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Journal ArticleDOI

Piecewise shear deformation theory and finite element formulation for vibration analysis of laminated composite and sandwich plates in thermal environments

15 Jan 2017-Composite Structures (Elsevier)-Vol. 160, pp 1060-1083
TL;DR: In this paper, a piecewise shear deformation theory for laminated composite and sandwich plates is presented by integrating the advantages of the layerwise theory and equivalent single layer theory.
About: This article is published in Composite Structures.The article was published on 2017-01-15. It has received 31 citations till now. The article focuses on the topics: Finite element method & Piecewise.
Citations
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Journal ArticleDOI
TL;DR: A critical review of available literature for the prediction of the behavior of laminated composites and sandwich structures under hygrothermal conditions is carried out and summarized under different categories namely: static, vibration, buckling, postbuckling and miscellaneous studies as mentioned in this paper.
Abstract: Extensive numerical results available in published articles reflect the importance of the effects of geometric parameters, material properties, end conditions, hygrothermal fields, etc. on the behavior of laminated composite and sandwich structures when exposed to environmental conditions. A critical review of available literature for the prediction of the behavior of laminated composites and sandwich structures under hygrothermal conditions is carried out and summarized under different categories namely: static, vibration, buckling, post-buckling and miscellaneous studies (transient, dynamic, impact studies). Each category is further discussed separately in details highlighting the important outcomes of the research. In addition to that, each category is again grouped on the basis of the type of theory used by different researchers in their work. The displacement fields, thermal fields and the method adopted in different papers are also summarized.

82 citations

Journal ArticleDOI
TL;DR: In this article, the dynamic buckling behavior of a sandwich plate composed of laminated viscoelastic nanocomposite layers integrated with visco-elastic piezoelectric layers is investigated.
Abstract: In this article, the dynamic buckling behavior of a sandwich plate composed of laminated viscoelastic nanocomposite layers integrated with viscoelastic piezoelectric layers is investigated. The cor...

41 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of thermal stresses on the band structure of elastic metamaterial plates was investigated by developing a useful finite-element based method, where the thermal field is assumed to be uniform throughout the whole plate.

34 citations

Journal ArticleDOI
TL;DR: In this paper, a general mathematical model for laminated curved structure of different geometries using higher-order shear deformation theory was developed to evaluate in-plane and out-of-plane shear stress and strains correctly.
Abstract: Purpose – The purpose of this paper is to develop a general mathematical model for laminated curved structure of different geometries using higher-order shear deformation theory to evaluate in-plane and out of plane shear stress and strains correctly. Subsequently, the model has to be validated by comparing the responses with developed simulation model (ANSYS) as well as available published literature. It is also proposed to analyse thermal buckling load parameter of laminated structures using Green–Lagrange type non-linear strains for excess thermal distortion under uniform temperature loading. Design/methodology/approach – Laminated structures known for their flexibility as compared to conventional material and the deformation behaviour are greatly affected due to combined thermal/aerodynamic environment. The vibration/buckling behaviour of shell structures are very different than that of the plate structures due to their curvature effect. To model the exact behaviour of laminated structures mathematica...

30 citations

Journal ArticleDOI
TL;DR: In this article, a sandwich structure composed of carbon fiber woven skins and a Nomex honeycomb core is taken as the research object, and temperature effects on its modal characteristics are investigated by experiments and simulations.

30 citations

References
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Journal ArticleDOI
TL;DR: A review of the Zig-Zag theories for multilayered structures can be found in this article, where the authors refer to these three theories by using the following three names: Lekhnitskii Multi-layered Theory, ~LMT!, Ambartsumian Multi-Layered Theory ~AMT!, and Reissner Multilayed Theory ~RMT.
Abstract: This paper gives a historical review of the theories that have been developed for the analysis of multilayered structures. Attention has been restricted to the so-called Zig-Zag theories, which describe a piecewise continuous displacement field in the plate thickness direction and fulfill interlaminar continuity of transverse stresses at each layer interface. Basically, plate and shell geometries are addressed, even though beams are also considered in some cases. Models in which the number of displacement variables is kept independent of the number of constitutive layers are discussed to the greatest extent. Attention has been restricted to those plate and shell theories which are based on the so-called method of hypotheses or axiomatic approach in which assumptions are introduced for displacements and/or transverse stresses. Mostly, the work published in the English language is reviewed. However, an account of a few articles originally written in Russian is also given. The historical review conducted has led to the following main conclusions. 1! Lekhnitskii ~1935! was the first to propose a Zig-Zag theory, which was obtained by solving an elasticity problem involving a layered beam. 2! Two other different and independent Zig-Zag theories have been singled out. One was developed by Ambartsumian ~1958!, who extended the well-known Reissner-Mindlin theory to layered, anisotropic plates and shells; the other approach was introduced by Reissner ~1984!, who proposed a variational theorem that permits both displacements and transverse stress assumptions. 3 ! On the basis of historical considerations, which are detailed in the paper, it is proposed to refer to these three theories by using the following three names: Lekhnitskii Multilayered Theory, ~LMT!, Ambartsumian Multilayered Theory ~AMT!, and Reissner Multilayered Theory ~RMT!. As far as subsequent contributions to these three theories are concerned, it can be remarked that: 4! LMT although very promising, has almost been ignored in the open literature. 5! Dozens of papers have instead been presented which consist of direct applications or particular cases of the original AMT. The contents of the original works have very often been ignored, not recognized, or not mentioned in the large number of articles that were published in journals written in the English language. Such historical unfairness is detailed in Section 3.2. 6! RMT seems to be the most natural and powerful method to analyze multilayered structures. Compared to other theories, the RMT approach has allowed from the beginning development of models which retain the fundamental effect related to transverse normal stresses and strains. This review article cites 138 references. @DOI: 10.1115/1.1557614#

972 citations

Journal ArticleDOI
TL;DR: Theories and finite elements for multilayered structures have been reviewed in this article, where the authors present an extensive numerical evaluation of available results, along with assessment and benchmarking.
Abstract: This work is a sequel of a previous author’s article: “Theories and Finite Elements for Multilayered. Anisotropic, Composite Plates and Shell”, Archive of Computational Methods in Engineering Vol 9, no 2, 2002; in which a literature overview of available modelings for layered flat and curved structures was given. The two following topics, which were not addressed in the previous work, are detailed in this review: 1. derivation of governing equations and finite element matrices for some of the most relevant plate/shell theories; 2. to present an extensive numerical evaluations of available results, along with assessment and benchmarking. The article content has been divided into four parts. An introduction to this review content is given in Part I. A unified description of several modelings based on displacements and transverse stress assumptions ins given in Part II. The order of the expansion in the thickness directions has been taken as a free parameter. Two-dimensional modelings which include Zig-Zag effects, Interlaminar Continuity as well as Layer-Wise (LW), and Equivalent Single Layer (ESL) description have been addressed. Part III quotes governing equations and FE matrices which have been written in a unified manner by making an extensive use of arrays notations. Governing differential equations of double curved shells and finite element matrices of multilayered plates are considered. Principle of Virtual Displacement (PVD) and Reissner’s Mixed Variational Theorem (RMVT), have been employed as statements to drive variationally consistent conditions, e.g.C 0 -Requirements, on the assumed displacements and stransverse stress fields. The number of the nodes in the element has been taken as a free parameter. As a results both differential governing equations and finite element matrices have been written in terms of a few 3×3 fundamental nuclei which have 9 only terms each. A vast and detailed numerical investigation has been given in Part IV. Performances of available theories and finite elements have been compared by building about 40 tables and 16 figures. More than fifty available theories and finite elements have been compared to those developed in the framework of the unified notation discussed in Parts II and III. Closed form solutions and and finite element results related to bending and vibration of plates and shells have been addressed. Zig-zag effects and interlaminar continuity have been evaluated for a number of problems. Different possibilities to get transverse normal stresses have been compared. LW results have been systematically compared to ESL ones. Detailed evaluations of transverse normal stress effects are given. Exhaustive assessment has been conducted in the Tables 28–39 which compare more than 40 models to evaluate local and global response of layered structures. A final Meyer-Piening problem is used to asses two-dimensional modelings vs local effects description.

951 citations

Book
30 Sep 1992
TL;DR: The finite element method is the most effective method for the solution of composite laminates as discussed by the authors, but it is limited to simple geometries because of the difficulty in constructing the approximation functions for complicated geometrie.
Abstract: The partial differential equations governing composite laminates (see Section 2.4) of arbitrary geometries and boundary conditions cannot be solved in closed form. Analytical solutions of plate theories are available (see Reddy [1–5]) mostly for rectangular plates with all edges simply supported (i.e., the Navier solutions) or with two opposite edges simply supported and the remaining edges having arbitrary boundary conditions (i.e., the Levy solutions). The Rayleigh-Ritz and Galerkin methods can also be used to determine approximate analytical solutions, but they too are limited to simple geometries because of the difficulty in constructing the approximation functions for complicated geometries. The use of numerical methods facilitates the solution of these equations for problems of practical importance. Among the numerical methods available for the solution of differential equations defined over arbitrary domains, the finite element method is the most effective method. A brief introduction to the finite element method is presented in Section 3.2.

340 citations

Journal ArticleDOI
TL;DR: In this paper, the free vibration analysis of multilayered laminated composite and sandwich plates using various methods available for the analysis of plates is presented and compared with other higher order shear deformation theories.

284 citations

Journal ArticleDOI
TL;DR: In this article, a survey of plate/shell analysis is presented, where the authors evaluate a large variety of plate theories to evaluate the bending and vibration of sandwich structures, including classical, higher order, zigzag, layerwise, and mixed theories.
Abstract: A large variety of plate theories are described and assessed in the present work to evaluate the bending and vibration of sandwich structures. A brief survey of available works is first given. Such a survey includes significant review papers and latest developments on sandwich structure modelings. The kinematics of classical, higher order, zigzag, layerwise, and mixed theories is described. An exhaustive numerical assessment of the whole theories is provided in the case of closed form solutions of simply supported panels made of orthotropic layers. Reference is made to the unified formulation that has recently been introduced by the first author for a plate/shell analysis. Attention has been given to displacements, stresses (both in-plane and out-of-plane components), and the free vibration response. Only simply supported orthotropic panels loaded by a transverse distribution of bisinusoidal pressure have been analyzed. Five benchmark problems are treated. The accuracy of the plate theories is established with respect to the length-to-thickness-ratio (LTR) geometrical parameters and to the face-to-core-stiffness-ratio (FCSR) mechanical parameters. Two main sources of error are outlined, which are related to LTR and FCSR, respectively. It has been concluded that higher order theories (HOTs) can be conveniently used to reduce the error due to LTR in thick plate cases. But HOTs are not effective in increasing the accuracy of the classical theory analysis whenever the error is caused by increasing FCSR values; layerwise analysis becomes mandatory in this case.

281 citations