Development of Isoparametric, Degenerate Constrained Layer Element for Plate and Shell Structures
01 Jan 2001-AIAA Journal (American Institute of Aeronautics and Astronautics Inc. (AIAA))-Vol. 39, Iss: 10, pp 1997-2005
TL;DR: In this paper, an 18-node degenerate element with nine nodes located on the base shell structure and nine nodes on the constraining layer is presented for constrained layer damping treatments. But, the element is not suitable for either plate or shell structures.
Abstract: An isoparametric, degenerate element for constrained layer damping treatments is presented The element is valid for either plate or shell structures The element is an 18-node degenerate element with nine nodes located on the base shell (or plate) structure and nine nodes on the constraining layer Each node has five degrees of freedom: translations in x,y, and z and bending rotations α and β about the midsurface where the node is located The displacement field of the viscoelastic layer is interpolated linearly from the nodal displacements; therefore, the viscoelastic layer allows both shear and normal deformations The base shell (or plate) structure and the constraining layer can be linearly elastic or piezoelectric for passive or active applications The viscoelastic layer is assumed to be linearly viscoelastic The equation of motion is derived through use of the principle of virtual work For thin plate structures, numerical results show that the isoparametric element can predict natural frequencies, loss factors, and mechanical impedances that are as accurate as NASTRAN with substantially fewer elements For thin shell structures, locking and spurious modes need to be resolved to yield reasonable results
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TL;DR: In this paper, the analysis of active constrained layer damping (ACLD) of laminated thin composite shells using piezoelectric fiber reinforced composite (PFRC) materials is considered to be made of the PFRC materials.
89 citations
TL;DR: In this paper, a micromechanics model has been derived to predict the effective elastic and piezoelectric coefficients of the composite material used for the distributed actuator of smart structures.
Abstract: This paper deals with the analysis of vertically reinforced 1–3 piezoelectric composite materials as the material used for the distributed actuator of smart structures A micromechanics model has been derived to predict the effective elastic and piezoelectric coefficients of these piezoelectric composites which are useful for the analysis of smart beams In order to investigate the performance of a layer of this 1–3 piezoelectric composite material as the distributed actuator of smart structures, active constrained layer damping (ACLD) of smart laminated composite beams has been studied The constraining layer in the ACLD treatment has been considered to be made of this piezoelectric composite A finite element model has been developed to study the dynamics of the overall beam/ACLD system Both in-plane and out-of-plane actuations of the constraining layer of the ACLD treatment have been utilized for deriving the finite element model It has been found that these vertically reinforced 1–3 piezoelectric composite materials which are in general being used as distributed sensors can be potentially used as distributed actuators of smart structures
80 citations
TL;DR: In this paper, a finite element model has been developed for analyzing the active constrained layer damping of laminated symmetric and antisymmetric cross-ply and angle-ply composite plates integrated with the patches of such ACLD treatment.
Abstract: This paper deals with the analysis of vertically reinforced 1-3 piezoelectric composite materials as the material for the distributed actuator of smart laminated composite plates. A simple micromechanics model has been derived to predict the effective elastic and piezoelectric coefficients of these piezoelectric composites which are useful for the three dimensional analysis of smart structures. The main concern of this study is to investigate the performance of a layer of this vertically reinforced 1-3 piezoelectric composite material as the constraining layer of the active constrained layer damping (ACLD) treatment. A finite element model has been developed for analyzing the active constrained layer damping of laminated symmetric and antisymmetric cross-ply and angle-ply composite plates integrated with the patches of such ACLD treatment. Both in-plane and out-of-plane actuation of the constraining layer of the ACLD treatment have been utilized for deriving the finite element model. The analysis revealed...
69 citations
Additional excerpts
...6) being the complex elastic constants [13, 14]....
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TL;DR: In this paper, a finite element formulation is presented to model the static and dynamic response of laminated composite shells containing integrated piezoelectric sensors and actuators subjected to electrical, mechanical and thermal loadings.
64 citations
TL;DR: In this paper, active constrained layer damping (ACLD) of smart laminated fuzzy fiber reinforced composite (FFRC) plates is investigated for the case of FLCs.
Abstract: This article is concerned with the investigation of active constrained layer damping (ACLD) of smart laminated fuzzy fiber reinforced composite (FFRC) plates. The distinctive feature of the constru...
55 citations
Cites background or methods from "Development of Isoparametric, Degen..."
...Using equation (14), the elastic coefficients of the viscoelastic material can be determined and the resulting elastic coefficients matrix ½CNþ1ij turns out to be a complex matrix (Shen, 1996; Ray and Baz, 1997; Jeung and Shen, 2001)....
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...Using equation (14), the elastic coefficients of the viscoelastic material can be determined and the resulting elastic coefficients matrix 1⁄2CNþ1 ij turns out to be a complex matrix (Shen, 1996; Ray and Baz, 1997; Jeung and Shen, 2001)....
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...The principle of virtual work is employed to derive the governing equations of the overall FFRC plate/ACLD system (Jeung and Shen, 2001); such that, XNþ2 k¼1 Z 2kb T kb þ d 2ks T ks dEz 233Ez d dtf gT k €dt n o d Z A d dtf gT ff gdA ¼ 0 ð15Þ in which k is the mass density of the kth layer, ff g is…...
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...The principle of virtual work is employed to derive the governing equations of the overall FFRC plate/ACLD system (Jeung and Shen, 2001); such that,...
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References
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Book•
01 Jan 1974
TL;DR: In this article, the authors present a formal notation for one-dimensional elements in structural dynamics and vibrational properties of a structural system, including the following: 1. Isoparametric Elements.
Abstract: Notation. Introduction. One-Dimensional Elements, Computational Procedures. Basic Elements. Formulation Techniques: Variational Methods. Formulation Techniques: Galerkin and Other Weighted Residual Methods. Isoparametric Elements. Isoparametric Triangles and Tetrahedra. Coordinate Transformation and Selected Analysis Options. Error, Error Estimation, and Convergence. Modeling Considerations and Software Use. Finite Elements in Structural Dynamics and Vibrations. Heat Transfer and Selected Fluid Problems. Constaints: Penalty Forms, Locking, and Constraint Counting. Solid of Revolution. Plate Bending. Shells. Nonlinearity: An Introduction. Stress Stiffness and Buckling. Appendix A: Matrices: Selected Definition and Manipulations. Appendix B: Simultaneous Algebraic Equations. Appendix C: Eigenvalues and Eigenvectors. References. Index.
6,126 citations
Book•
29 Mar 1991
TL;DR: In this article, the authors present a general solution based on the principle of virtual work for two-dimensional linear elasticity problems and their convergence rates in one-dimensional dimensions. But they do not consider the case of three-dimensional LEL problems.
Abstract: Mathematical Models and Engineering Decisions. Generalized Solutions Based on the Principle of Virtual Work. Finite Element Discretizations in One Dimension. Extensions and Their Convergence Rates in One Dimension. Two-Dimensional Linear Elastostatic Problems. Element-Level Basis Functions in Two Dimensions. Computation of Stiffness Matrices and Load Vectors for Two Dimensional Elastostatic Problems. Potential Flow Problems. Assembly, Constraint Enforcement, and Solution. Extensions and Their Convergence Rates in Two Dimensions. Computation of Displacements, Stresses and Stress Resultants. Computation of the Coefficients of Asymptotic Expansions. Three-Dimensional Linear Elastostatic Problems. Models for Plates and Shells. Miscellaneous Topics. Estimation and Control of Errors of Discretization. Mathematical Models. Appendices. Index.
2,748 citations
TL;DR: In this article, a simple extension is made which allows the element to be economically used in all situations by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties.
Abstract: The solution of plate and shell problems by an independent specification of slopes and middle surface displacements is attractive due to its simplicity and ability of reproducing shear deformation. Unfortunately elements of this type are much too stiff when thickness is reduced.
In an earlier paper a derivation of such an element was presented1 which proved very successful in ‘thick’ situations. Here a very simple extension is made which allows the element to be economically used in all situations.
The improved flexibility is achieved simply by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties. The process is of very wide applicability in improvement of element properties.
1,336 citations
TL;DR: In this article, a general formulation for the curved, arbitrary shape of thick shell finite elements is presented along with a simplified form for axisymmetric situations, which is suitable for thin to thick shell applications.
Abstract: A general formulation for the curved, arbitrary shape of thick shell finite elements is presented in this paper along with a simplified form for axisymmetric situations. A number of examples ranging from thin to thick shell applications are given, which include a cooling tower, water tanks, an idealized arch dam and an actual arch dam with deformable foundation.
A new process using curved, thick shell finite elements is developed overcoming the previous approximations to the geometry of the structure and the neglect of shear deformation.
A general formulation for a curved, arbitrary shape of shell is developed as well as a simplified form suitable for axisymmetric situations.
Several illustrated examples ranging from thin to thick shell applications are given to assess the accuracy of solution attainable. These examples include a cooling tower, tanks, and an idealized dam for which many alternative solutions were used.
The usefulness of the development in the context of arch dams, where a ‘thick shell’ situation exists, leads in practice to a fuller discussion of problems of foundation deformation, etc., so that practical application becomes possible and economical.
1,205 citations