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Article
Publication date: 1 February 1986

E. Hinton and H.C. Huang

Finite elements based on Mindlin plate theory are used to study the distribution of shear forces and twisting moments on the boundaries of plates with various support…

Abstract

Finite elements based on Mindlin plate theory are used to study the distribution of shear forces and twisting moments on the boundaries of plates with various support conditons and thickness‐to‐span ratios. Differences between results obtained using Mindlin and Kirchhoff plate theories are highlighted. Potential difficulties in the interpretation of results obtained from finite element analysis are discussed and appropriate shear force sampling procedures are reviewed. The present work is a pilot study for a larger project with the basic aim of providing engineers with an unambiguous method for obtaining stress resultants in Mindlin plate analysis. Some examples are presented which illustrate the excellent results which may be obtained with judicious mesh division even in regions with steep gradients of the stress resultants near plate corners. These examples also demonstrate some of the difficulties facing engineers who have to try to interpret finite element results for plates.

Details

Engineering Computations, vol. 3 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: 1 February 1989

Bahaa S. Al Janabi, E. Hinton and Dj. Vuksanovic

This paper presents a parametric study of the free vibrations of square plates with various thickness‐to‐span ratios and different boundary conditions. The numerical…

Abstract

This paper presents a parametric study of the free vibrations of square plates with various thickness‐to‐span ratios and different boundary conditions. The numerical analysis of these problems has been undertaken using the finite element method. In particular, a nine‐noded, quadrilateral Mindlin plate element has been adopted. The effects of rotatory inertia and shear deformation are included in this model. Results obtained by the finite element analysis are compared with results from various sources. It is suggested that this study might be used to supplement existing benchmark tests.

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Engineering Computations, vol. 6 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 March 1990

A. Selman, E. Hinton and W. Atamaz‐Sibai

An adaptive mesh refinement procedure is used in static plate bending finite element analysis to study the edge effects in Mindlin—Reissner plates.

Abstract

An adaptive mesh refinement procedure is used in static plate bending finite element analysis to study the edge effects in Mindlin—Reissner plates.

Details

Engineering Computations, vol. 7 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 5 November 2018

Changsheng Wang, Xiaoxiao Sun, Xiangkui Zhang and Ping Hu

A higher-order Reissner-Mindlin plate element method is presented based on the framework of assumed stress quasi-conforming method and Hellinger-Reissner variational…

Abstract

Purpose

A higher-order Reissner-Mindlin plate element method is presented based on the framework of assumed stress quasi-conforming method and Hellinger-Reissner variational principle. A novel six-node triangular plate element is proposed by utilizing this method for the static and free vibration analysis of Reissner-Mindlin plates.

Design/methodology/approach

First, the initial assumed stress field is derived by using the fundamental analytical solutions which satisfy all governing equations. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations after the strains are derived by using the constitutive equations. Finally, the arbitrary order Timoshenko beam function is adopted as the string-net functions along each side of the element for strain integration.

Findings

The proposed element can pass patch test and is free from shear locking and spurious zero energy modes. Numerical tests show that the element can give high-accurate solutions, good convergence and is a good competitor to other models.

Originality/value

This work gives new formulations to develop high-order Reissner-Mindlin plate element, and the new strategy exhibits advantages of both analytical and discrete methods.

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Article
Publication date: 1 April 1984

H.C. Huang and E. Hinton

This paper presents an improved nine node Mindlin plate element. An enhanced interpolation of the transverse shear strains is used in this formulation of the new element…

Abstract

This paper presents an improved nine node Mindlin plate element. An enhanced interpolation of the transverse shear strains is used in this formulation of the new element which has the requisite number of zero energy modes, does not lock and passes the appropriate patch tests exactly. Some examples are included to illustrate the accuracy of the proposed element. The new 9‐node element is compared with the Lagrangian and heterosis elements and the general performance of the new element is much better than the other quadratic elements especially for shear force distributions.

Details

Engineering Computations, vol. 1 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 18 April 2017

Yi Bao, Song Cen and Chenfeng Li

A simple shape-free high-order hybrid displacement function element method is presented for precise bending analyses of Mindlin–Reissner plates. Three distortion-resistant…

Abstract

Purpose

A simple shape-free high-order hybrid displacement function element method is presented for precise bending analyses of Mindlin–Reissner plates. Three distortion-resistant and locking-free eight-node plate elements are proposed by utilizing this method.

Design/methodology/approach

This method is based on the principle of minimum complementary energy, in which the trial functions for resultant fields are derived from two displacement functions, F and f, and satisfy all governing equations. Meanwhile, the element boundary displacements are determined by the locking-free arbitrary order Timoshenko’s beam functions. Then, three locking-free eight-node, 24-DOF quadrilateral plate-bending elements are formulated: HDF-P8-23β for general cases, HDF-P8-SS1 for edge effects along soft simply supported (SS1) boundary and HDF-P8-FREE for edge effects along free boundary.

Findings

The proposed elements can pass all patch tests, exhibit excellent convergence and possess superior precision when compared to all other existing eight-node models, and can still provide good and stable results even when extremely coarse and distorted meshes are used. They can also effectively solve the edge effect by accurately capturing the peak value and the dramatical variations of resultants near the SS1 and free boundaries. The proposed eight-node models possess potential in engineering applications and can be easily integrated into commercial software.

Originality/value

This work presents a new scheme, which can take the advantages of both analytical and discrete methods, to develop high-order mesh distortion-resistant Mindlin–Reissner plate-bending elements.

Details

Engineering Computations, vol. 34 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 4 July 2016

Nasrin Jafari and Mojtaba Azhari

The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of…

Abstract

Purpose

The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of general shape. This method is used to investigate the effects of thickness, geometry of various shapes, boundary conditions and material properties on the large deformation analysis of Mindlin plates.

Design/methodology/approach

Nonlinear analysis of plates based on Mindlin theory is presented. The equations are derived by the Von-Karman assumption and total Lagrangian formulations. Newton-Raphson method is applied to achieve linear equations from nonlinear equations. Simple HP-cloud method is used for the construction of the shape functions based on Kronecker-δ properties, so the essential boundary conditions can be enforced directly. Shepard function is utilized for a partition of unity and complete polynomial is used as an enrichment function.

Findings

The suitability and efficiency of the simple HP-cloud method for the geometrically nonlinear analysis of thin and moderately thick plates is studied for the first time. Large displacement analysis of various shapes of plates, rectangular, skew, trapezoidal, circular, hexagonal and triangular with different boundary conditions subjected to distributed loading are considered.

Originality/value

This paper shows that the simple HP-cloud method is well suited for the large deformation analysis of Mindlin plates with various geometries, because it uses a set of a few arbitrary nodes placed in a plate of general shape. Moreover the convergence rate of the proposed method is high and the cost of solving equations is low.

Details

Engineering Computations, vol. 33 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 25 February 2014

Dragan Ribarić and Gordan Jelenić

In this work, the authors aim to employ the so-called linked-interpolation concept already tested on beam and quadrilateral plate finite elements in the design of…

Abstract

Purpose

In this work, the authors aim to employ the so-called linked-interpolation concept already tested on beam and quadrilateral plate finite elements in the design of displacement-based higher-order triangular plate finite elements and test their performance.

Design/methodology/approach

Starting from the analogy between the Timoshenko beam theory and the Mindlin plate theory, a family of triangular linked-interpolation plate finite elements of arbitrary order are designed. The elements are tested on the standard set of examples.

Findings

The derived elements pass the standard patch tests and also the higher-order patch tests of an order directly related to the order of the element. The lowest-order member of the family of developed elements still suffers from shear locking for very coarse meshes, but the higher-order elements turn out to be successful when compared to the elements from literature for the problems with the same total number of the degrees of freedom.

Research limitations/implications

The elements designed perform well for a number of standard benchmark tests, but the well-known Morley's skewed plate example turns out to be rather demanding, i.e. the proposed design principle cannot compete with the mixed-type approach for this test. Work is under way to improve the proposed displacement-based elements by adding a number of internal bubble functions in the displacement and rotation fields, specifically chosen to satisfy the basic patch test and enable a softer response in the bench-mark test examples.

Originality/value

A new family of displacement-based higher-order triangular Mindlin plate finite elements has been derived. The higher-order elements perform very well, whereas the lowest-order element requires improvement.

Details

Engineering Computations, vol. 31 no. 1
Type: Research Article
ISSN: 0264-4401

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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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