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Article
Publication date: 10 May 2019

Wenan Wu and Hong Zheng

This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable…

114

Abstract

Purpose

This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable mixed formulation for incompressible linear elasticity which circumvents the need to satisfy inf-sup condition.

Design/methodology/approach

Using the hybrid FE–meshfree method, the displacement and pressure are interpolated conveniently with the same order so that a continuous pressure field can be obtained with low-order elements. The multiscale variational principle is then introduced into the Galerkin form to obtain stable and convergent results.

Findings

The present method is capable of overcoming volume locking and does not exhibit unphysical oscillations near the incompressible limit. Moreover, there are no extra unknowns introduced in the present method because the fine-scale unknowns are eliminated using the static condensation technique, and there is no need to evaluate any user-defined stability parameter as the classical stabilization methods do. The shape functions constructed in the present model possess continuous derivatives at nodes, which gives a continuous and more precise stress field with no need of an additional smooth process. The shape functions in the present model also possess the Kronecker delta property, so that it is convenient to impose essential boundary conditions.

Originality/value

The proposed model can be implemented easily. Its convergence rates and accuracy in displacement, energy and pressure are even comparable to those of second-order mixed elements.

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Article
Publication date: 1 March 1993

J. PETERA, V. NASSEHI and J.F.T. PITTMAN

A number of finite element formulations involving discontinuous weighting functions have been tested against analytic solutions for a steady scalar convection—diffusion problem at…

137

Abstract

A number of finite element formulations involving discontinuous weighting functions have been tested against analytic solutions for a steady scalar convection—diffusion problem at intermediate Peclet number, with a ‘hard’ downstream boundary condition. The emphasis is on extending these methods to isoparametric bilinear and biquadratic elements. In order to do this a procedure is given for the exact calculation of shape function Laplacians. Having confirmed the success of the Brooks—Hughes streamline upwind Petrov—Galerkin (SUPG) method for isoparametric bilinear elements, formulations for biquadratic elements are examined. Galerkin least squares offers little advantage over SUPG in the test problem. The generalized Galerkin method of Donea et al. gave excellent results, but because of concern over the possibility of cross‐streamline artificial diffusion in some cases, a strictly streamline formulation incorporating the optimal parameters of Donea et al. is proposed. This gave excellent results on a sufficiently refined mesh.

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International Journal of Numerical Methods for Heat & Fluid Flow, vol. 3 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 5 June 2007

Shuenn‐Yih Chang

It has been verified that the WBZ‐α method of Wood, Bossak and Zienkiewicz can have unconditional stability and numerical dissipation for linear elastic systems. However, it is…

405

Abstract

Purpose

It has been verified that the WBZ‐α method of Wood, Bossak and Zienkiewicz can have unconditional stability and numerical dissipation for linear elastic systems. However, it is still unclear about its performance in the solution of nonlinear systems analytically. Hence, this study proposes to analytically investigate its numerical characteristics for solving nonlinear systems.

Design/methodology/approach

Two parameters are introduced to facilitate the basic analysis for nonlinear systems. One is the step degree of nonlinearity, which describes the stiffness change within a time step, and the other is the step degree of convergence, which describes the convergence error due to an iteration procedure.

Findings

It is theoretically proved that the sub‐family of WBZ‐α method of −1≤α<0, β=(1/4)(1−α)2 and γ=(1/2)−α is unconditionally stable and has desired numerical dissipation for any nonlinear systems even with the presence of convergence error. These theoretical results are confirmed by numerical examples.

Originality/value

This analytical study reveals that the performance of the WBZ‐α method for nonlinear systems is in general the same as that for linear elastic systems.

Details

Engineering Computations, vol. 24 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 August 2002

Pawan Budhwar, Andy Crane, Annette Davies, Rick Delbridge, Tim Edwards, Mahmoud Ezzamel, Lloyd Harris, Emmanuel Ogbonna and Robyn Thomas

Wonders whether companies actually have employees best interests at heart across physical, mental and spiritual spheres. Posits that most organizations ignore their workforce �…

64474

Abstract

Wonders whether companies actually have employees best interests at heart across physical, mental and spiritual spheres. Posits that most organizations ignore their workforce – not even, in many cases, describing workers as assets! Describes many studies to back up this claim in theis work based on the 2002 Employment Research Unit Annual Conference, in Cardiff, Wales.

Details

Management Research News, vol. 25 no. 8/9/10
Type: Research Article
ISSN: 0140-9174

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Article
Publication date: 1 February 1996

Jaroslav Mackerle

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included…

677

Abstract

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

Details

Engineering Computations, vol. 13 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 11 February 2021

Mingyang Liu, Huifen Zhu, Guangjun Gao, Chen Jiang and G.R Liu

The purpose of this paper is to investigate a novel stabilization scheme to handle convection and pressure oscillation in the process of solving incompressible laminar flows by…

168

Abstract

Purpose

The purpose of this paper is to investigate a novel stabilization scheme to handle convection and pressure oscillation in the process of solving incompressible laminar flows by finite element method (FEM).

Design/methodology/approach

The semi-implicit stabilization scheme, characteristic-based polynomial pressure projection (CBP3) consists of the Characteristic-Galerkin method and polynomial pressure projection. Theoretically, the proposed scheme works for any type of element using equal-order approximation for velocity and pressure. In this work, linear 3-node triangular and 4-node tetrahedral elements are the focus, which are the simplest but most difficult elements for pressure stabilizations.

Findings

The present paper proposes a new scheme, which can stabilize FEM solution for flows of both low and relatively high Reynolds numbers. And the influence of stabilization parameters of the CBP3 scheme has also been investigated.

Research limitations/implications

The research in this work is limited to the laminar incompressible flow.

Practical implications

The verification and validation of the CBP3 scheme are conducted by several 2 D and 3 D numerical examples. The scheme could be used to deal with more practical fluid problems.

Social implications

The application of scheme to study complex hemodynamics of patient-specific abdominal aortic aneurysm is also presented, which demonstrates its potential to solve bio-flows.

Originality/value

The paper simulated 2 D and 3 D numerical examples with superior results compared to existing results and experiments. The novel CBP3 scheme is verified to be very effective in handling convection and pressure oscillation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 4 June 2021

Junning Qin and Hongzhi Zhong

Various time integration methods and time finite element methods have been developed to obtain the responses of structural dynamic problems, but the accuracy and computational…

153

Abstract

Purpose

Various time integration methods and time finite element methods have been developed to obtain the responses of structural dynamic problems, but the accuracy and computational efficiency of them are sometimes not satisfactory. The purpose of this paper is to present a more accurate and efficient formulation on the basis of the weak form quadrature element method to solve linear structural dynamic problems.

Design/methodology/approach

A variational principle for linear structural dynamics, which is inspired by Noble's work, is proposed to develop the weak form temporal quadrature element formulation. With Lobatto quadrature rule and the differential quadrature analog, a system of linear equations is obtained to solve the responses at sampling time points simultaneously. Computation for multi-elements can be carried out by a time-marching technique, using the end point results of the last element as the initial conditions for the next.

Findings

The weak form temporal quadrature element formulation is conditionally stable. The relation between the normalized length of element and the suggested number of integration points in one element is given by a simple formula. Results show that the present formulation is much more accurate than other time integration methods and its dissipative property is also illustrated.

Originality/value

The weak form temporal quadrature element formulation provides a choice with high accuracy and efficiency for solution of linear structural dynamic problems.

Details

Engineering Computations, vol. 38 no. 10
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 January 1987

J.P. Coyette

The numerical treatment of coupled field interaction problems frequently uses mixed time integration methods. These methods permit different time integration methods (implicit…

46

Abstract

The numerical treatment of coupled field interaction problems frequently uses mixed time integration methods. These methods permit different time integration methods (implicit, explicit) and/or different timesteps to be used simultaneously in different parts of the mesh. This paper summarizes the various mixed time integration methods and provides a unified presentation. Computer implementation of the generalized scheme is provided through a 1D linear structural dynamics program (GEMIX). Two common examples illustrate the use of GEMIX program.

Details

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

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Article
Publication date: 1 January 1992

ZHI‐HUA ZHONG and JAROSLAV MACKERLE

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite…

563

Abstract

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.

Details

Engineering Computations, vol. 9 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 November 2000

Stefan Doll, Karl Schweizerhof, Ralf Hauptmann and Christof Freischläger

As known from nearly incompressible elasticity, selective reduced integration (SRI) is a simple and effective method of overcoming the volumetric locking problem in 2D and 3D…

960

Abstract

As known from nearly incompressible elasticity, selective reduced integration (SRI) is a simple and effective method of overcoming the volumetric locking problem in 2D and 3D solid elements. This method of finite elastoviscoplasticity is discussed as are its well‐known limitations. In this context, an isochoric‐volumetric decoupled material behavior is assumed and thus the additive deviatoric‐volumetric decoupling of the consistent algorithmic moduli tensor is essential. By means of several numerical examples, the performance of elements using selective reduced integration is demonstrated and compared to the performance of other elements such as the enhanced assumed strain elements. It is shown that a minor modification, with little numerical effort, leads to rather robust element behaviour. The application of this process to so‐called solid‐shell elements for thin‐walled structures is also discussed.

Details

Engineering Computations, vol. 17 no. 7
Type: Research Article
ISSN: 0264-4401

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