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Article
Publication date: 15 September 2023

Chen Jiang, Ekene Paul Odibelu and Guo Zhou

This paper aims to investigate the performance of two novel numerical methods, the face-based smoothed finite element method (FS-FEM) and the edge-based smoothed finite element…

Abstract

Purpose

This paper aims to investigate the performance of two novel numerical methods, the face-based smoothed finite element method (FS-FEM) and the edge-based smoothed finite element method (ES-FEM), which employ linear tetrahedral elements, for the purpose of strength assessment of a high-speed train hollow axle.

Design/methodology/approach

The calculation of stress for the wheelset, comprising an axle and two wheels, is facilitated through the application of the European axle strength design standard. This standard assists in the implementation of loading and boundary conditions and is exemplified by the typical CRH2 high-speed train wheelset. To evaluate the performance of these two methods, a hollow cylinder cantilever beam is first used as a benchmark to compare the present methods with other existing methods. Then, the strength analysis of a real wheelset model with a hollow axle is performed using different numerical methods.

Findings

The results of deflection and stress show that FS-FEM and ES-FEM offer higher accuracy and better convergence than FEM using linear tetrahedral elements. ES-FEM exhibits a superior performance to that of FS-FEM using linear tetrahedral elements, showing accuracy and convergence close to FEM using hexahedral elements.

Originality/value

This study channels the novel methods (FS-FEM and ES-FEM) in the static stress analysis of a railway wheelset. Based on the careful testing of FS-FEM and ES-FEM, both methods hold promise as more efficient tools for the strength analysis of complex railway structures.

Details

Engineering Computations, vol. 40 no. 9/10
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 2 November 2015

Zhicheng He, Guangyao Li, Guiyong Zhang, Gui-Rong Liu, Yuantong Gu and Eric Li

In this work, an SFEM is proposed for solving acoustic problems by redistributing the entries in the mass matrix to “tune” the balance between “stiffness” and “mass” of discrete…

Abstract

Purpose

In this work, an SFEM is proposed for solving acoustic problems by redistributing the entries in the mass matrix to “tune” the balance between “stiffness” and “mass” of discrete equation systems, aiming to minimize the dispersion error. The paper aims to discuss this issue.

Design/methodology/approach

This is done by simply shifting the four integration points’ locations when computing the entries of the mass matrix in the scheme of SFEM, while ensuring the mass conservation. The proposed method is devised for bilinear quadratic elements.

Findings

The balance between “stiffness” and “mass” of discrete equation systems is critically important in simulating wave propagation problems such as acoustics. A formula is also derived for possibly the best mass redistribution in terms of minimizing dispersion error reduction. Both theoretical and numerical examples demonstrate that the present method possesses distinct advantages compared with the conventional SFEM using the same quadrilateral mesh.

Originality/value

After introducing the mass-redistribution technique, the magnitude of the leading relative dispersion error (the quadratic term) of MR-SFEM is bounded by (5/8), which is much smaller than that of original SFEM models with traditional mass matrix (13/4) and consistence mass matrix (2). Owing to properly turning the balancing between stiffness and mass, the MR-SFEM achieves higher accuracy and much better natural eigenfrequencies prediction than the original SFEM does.

Details

Engineering Computations, vol. 32 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 March 1993

P.P. SILVESTER and D. OMERAGIĆ

The gradient recovery method proposed by Zhu and Zienkiewicz for one‐dimensional problems is generalized to two dimensions, using quadrilateral elements. Its performance is…

Abstract

The gradient recovery method proposed by Zhu and Zienkiewicz for one‐dimensional problems is generalized to two dimensions, using quadrilateral elements. Its performance is compared with that of conventional local smoothing techniques and of direct differentiation of the finite‐element solution, on finite‐element approximations to analytically known polynomial and transcendental functions on a quadrilateral second‐order finite‐element mesh. The new method appears to be reliable and more stable than local smoothing, and to provide better accuracy than direct differentiation, at low computational cost.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 12 no. 3
Type: Research Article
ISSN: 0332-1649

Article
Publication date: 1 April 2022

Can Ban, Na Na Pu, Yi Fei Zhang and Ma Wentao

This article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.

Abstract

Purpose

This article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.

Design/methodology/approach

This paper proposed a generalized linear smoothed meshfree method (LSMM), in which the compatible strain is reconstructed by the linear smoothed strains. Based on the idea of the weighted residual method and employing three linearly independent weight functions, the linear smoothed strains can be created easily in a smoothing domain. Using various types of basic functions, LSMM can solve the linear elastic continuous and fracture problems in a unified way.

Findings

On the one hand, the LSMM inherits the properties of high efficiency and stability from the stabilized conforming nodal integration (SCNI). On the other hand, the LSMM is more accurate than the SCNI, because it can produce continuous strains instead of the piece-wise strains obtained by SCNI. Those excellent performances ensure that the LSMM has the capability to precisely track the crack propagation problems. Several numerical examples are investigated to verify the accurate, convergence rate and robustness of the present LSMM.

Originality/value

This study provides an accurate and efficient meshfree method for simulating crack growth.

Details

Engineering Computations, vol. 39 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 24 November 2021

Mingyang Liu, Guangjun Gao, Huifen Zhu and Chen Jiang

The purpose of this paper is to investigate the feasibility of solving turbulent flows based on smoothed finite element method (S-FEM). Then, the differences between S-FEM and…

Abstract

Purpose

The purpose of this paper is to investigate the feasibility of solving turbulent flows based on smoothed finite element method (S-FEM). Then, the differences between S-FEM and finite element method (FEM) in dealing with turbulent flows are compared.

Design/methodology/approach

The stabilization scheme, the streamline-upwind/Petrov-Galerkin stabilization is coupled with stabilized pressure gradient projection in the fractional step framework. The Reynolds-averaged Navier-Stokes equations with standard k-epsilon model are selected to solve turbulent flows based on S-FEM and FEM. Standard wall functions are applied to predict boundary layer profiles.

Findings

This paper explores a completely new application of S-FEM on turbulent flows. The adopted stabilization scheme presents a good performance on stabilizing the flows, especially for very high Reynolds numbers flows. An advantage of S-FEM is found in applying wall functions comparing with FEM. The differences between S-FEM and FEM have been investigated.

Research limitations/implications

The research in this work is limited to the two-dimensional incompressible turbulent flow.

Practical implications

The verification and validation of a new combination are conducted by several numerical examples. The new combination could be used to deal with more complicated turbulent flows.

Social implications

The applications of the new combination to study basic and complex turbulent flow are also presented, which demonstrates its potential to solve more turbulent flows in nature and engineering.

Originality/value

This work carries out a great extension of S-FEM in simulations of fluid dynamics. The new combination is verified to be very effective in handling turbulent flows. The performances of S-FEM and FEM on turbulent flows were analyzed by several numerical examples. Superior results were found compared with existing results and experiments. Meanwhile, S-FEM has an advantage of accuracy in predicting boundary layer profile.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 July 2015

Guanxin Huang, Hu Wang and Guangyao Li

– The purpose of this paper is to enhance the feasibility of the edge-based smoothed triangular (EST) element, some modifications are made in this study.

Abstract

Purpose

The purpose of this paper is to enhance the feasibility of the edge-based smoothed triangular (EST) element, some modifications are made in this study.

Design/methodology/approach

First, an efficient strategy based on graph theory is proposed to construct the edge system. Second, the stress is smoothed in global coordinate system based on edge instead of strain, which makes the theory of EST more rigorous and can be easily extended to the situation of multi elements sharing the same edge. Third, the singular degree of freedoms (DOFs) of the nodes linked by edges are restrained in edge local coordinate system, which makes the global stiffness matrix non-singular and can be decomposed successfully.

Findings

First, an efficient edge constructing strategy can make EST element more standout. Second, some modifications should be made to EST element to extend it to the situation with multi elements sharing the same edge, so that EST element can deal with the geometrical models with this kind of features. Third, the way to restrain the singular DOFs of EST element must be different from normal isoparametric triangle element, because the stiffness matrix of the smoothing domain is not computed in local coordinate system.

Originality/value

The modified EST element performs stably in engineering analysis including large scale problems and the situation with multi elements sharing the same edge, and the efficiency of edge system constructing is no longer the bottleneck.

Details

Engineering Computations, vol. 32 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 5 June 2017

Yijun Liu, Guiyong Zhang, Huan Lu and Zhi Zong

Due to the strong reliance on element quality, there exist some inherent shortcomings of the traditional finite element method (FEM). The model of FEM behaves overly stiff, and…

Abstract

Purpose

Due to the strong reliance on element quality, there exist some inherent shortcomings of the traditional finite element method (FEM). The model of FEM behaves overly stiff, and the solutions of automated generated linear elements are generally of poor accuracy about especially gradient results. The proposed cell-based smoothed point interpolation method (CS-PIM) aims to improve the results accuracy of the thermoelastic problems via properly softening the overly-stiff stiffness.

Design/methodology/approach

This novel approach is based on the newly developed G space and weakened weak (w2) formulation, and of which shape functions are created using the point interpolation method and the cell-based gradient smoothing operation is conducted based on the linear triangular background cells.

Findings

Owing to the property of softened stiffness, the present method can generally achieve better accuracy and higher convergence results (especially for the temperature gradient and thermal stress solutions) than the FEM does by using the simplest linear triangular background cells, which has been examined by extensive numerical studies.

Practical implications

The CS-PIM is capable of producing more accurate results of temperature gradients as well as thermal stresses with the automated generated and unstructured background cells, which make it a better candidate for solving practical thermoelastic problems.

Originality/value

It is the first time that the novel CS-PIM was further developed for solving thermoelastic problems, which shows its tremendous potential for practical implications.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 March 1994

D. OMERAGIĆ and P.P. SILVESTER

The gradient recovery method proposed by Zhu and Zienkiewicz for one‐dimensional problems and extended to two dimensions by Silvester and Omeragi? is generalized to…

Abstract

The gradient recovery method proposed by Zhu and Zienkiewicz for one‐dimensional problems and extended to two dimensions by Silvester and Omeragi? is generalized to three‐dimensional solutions based on rectangular prism (brick) elements. The extension is not obvious so its details are presented, and the method compared with conventional local smoothing and direct differentiation. Illustrative examples are given, with an extensive experimental study of error. The method is computationally cheap and provides better accuracy than conventional local smoothing, but its accuracy is position dependent.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 13 no. 3
Type: Research Article
ISSN: 0332-1649

Article
Publication date: 30 October 2018

Farhoud Kalateh and Ali Koosheh

This paper aims to propose a new smoothed particle hydrodynamics (SPH)-finite element (FE) algorithm to study fluid–structure interaction (FSI) problems.

Abstract

Purpose

This paper aims to propose a new smoothed particle hydrodynamics (SPH)-finite element (FE) algorithm to study fluid–structure interaction (FSI) problems.

Design/methodology/approach

The fluid domain is discretized based on the theory of SPH), and solid part is solved through FE method, similar to other SPH-FE methods in the previous studies. Instead of master-slave technique, the interpolating (kernel) functions of immersed boundary method are implemented to couple fluid and solid domains. The procedure of modeling completely follows the classic IB framework where forces and velocities are transferred between interacting parts. Three benchmark FSI problems are simulated and the results are compared with those of similar numerical and experimental works.

Findings

The proposed SPH-FE algorithm with promising and acceptable results can be utilized as a reliable method to simulate FSI problems.

Originality/value

Contrary to most SPH-FE algorithms, the calculation of contact force is not required at interacting boundaries and no iterative process is proposed to calculate forces, velocities and positions at new time step.

Details

Engineering Computations, vol. 35 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 27 May 2014

Hu De’an, Liu Chunhan, Xiao YiHua and Han Xu

The purpose of this paper is to confirm that the axisymmetric finite element and smoothed particle hydrodynamics (FE-SPH) adaptive coupling method is effective to solve explosion…

Abstract

Purpose

The purpose of this paper is to confirm that the axisymmetric finite element and smoothed particle hydrodynamics (FE-SPH) adaptive coupling method is effective to solve explosion problem in concrete based on the experiments.

Design/methodology/approach

Axisymmetric FE-SPH adaptive coupling method is first presented to simulate dynamic deformation process of concrete under internal blast loading. Using calculation codes of FE-SPH coupling method, numerical model of explosion is approximated initially by finite element method (FEM), and distorted finite elements are automatically converted into meshless particles to simulate damage, splash of concrete by SPH method, when equivalent plastic strain of elements reaches a specified value.

Findings

In this paper, damage process and pressure curve of concrete around explosive are analyzed and buried depth of explosive in concrete influence on damage effect under internal blast loading are obtained. Numerical analyses show that FE-SPH coupling method integrates high computational efficiency of FEM and advantages of SPH method, such as natural simulation to damage, splash and other characteristics of explosion in concrete.

Originality/value

This work shows that FE-SPH coupling method has good performance to solve the explosion problem.

Details

Engineering Computations, vol. 31 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

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