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Article
Publication date: 8 October 2018

Pankaj V. Katariya, Subrata Kumar Panda and Trupti Ranjan Mahapatra

The purpose of this paper is to develop a general mathematical model for the evaluation of the bending and vibration responses of the skew sandwich composite plate using…

Abstract

Purpose

The purpose of this paper is to develop a general mathematical model for the evaluation of the bending and vibration responses of the skew sandwich composite plate using higher-order shear deformation theory. The sandwich structural components are highly preferable in modern engineering application because of their desirable structural advantages despite the manufacturing and analysis complexities. The present model is developed to solve the bending and vibration problem of the skew sandwich composite plate with adequate accuracy numerically in the absence of the experimental analysis.

Design/methodology/approach

The skew sandwich composite plate structure is modelled in the present analysis by considering laminated face sheet in conjunction with isotropic and/or orthotropic core numerically with the help of the higher-order mathematical model. Further, the responses are computed numerically with the help of in-house computer code developed in matrix laboratory (MATLAB) environment in conjunction with finite element (FE) steps. The system governing equations are derived via variational technique for the computation of the static and the frequency responses.

Findings

The skew sandwich composite plate is investigated using the higher-order kinematic model where the transverse displacement through the thickness is considered to be linear. The convergence and the validation study of the bending and the frequency values of the sandwich structure indicate the necessary accuracy. Further, the current model has been used to highlight the applicability of the higher-order kinematics for the evaluation of the sandwich structural responses (frequency and static deflections) for different design parameters.

Originality/value

In the present paper, the bending and the vibration responses of the skew sandwich composite plate are analysed numerically using the equivalent single-layer higher-order kinematic theory for the isotropic and the orthotropic core numerically with the help of isoparametric FE steps. Finally, it is understood that the present model is capable of solving the sandwich structural responses with less computation cost and adequate accuracy.

Details

Aircraft Engineering and Aerospace Technology, vol. 90 no. 6
Type: Research Article
ISSN: 1748-8842

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Article
Publication date: 15 July 2019

R.R. Kumar, P.K. Karsh, Vaishali , K.M. Pandey and S. Dey

The purpose of this paper is to investigate the first three stochastic natural frequencies of skewed sandwich plates, considering uncertain system parameters. To conduct…

Abstract

Purpose

The purpose of this paper is to investigate the first three stochastic natural frequencies of skewed sandwich plates, considering uncertain system parameters. To conduct the sensitivity analysis for checking the criticality of input parameters.

Design/methodology/approach

The theoretical formulation is developed based on higher-order-zigzag theory in accordance with the radial basis function (RBF) and stochastic finite element (FE) model. A cubic function is considered for in-plane displacement over thickness while a quadratic function is considered for transverse displacement within the core and remains constant in the facesheet. RBF is used as a surrogate model to achieve computational efficiency and accuracy. In the present study, the individual and combined effect of ply-orientation angle, skew angle, number of lamina, core thickness and material properties are considered for natural frequency analysis of sandwich plates.

Findings

Results presented in this paper illustrates that the skewness in the sandwich plate significantly affects the global dynamic behaviour of the structure. RBF surrogate model coupled with stochastic FE approach significantly reduced the computational time (more than 1/18 times) compared to direct Monte Carlo simulation approach.

Originality/value

The stochastic results for dynamic stability of sandwich plates show that the inevitable source uncertainties present in the input parameters result in significant variation from the deterministic value demonstrates the need for inclusive design paradigm considering stochastic effects. The present paper comprehensively establishes a generalized new RBF-based FE approach for efficient stochastic analysis, which can be applicable to other complex structures too.

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Article
Publication date: 1 March 2002

Jaroslav Mackerle

Gives a bibliographical review of the finite element analyses of sandwich structures from the theoretical as well as practical points of view. Both isotropic and composite…

Abstract

Gives a bibliographical review of the finite element analyses of sandwich structures from the theoretical as well as practical points of view. Both isotropic and composite materials are considered. Topics include: material and mechanical properties of sandwich structures; vibration, dynamic response and impact problems; heat transfer and thermomechanical responses; contact problems; fracture mechanics, fatigue and damage; stability problems; special finite elements developed for the analysis of sandwich structures; analysis of sandwich beams, plates, panels and shells; specific applications in various fields of engineering; other topics. The analysis of cellular solids is also included. The bibliography at the end of this paper contains 655 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1980 and 2001.

Details

Engineering Computations, vol. 19 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 June 1997

Jaroslav Mackerle

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…

Abstract

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Details

Engineering Computations, vol. 14 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 9 August 2011

Mondher Wali, Moez Abdennadher, Tahar Fakhfakh and Mohamed Haddar

The purpose of this paper is to analyse the dynamic behaviour of an elasto‐plastic sandwich subjected to low velocity impact.

Abstract

Purpose

The purpose of this paper is to analyse the dynamic behaviour of an elasto‐plastic sandwich subjected to low velocity impact.

Design/methodology/approach

A numerical model is developed with the assumption that the plastic deformation is confined under the contact area. The structure is analyzed using the in‐house finite element code with an appropriate contact law. During the impact progression, two phases (elastic and plastic) related to the impact intensity are considered in the dynamic model. The proportional viscous damping is incorporated in the model. An elasto‐plastic impact algorithm is established to determine the impact force, the sandwich structure displacement and indentation.

Findings

The numerical results are validated by experimental dropping weight impact tests. The influences of the impactor radius, the core material variation and the impactor initial velocity on the dynamic behaviour of the impacted structure are studied.

Originality/value

In order to study the low velocity impact problems by considering the caused plastic deformations, a simple numerical elasto‐plastic impact model of sandwich structure is proposed.

Details

Multidiscipline Modeling in Materials and Structures, vol. 7 no. 2
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 22 June 2012

Salvatore Brischetto and Erasmo Carrera

The purpose of this paper is to consider the static analysis of nanocomposite plates. Nanocomposites consist of a small amount of nanoscale reinforcements which can have…

Abstract

Purpose

The purpose of this paper is to consider the static analysis of nanocomposite plates. Nanocomposites consist of a small amount of nanoscale reinforcements which can have an observable effect on the macroscale properties of the composites.

Design/methodology/approach

In the present study the reinforcements considered are non‐spherical, high aspect ratio fillers, in particular nanometer‐thin platelets (clays) and nanometer‐diameter cylinders (carbon nanotubes, CNTs). These plates are considered simply supported with a bi‐sinusoidal pressure applied at the top. These conditions allow the solving of the governing equations in a closed form. Four cases are investigated: a single layered plate with CNT reinforcements in elastomeric or thermoplastic polymers, a single layered plate with CNT reinforcements in a polymeric matrix embedding carbon fibers, a sandwich plate with external skins in aluminium alloy and an internal core in silicon foam filled with CNTs and a single layered plate with clay reinforcements in a polymeric matrix. A short review of the most important results in the literature is given to determine the elastic properties of the suggested nanocomposites which will be used in the proposed static analysis. The static response of the plates is obtained by using classical two‐dimensional models such as classical lamination theory (CLT) and first order shear deformation theory (FSDT), and an advanced mixed model based on the Carrera Unified Formulation (CUF) which makes use of a layer‐wise description for both displacement and transverse stress components.

Findings

The paper has two aims: to demonstrate that the use of classical theories, originally developed for traditional plates, is inappropriate to investigate the static response of nanocomposite plates and to quantify the beneficial effect of the nanoreinforcements in terms of static response (displacements and stresses).

Originality/value

In the literature these effects are usually given only in terms of elastic properties such as Young moduli, shear moduli and Poisson ratios, and not in terms of displacements and stresses.

Details

Multidiscipline Modeling in Materials and Structures, vol. 8 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 May 2000

Jaroslav Mackerle

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…

Abstract

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.

Details

Engineering Computations, vol. 17 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 9 November 2015

Mokhtar Bouazza and Noureddine Benseddiq

The purpose of this paper is to investigate an analytical modeling for the thermoelastic buckling behavior of functionally graded (FG) rectangular plates (FGM) under…

Abstract

Purpose

The purpose of this paper is to investigate an analytical modeling for the thermoelastic buckling behavior of functionally graded (FG) rectangular plates (FGM) under thermal loadings. The material properties of FGM are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Derivations of equations are based on novel refined theory using a new hyperbolic shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. In addition, numerical results for a variety of FG plates with simply supported edge are presented and compared with those available in the literature. Moreover, the effects of geometrical parameters of dimension the length to width aspect ratio (a/b), the plate width to thickness ratio (b/h), and material properties index (k) on the FGM buckling temperature difference are determined and discussed.

Design/methodology/approach

In the current paper, the application of the refined theory proposed by Shimpi is based on the assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. It is extended to the analysis of buckling behavior of ceramic-metal FG plates subjected to the three types of thermal loadings, namely; uniform temperature rise, linear temperature change across the thickness, and nonlinear temperature change across the thickness. The material properties of the FG plates are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results, wherever possible. Additionally, the effects of geometrical parameters and material properties on the buckling temperature difference of FGM plates are determined and discussed.

Findings

Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power-law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions.

Originality/value

To the best of the authors’ knowledge, there are no research works for thermal buckling analysis of FG rectangular plates based on new four-variable refined plate theory (RPT). The novelty of this paper is extended the use of the above-mentioned RPT with the addition of a new function proposed by Shimpi for thermal buckling analysis of plates made of FG materials. Unlike any other theory, the number of unknown functions involved is only four, as against five in the case of other shear deformation theories. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. The plates subjected to the two types of thermal loadings, namely; uniform temperature rise and nonlinear temperature change across the thickness. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 4
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 12 October 2015

Amale Mahi, El Abbas Adda Bedia, Abdelouahed Tounsi and Amina Benkhedda

A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides…

Abstract

Purpose

A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The paper aims to discuss these issues.

Design/methodology/approach

Material properties are temperature-dependent and vary continuously through the thickness according to a power law distribution. The plate is assumed to be initially stressed by a temperature rise through the thickness. The energy functional of the system is obtained using Hamilton’s principle. Free vibration frequencies are then calculated using a set of characteristic orthogonal polynomials and by applying Ritz method for different boundary conditions.

Findings

In the light of good performance of the present theory for all boundary conditions considered, it can be considered as an excellent alternative to some two-dimensional (2D) theories for approximating the tedious and time consuming three-dimensional plate problems.

Originality/value

To the best of the authors’ knowledge and according to literature survey, almost all published higher order shear deformation theories have been limited to simply supported boundary conditions and without taking into account the thermal stresses effects. The existing 2D shear deformation theories of Reddy, Karama and Touratier can be easily recovered. Furthermore, this feature can be highly appreciated in an iterative design process where a large number of derived plate models can be tested by selecting only two parameters in a simple polynomial function which is computationally efficient. Finally, new results are presented to show the effect of material variation, and temperature rise on natural frequencies of the FG plate for different boundary conditions.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 3
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 August 2002

Jaroslav Mackerle

This paper gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural…

Abstract

This paper gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The bibliography at the end of the paper contains more than 1330 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1999–2002.

Details

Engineering Computations, vol. 19 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

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