes. Comparison of frequency predictions based upon the presented structural model with a number of results spread throughout the specialized literature and obtained via other models reveals that this advanced model provides results in excellent agreement with the ones based on three-dimensional elasticity theory, and better as compared to the ones violating the interlaminar stress continuity requirements and/or transverse normal stress and related effects.

Refined Multilayered Plate Elements for Coupled Magneto‐Electro‐Elastic Analysis

2009 ◽  
Vol 5 (2) ◽  
pp. 119-138 ◽  
Author(s):  
M. Di Gifico ◽  
P. Nali ◽  
S. Brischetto
Keyword(s):  
Finite Elements ◽  
Kinematic Model ◽  
Single Layer ◽  
Laminated Plates ◽  
Governing Equations ◽  
Elastic Fields ◽  
Plate Elements ◽  
Plate Models ◽  
Multilayered Plates ◽  
Principle Of Virtual Displacements

Finite elements for the analysis of multilayered plates subjected to magneto‐electro‐elastic fields are developed in this work. An accurate description of the various field variables has been provided by employing a variable kinematic model which is based on the Unified Formulation, UF. Displacements, magnetic and electric potential have been chosen as independent unknowns. Equivalent single layer and layer‐wise descriptions have been accounted for. Plate models with linear up to fourth‐order distribution in the thickness direction have been compared. The extension of the principle of virtual displacements to magneto‐electro‐elastic continua has been employed to derive finite elements governing equations. According to UF these equations are presented in terms of fundamental nuclei whose form is not affected by kinematic assumptions. Results show the effectiveness of the proposed elements as well as their capability, by choosing appropriate kinematics, to accurately trace the static response of laminated plates subject to magneto‐electro‐elastic fields.

Dynamical contact problems with friction for hemitropic elastic solids

2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Avtandil Gachechiladze ◽  
Roland Gachechiladze ◽  
David Natroshvili
Keyword(s):  
Variational Inequality ◽  
Contact Problem ◽  
A Priori Estimates ◽  
Variational Equation ◽  
A Priori ◽  
Three Dimensional ◽  
Contact Problems ◽  
Positive Definiteness ◽  
Elastic Solids ◽  
Dimensional Boundary

Abstract.In the present paper we investigate a three-dimensional boundary-contact problem of dynamics for a homogeneous hemitropic elastic medium with regard to friction. We prove the uniqueness theorem using the corresponding Green formulas and positive definiteness of the potential energy. To analyze the existence of solutions we reduce equivalently the problem under consideration to a spatial variational inequality. We consider a special parameter-dependent regularization of this variational inequality which is equivalent to the relevant regularized variational equation depending on a real parameter and study its solvability by the Faedo–Galerkin method. Some a priori estimates for solutions of the regularized variational equation are established and with the help of an appropriate limiting procedure the existence theorem for the original contact problem with friction is proved.

Asymptotic Construction of a Generalized Reissner-Mindlin Model for Multilayer Piezoelectric Plates

2007 ◽  
Author(s):  
Lin Liao ◽  
Wenbin Yu
Keyword(s):  
A Priori ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Single Layer ◽  
Plate And Shell ◽  
Shell Analysis ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Plate Analysis ◽  
Piezoelectric Plates

The variational asymptotic method is used to construct a generalized Reissner-Mindlin model for multilayer piezoelectric plates with faces surfaces or other surfaces parallel to the reference surface coated with electrodes. Without invoking a priori kinematic assumptions, we asymptotically split the original three-dimensional electromechanical problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The through-the-thickness analysis is implemented using the finite element method into the computer program VAPAS (Variational Asymptotic Plate and Shell Analysis). The resulting model is as simple as an equivalent single-layer, first-order shear deformation theory with accuracy comparable to higher-order layerwise theories. Numerical results of cylindrical bending problems for piezoelectric plates have been compared with 3D exact solutions to validate the present model.

Hierarchical Finite Element Analysis of Multilayered Plates Subjected to Mechanical, Thermal and Electrical Loadings

2006 ◽  
Author(s):  
Erasmo Carrera ◽  
Christian Fagiano
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Single Layer ◽  
Two Dimensional ◽  
Dynamic Problems ◽  
Element Analysis ◽  
Plate Elements ◽  
Piezoelectric Layers ◽  
Multilayered Plates ◽  
Principle Of Virtual Displacements

This paper addresses to static and dynamic problems of multilayered plate and also embedded piezoelectric layers by means of finite element methods (FEM). Formulation on the basis of Principle of Virtual Displacements (PVD) and Reissner Mixed Variational Theorem (RMVT) are considered. A series of hierarchic, two-dimensional plate elements are presented within the “Unified Formulation” recently introduced by the first author. Finite element matrices are derived for static and dynamic problems of piezoelectric laminates. Numerical solutions are compared to available ones to assess mixed and classical finite elements in both case of Layer-Wise (LW) and Equivalent-Single-Layer (ESL) variable description. The superiority of RMVT applications with respect to classical ones based on Principle of Virtual Displacements (PVD) has been confirmed by the conducted numerical investigation.

scholarly journals Partial-mixed special finite element for the analysis of multilayer composites and FGM

2012 ◽  
Author(s):  
Orlando Andrianarison ◽  
Ayech Benjeddou
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Hamiltonian Formalism ◽  
Single Layer ◽  
Static Problem ◽  
Functionally Graded ◽  
Elasticity Equations ◽  
Graded Material ◽  
Transverse Stresses ◽  
Three Dimensional Elasticity

A partial-mixed special finite element (FE) is proposed for the static analysis of multilayer composite and functionally graded material plates. Using the Hamiltonian formalism, the three-dimensional elasticity equations are first reformulated so that a partial-mixed variational formulation, retaining as primary variables the translational displacements augmented with the transverse stresses only, is obtained; this allows, in particular, a straightforward fulfilment of the multilayer interfaces continuity conditions. After an only in-plane FE discretisation, the static problem is then reduced, for a single layer, to a Hamiltonian eigenvalue problem that is solved analytically, through the layer thickness, using the symplectic formalism; the multilayer solution is finally reached via the state-space method and the propagator matrix concept. The performance, in convergence and accuracy, of the proposed approach, applied to representative examples, is shown to be very satisfactory.

Characterization of a monolayer graphitic structure

1994 ◽  
Vol 52 ◽  
pp. 760-761
Author(s):  
X. Lin ◽  
X. K. Wang ◽  
V. P. Dravid ◽  
J. B. Ketterson ◽  
R. P. H. Chang
Keyword(s):  
Three Dimensional ◽  
Single Layer ◽  
Synthesis Process ◽  
Graphitic Structure ◽  
Positive Gaussian Curvature ◽  
Graphitic Sheet ◽  
Structural And Electronic Properties ◽  
New Material ◽  
Hexagonal Network

For small curvatures of a graphitic sheet, carbon atoms can maintain their preferred sp2 bonding while allowing the sheet to have various three-dimensional geometries, which may have exotic structural and electronic properties. In addition the fivefold rings will lead to a positive Gaussian curvature in the hexagonal network, and the sevenfold rings cause a negative one. By combining these sevenfold and fivefold rings with sixfold rings, it is possible to construct complicated carbon sp2 networks. Because it is much easier to introduce pentagons and heptagons into the single-layer hexagonal network than into the multilayer network, the complicated morphologies would be more common in the single-layer graphite structures. In this contribution, we report the observation and characterization of a new material of monolayer graphitic structure by electron diffraction, HREM, EELS.The synthesis process used in this study is reported early. We utilized a composite anode of graphite and copper for arc evaporation in helium.

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