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Article
Publication date: 1 August 1995

Albert A. Groenwold and Nielen Stander

A 4‐node flat shell quadrilateral finiteelement with 6 degrees of freedom per node, denoted QC5D‐SA, ispresented. The element is an assembly of a modification of thedrilling…

Abstract

A 4‐node flat shell quadrilateral finite element with 6 degrees of freedom per node, denoted QC5D‐SA, is presented. The element is an assembly of a modification of the drilling degree of freedom membrane presented by Ibrahimbegovic et al., and the assumed strain plate element presented by Bathe and Dvorkin. The part of the stiffness matrix associated with in—plane displacements and rotations is integrated over the element domain by a modified 5‐point reduced integration scheme, resulting in greater efficiency without the sacrifice of rank sufficiency. The scheme produces a soft higher order deformation mode which increases numerical accuracy. A large number of standard benchmark problems are analyzed. Some examples show that the effectiveness of a previously proposed “membrane locking correction” technique is significantly reduced when employing distorted elements. However, the element is shown to be generally accurate and in many cases superior to existing elements.

Details

Engineering Computations, vol. 12 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 March 1984

H. Stolarski, T. Belytschko, N. Carpenter and J.M. Kennedy

A simple triangular shell element which incorporates the effects of coupling between membrane and flexural behaviour and avoids membrane locking is described. The element uses a…

Abstract

A simple triangular shell element which incorporates the effects of coupling between membrane and flexural behaviour and avoids membrane locking is described. The element uses a discrete Kirchhoff bending formulation and a constant strain membrane element. For the purpose of permitting inextensional modes and thus avoiding membrane locking, a decomposition technique, which can also be viewed as a strain projection method, is used. The method is illustrated first for a beam element and then for a triangular shell element. Results are presented for a variety of linear static problems to illustrate its accuracy and some highly non‐linear problems to indicate its applicability to collapse analysis.

Details

Engineering Computations, vol. 1 no. 3
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 1 April 1990

D.Y. Yang, H.B. Shim and W.J. Chung

The effect of bending is investigated through the comparison of the membrane analysis and the shell analysis for stretching and deep drawing. An incremental formulation…

Abstract

The effect of bending is investigated through the comparison of the membrane analysis and the shell analysis for stretching and deep drawing. An incremental formulation incorporating the effect of shape change and anisotropy is used for the analysis of elastic‐plastic non‐steady large deformation. The deformation during a step is considered using the natural convected coordinate system. Stretching of a square blank with a hemispherical punch and deep drawing of a cyclindrical cup is analysed and the corresponding experiments are carried out. The computational results are compared with the experiments. In stretching, the comparison has shown that both the membrane analysis and the shell analysis are in good agreement with the experiment for punch load and strain distribution. In deep drawing, the computed loads of both the membrane analysis and the shell analysis are generally in good agreement with the experiment. The computed thickness strain of the membrane analysis, however, shows a wide difference with the experiment. In the shell analysis, the thickness strain shows good agreement with the experiment. It has been shown that the membrane approach shows a limitation for the deep drawing process in which the effect of bending is not negligible and more exact informations on the thickness strain distribution are required.

Details

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

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: 5 October 2015

Shi Zhang, Yun Zhang, Zhigao Huang, Huamin Zhou and Jianhui Li

– The purpose of this paper is to study the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary.

Abstract

Purpose

The purpose of this paper is to study the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary.

Design/methodology/approach

In this paper, three triangular flat shells developed by combining an excellent membrane element (OPT) with three outstanding plate bending elements (DKT, RDKTM and DST-BK), respectively, are used to study this phenomenon. Benchmark tests are implemented to evaluate the performance of three selected plate elements and the formulated flat shells.

Findings

The inter-element coupling effect of membrane and plate components belonging, respectively, to two adjacent shells deteriorate the performance of shells. Therefore, a shell’s performance cannot be guaranteed certainly by the superimposed membrane and plate behaviors.

Practical implications

The “order matching” criterion is proposed to explain this phenomenon and it is concluded that the flat shell that follows this criterion explicitly may alleviate or even overcome the inter-element coupling effect.

Originality/value

Previous studies mainly focus on formulation of high-performance membrane and plate elements. However, the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary, has attracted less attention. Thorough benchmark tests for three flat shells are implemented to investigate the phenomenon. The results shows that the inter-element coupling effect deteriorates the performance of shells. And the “order matching” criterion is proposed to explain this phenomenon and it is concluded that the flat shell that follows this criterion explicitly may alleviate or even overcome the inter-element coupling effect.

Details

Engineering Computations, vol. 32 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 April 1990

P. Wriggers and R.L. Taylor

An axisymmetrical membrane element for large deformations is developed which is based on Ogden's non‐linear elastic material law. Special attention is given to the linearization…

Abstract

An axisymmetrical membrane element for large deformations is developed which is based on Ogden's non‐linear elastic material law. Special attention is given to the linearization procedure to obtain a quadratically convergence behaviour within Newton's method. Several examples show the applicability and performance of the proposed formulation.

Details

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

Article
Publication date: 1 January 1989

Gerhard Krause

Two isoparametric Lagrangian shallow shell elements are presented: a 4‐node element QUAD4 and a 9‐node element QUAD9. These elements are based on Mindlin/Reissner plate elements…

Abstract

Two isoparametric Lagrangian shallow shell elements are presented: a 4‐node element QUAD4 and a 9‐node element QUAD9. These elements are based on Mindlin/Reissner plate elements as described in a series of papers. These elements are sophisticated by adding conventional membrane stiffness and membrane‐bending coupling terms based on Maguerre's approximate shallow shell theory. This results in double curved shell elements which originally possess severe membrane locking behaviour. This defect is overcome in the same way as the shear locking problem is solved.

Details

Engineering Computations, vol. 6 no. 1
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 7 August 2019

Djamel Boutagouga

This paper aims to describe the formulation of a displacement-based triangular membrane finite element with true drilling rotational degree of freedom (DOF).

Abstract

Purpose

This paper aims to describe the formulation of a displacement-based triangular membrane finite element with true drilling rotational degree of freedom (DOF).

Design/methodology/approach

The presented formulation incorporates the true drilling rotation provided by continuum mechanics into the displacement field by way of using the polynomial interpolation. Unlike the linked interpolation, that uses a geometric transformation between displacement and vertex rotations, in this work, the interpolation of the displacement field in terms of nodal drilling rotations is obtained following an unusual approach that does not imply any presumed geometric transformation.

Findings

New relationship linking the mid-side normal displacement to corner node drilling rotations is derived. The resulting new element with true drilling rotation is compatible and does not include any problem-dependent parameter that may influence the results. The spurious zero-energy mode is stabilized in a careful way that preserves the true drilling rotational degrees of freedom (DOFs).

Originality/value

Several works dealing with membrane elements with vertex rotational DOFs have been published with improved convergence rate, however, owing to the need for incorporating rotations in the finite element meshes involving solids, shells and beam elements, having finite elements with true drilling rotational DOFs is more appreciated.

Article
Publication date: 1 January 1987

M. Talbot and G. Dhatt

The comparative efficiency of three flat triangular shell elements is being assessed for analysing non‐linear behaviour of general shell structures. The bending formulation of the…

Abstract

The comparative efficiency of three flat triangular shell elements is being assessed for analysing non‐linear behaviour of general shell structures. The bending formulation of the three elements is based on a discrete Kirchhoff model (namely the well‐known 3‐node DKT element and a new 6‐node DKTP element). The in‐plane behaviour is defined by constant (CST), linear (LST)and quadratic (QST) strain approximations. The super‐position of bending and membrane elements leads to the 3‐node DCT element (DKT plus CST), the 3‐node DQT element (DKT plus QST) and the 6‐node DLT element (DKTP plus LST). The geometrically non‐linear formulation is based on an approximate updated Lagrangian formulation (AULF) and the solution is obtained by using the Newton‐Raphson method with an automatic arc‐length control method. Illustrative examples include pre‐ and post‐buckling of different shell structures showing, in particular, some bifurcation points, large rotations and displacements and very important membrane‐bending coupling.

Details

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

Article
Publication date: 9 April 2020

Xiaofeng Wang, Haoyue Chu and Qingshan Yang

This paper aims to numerically study the effects of boundary conditions, pre-stress, material constants and thickness on the dynamic performance of a wrinkled thin membrane.

Abstract

Purpose

This paper aims to numerically study the effects of boundary conditions, pre-stress, material constants and thickness on the dynamic performance of a wrinkled thin membrane.

Design/methodology/approach

Based on the stability theory of plates and shells, the dynamic equations of a wrinkled thin membrane were developed, and they were solved with the Lanczos method

Findings

The effects of wrinkle-influencing factors on the dynamic performance of a wrinkled membrane are determined by the wrinkling stage. The effects are prominent when wrinkling deformation is evolving, but they are very small and can hardly be observed when wrinkling deformation is stable. Mode shapes of a wrinkled membrane are sensitive to boundary conditions, pre-stress and Poisson’s ratio, but its natural frequencies are sensitive to all these five factors.

Practical implications

The research work in this paper is expected to help understand the dynamic behavior of a wrinkled membrane and present access to ensuring its dynamic stability by controlling the wrinkle-influencing factors.

Originality/value

Very few documents investigated the dynamic properties of wrinkled membranes. No attention has yet been paid by the present literature to the global dynamic performance of a wrinkled membrane under the influences of the factors that play a pivotal role in the wrinkling deformation. In view of this, this paper numerically studied the global modes and corresponding frequencies of a wrinkled membrane and their variation with the wrinkle-influencing factors. The results indicate that the global dynamic properties of a wrinkled membrane are sensitive to these factors at the stage of wrinkling evolution.

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