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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…

6041

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

Keywords

Article
Publication date: 1 April 1991

SAID T. GOMAA, MOHAMMED H. BALUCH, HAMDY H. ABDEL‐RAHMAN and AMMAR K. MOHAMMED

A finite element formulation for flexure of isotropic plates based on a recent refined theory is developed. The refined theory incorporates effects of transverse shear, transverse…

Abstract

A finite element formulation for flexure of isotropic plates based on a recent refined theory is developed. The refined theory incorporates effects of transverse shear, transverse normal stress and transverse normal strain. The Galerkin finite element method was used to develop the finite element equations for both plate bending and inplane problems. The performance of the proposed finite element model was evaluated by solving problems of uniformly loaded thick plates with different support conditions. The results of the present formulation are compared with Mindlin/Reissner and elasticity solutions.

Details

Engineering Computations, vol. 8 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 June 1993

E. OÑATE and M. CERVERA

A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0…

Abstract

A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume‐like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.

Details

Engineering Computations, vol. 10 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 June 1992

Y.W. KWON

A formulation has been developed for thermo‐elastoviscoplastic finite element analyses of continuous fibre‐reinforced composite plates subject to bending loading using a…

Abstract

A formulation has been developed for thermo‐elastoviscoplastic finite element analyses of continuous fibre‐reinforced composite plates subject to bending loading using a generalized continuum mechanics approach. Such an approach is used to model the non‐homogeneity in a composite, which is constituted by fibres embedded in a matrix material. The present formulation computes the respective stresses occurring in each constituent so that the respective yield criterion and flow rule of each constituent may be used if there is a material yielding in any constituent. Thermo‐elastic deformation of fibre and thermo‐elastoviscoplastic deformation of matrix are considered in the present study because the yield strength of fibre is substantially higher than that of matrix in many cases. Both constituents are assumed to be isotropic so that the von‐Mises yield criterion may be used for viscoplastic yielding of matrix. As numerical examples, a parametric study is performed for thermo‐elastoviscoplastic deformations of laminated composite plates subject to thermal bending loads.

Details

Engineering Computations, vol. 9 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 February 1988

P.A. Thompson, P. Bettess and J.B. Caldwell

An 8 noded, eccentrically stiffened, plate bending element is introduced. The formulation allows for any number of stiffeners arbitrarily orientated within a plate element without…

Abstract

An 8 noded, eccentrically stiffened, plate bending element is introduced. The formulation allows for any number of stiffeners arbitrarily orientated within a plate element without disturbing their individual properties and positions. This is a distinct improvement over conventional lumped stiffener modelling and equivalent orthotropic plate theory and considerably simplifies the modelling of stiffened structures. A technique is also presented which transforms stiffener positions defined in the global cartesian system to the local, isoparametric coordinates of the plate element which contains the given stiffener. Several examples are given which demonstrate the usefulness of the element.

Details

Engineering Computations, vol. 5 no. 2
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 1 April 1990

Klaus‐Jürgen Bathe, Miguel Luiz Bucalem and Franco Brezzi

We briefly summarize the theoretical formulations of our MITC plate bending elements and then present numerical convergence results. The elements are based on Reissner‐Mindlin…

Abstract

We briefly summarize the theoretical formulations of our MITC plate bending elements and then present numerical convergence results. The elements are based on Reissner‐Mindlin plate theory and a mixed‐interpolation of the transverse displacement, section rotations and transverse shear strain components. We consider our 4, 9 and 16‐node quadrilateral elements and our 7 and 12‐node triangular elements. The theoretical and numerical results indicate the high reliability and effectiveness of our elements.

Details

Engineering Computations, vol. 7 no. 4
Type: Research Article
ISSN: 0264-4401

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 and…

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

Keywords

Article
Publication date: 1 April 1990

H. Kebari

The 4‐node assumed strain elements are among the best elements available today but the bending moments at their full integration points oscillate severely. This paper presents a…

Abstract

The 4‐node assumed strain elements are among the best elements available today but the bending moments at their full integration points oscillate severely. This paper presents a one point integrated version of the 4‐node assumed strain plate element of Bathe‐Dvorkin. A Taylor series expansion approach is used to accommodate the linear variation of strains/stresses within the element and hence to stabilize the spurious zero energy modes. An extensive number of benchmark results are presented and compared.

Details

Engineering Computations, vol. 7 no. 4
Type: Research Article
ISSN: 0264-4401

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

Keywords

Article
Publication date: 1 March 1987

A. Venkatesh and J. Jirousek

This paper presents a new 9 DOF triangular element for plate bending. It is an analytically integrated improved version of the simplest member in the hierarchy of numerically…

Abstract

This paper presents a new 9 DOF triangular element for plate bending. It is an analytically integrated improved version of the simplest member in the hierarchy of numerically integrated elements. These elements have been based on the so‐called Hybrid—Trefftz model (HT), a recently developed hybrid model associated with enforcing interelement continuity on locally based displacement fields chosen such that they a priori verify the Lagrange plate equation over the element. In the process of development of the element stiffness matrix in a standard HT model, one has to invert the so‐called natural stiffness matrix, a 7 × 7 matrix associated with the expression of the strain energy in terms of the Trefftz's functions of the element. The inversion of this fully populated matrix represents the most expensive part of the calculation of the element. The basic improvement of the standard Hybrid—Trefftz 9 DOF triangle consists in replacing the original Trefftz's functions by new ones which are energy orthogonal and consequently, result in a diagonal natural stiffness matrix. This not only alleviates considerably the computer cost, but also significantly simplifies the algebra making analytical integrations possible. The practical efficiency of the new element which passes the patch test is demonstrated through numerical examples including the difficult simply supported skew plate problem with a strong singularity at its 150° obtuse corner.

Details

Engineering Computations, vol. 4 no. 3
Type: Research Article
ISSN: 0264-4401

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