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Article
Publication date: 27 September 2011

Mohammad Rezaiee‐Pajand, Cyrus Nasirai and Mehrzad Sharifian

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

Abstract

Purpose

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

Design/methodology/approach

By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.

Findings

The numerical tests show the robustness and high efficiency of the proposed integration scheme.

Research limitations/implications

The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.

Practical implications

Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.

Originality/value

The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponentialbased integration method is more efficient than the classical strategies.

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Article
Publication date: 6 November 2017

Jiawei Wang, Feng Chen, Jinghui Shao, Weichen Zhang and Xikui Ma

This paper aims to present a novel hybrid time integration approach for efficient numerical simulations of multiscale problems involving interactions of electromagnetic…

Abstract

Purpose

This paper aims to present a novel hybrid time integration approach for efficient numerical simulations of multiscale problems involving interactions of electromagnetic fields with fine structures.

Design/methodology/approach

The entire computational domain is discretized with a coarse grid and a locally refined subgrid containing the tiny objects. On the coarse grid, the time integration of Maxwell’s equations is realized by the conventional finite-difference technique, while on the subgrid, the unconditionally stable Krylov-subspace-exponential method is adopted to breakthrough the Courant–Friedrichs–Lewy stability condition.

Findings

It is shown that in contrast with the conventional finite-difference time-domain method, the proposed approach significantly reduces the memory costs and computation time while providing comparative results.

Originality/value

An efficient hybrid time integration approach for numerical simulations of multiscale electromagnetic problems is presented.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 6
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 March 1997

Guido E. Sartoris

Presents a fast numerical method for computing the lowest degree moments of the exponential function for a segment, square or cubic domain. An exponential function with…

Abstract

Presents a fast numerical method for computing the lowest degree moments of the exponential function for a segment, square or cubic domain. An exponential function with the argument a multivariate polynomial with a maximum degree of one in each single variable is considered. These kinds of integral are encountered in exponential‐fitting finite element methods. For the 1D and 2D cases, a fast method based on the direct evaluation of the moments is used, whereas for the 3D case, a quadrature of 2D moments is considered together with some schemes based on the knowledge of the integrand function in order to improve the computational efficiency.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 16 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 17 October 2019

J.I. Ramos

The purpose of this paper is to develop a new transversal method of lines for one-dimensional reactiondiffusion equations that is conservative and provides…

Abstract

Purpose

The purpose of this paper is to develop a new transversal method of lines for one-dimensional reactiondiffusion equations that is conservative and provides piecewise–analytical solutions in space, analyze its truncation errors and linear stability, compare it with other finite-difference discretizations and assess the effects of the nonlinear diffusion coefficients, reaction rate terms and initial conditions on wave propagation and merging.

Design/methodology/approach

A conservative, transversal method of lines based on the discretization of time and piecewise analytical integration of the resulting two-point boundary-value problems subject to the continuity of the dependent variables and their fluxes at the control-volume boundaries, is presented. The method provides three-point finite difference expressions for the nodal values and continuous solutions in space, and its accuracy has been determined first analytically and then assessed in numerical experiments of reaction-diffusion problems, which exhibit interior and/or boundary layers.

Findings

The transversal method of lines presented here results in three-point finite difference equations for the nodal values, treats the diffusion terms implicitly and is unconditionally stable if the reaction terms are treated implicitly. The method is very accurate for problems with the interior and/or boundary layers. For a system of two nonlinearly-coupled, one-dimensional reactiondiffusion equations, the formation, propagation and merging of reactive fronts have been found to be strong function of the diffusion coefficients and reaction rates. For asymmetric ignition, it has been found that, after front merging, the temperature and concentration profiles are almost independent of the ignition conditions.

Originality/value

A new, conservative, transversal method of lines that treats the diffusion terms implicitly and provides piecewise exponential solutions in space without the need for interpolation is presented and applied to someone.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 21 February 2020

J.I. Ramos

The purpose of this study is to develop a new method of lines for one-dimensional (1D) advection-reaction-diffusion (ADR) equations that is conservative and provides…

Abstract

Purpose

The purpose of this study is to develop a new method of lines for one-dimensional (1D) advection-reaction-diffusion (ADR) equations that is conservative and provides piecewise analytical solutions in space, compare it with other finite-difference discretizations and assess the effects of advection and reaction on both 1D and two-dimensional (2D) problems.

Design/methodology/approach

A conservative method of lines based on the piecewise analytical integration of the two-point boundary value problems that result from the local solution of the advection-diffusion operator subject to the continuity of the dependent variables and their fluxes at the control volume boundaries is presented. The method results in nonlinear first-order, ordinary differential equations in time for the nodal values of the dependent variables at three adjacent grid points and triangular mass and source matrices, reduces to the well-known exponentially fitted techniques for constant coefficients and equally spaced grids and provides continuous solutions in space.

Findings

The conservative method of lines presented here results in three-point finite difference equations for the nodal values, implicitly treats the advection and diffusion terms and is unconditionally stable if the reaction terms are implicitly treated. The method is shown to be more accurate than other three-point, exponentially fitted methods for nonlinear problems with interior and/or boundary layers and/or source/reaction terms. The effects of linear advection in 1D reacting flow problems indicates that the wave front steepens as it approaches the downstream boundary, whereas its back corresponds to a translation of the initial conditions; for nonlinear advection, the wave front exhibits steepening but the wave back shows a linear dependence on space. For a system of two nonlinearly coupled, 2D ADR equations, it is shown that a counter-clockwise rotating vortical field stretches the spiral whose tip drifts about the center of the domain, whereas a clock-wise rotating one compresses the wave and thickens its arms.

Originality/value

A new, conservative method of lines that implicitly treats the advection and diffusion terms and provides piecewise-exponential solutions in space is presented and applied to some 1D and 2D advection reactions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 11
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 16 April 2018

Yan Zhao, L.T. Si and H. Ouyang

A novel frequency domain approach, which combines the pseudo excitation method modified by the authors and multi-domain Fourier transform (PEM-FT), is proposed for…

Abstract

Purpose

A novel frequency domain approach, which combines the pseudo excitation method modified by the authors and multi-domain Fourier transform (PEM-FT), is proposed for analyzing nonstationary random vibration in this paper.

Design/methodology/approach

For a structure subjected to a nonstationary random excitation, the closed-form solution of evolutionary power spectral density of the response is derived in frequency domain.

Findings

The deterministic process and random process in an evolutionary spectrum are separated effectively using this method during the analysis of nonstationary random vibration of a linear damped system, only modulation function of the system needs to be estimated, which brings about a large saving in computational time.

Originality/value

The method is general and highly flexible as it can deal with various damping types and nonstationary random excitations with different modulation functions.

Details

Engineering Computations, vol. 35 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 13 February 2020

Haichao Cui, Qiang Gao, Xiaolan Li and Huajiang Ouyang

This paper aims to propose an efficient and accurate method to analyse the transient heat conduction in a periodic structure with moving heat sources.

Abstract

Purpose

This paper aims to propose an efficient and accurate method to analyse the transient heat conduction in a periodic structure with moving heat sources.

Design/methodology/approach

The moving heat source is modelled as a localised Gaussian distribution in space. Based on the spatial distribution, the physical feature of transient heat conduction and the periodic property of structure, a special feature of temperature responses caused by the moving heat source is illustrated. Then, combined with the superposition principle of linear system, within a small time-step, computation of results corresponding to the whole structure excited by the Gaussian heat source is transformed into that of some small-scale structures. Lastly, the precise integration method (PIM) is used to solve the temperature responses of each small-scale structure efficiently and accurately.

Findings

Within a reasonable time-step, the heat source applied on a unit cell can only cause the temperature responses of a limited number of adjacent unit cells. According to the above feature and the periodic property of a structure, the contributions caused by the moving heat source for the most of time-steps are repeatable, and the temperature responses of the entire periodic structure can be obtained by some small-scale structures.

Originality/value

A novel numerical method is proposed for analysing moving heat source problems, and the numerical examples demonstrate that the proposed method is much more efficient than the traditional methods, even for larger-scale problems and multiple moving heat source problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 28 August 2007

M. Rezaiee‐Pajand and Cyrus Nasirai

This paper aims to provide a more rapid stress updating algorithm for von‐Mises plasticity with mixed‐hardening and to compare it with the previous works.

Abstract

Purpose

This paper aims to provide a more rapid stress updating algorithm for von‐Mises plasticity with mixed‐hardening and to compare it with the previous works.

Design/methodology/approach

An augmented stress vector is defined. This can convert the original nonlinear differential equation system to a quasi‐linear one. Then the dynamical system can be solved with an exponential map approach in a semi‐implicit manner.

Findings

The presented stress updating algorithm gives very accurate results and it has a quadratic convergence rate.

Research limitations/implications

Von‐Mises plasticity in a small strain regime is considered. Furthermore, the material is supposed to have linear hardening.

Practical implications

Stress updating is the heart of a nonlinear finite element analysis due to the large consumption of computation time. The efficiency and accuracy of the calculations of nonlinear finite element analysis are strongly influenced by the efficiency and accuracy of stress updating schemes.

Originality/value

The paper offers a new stress updating strategy based on exponential maps. This may be used as a routine in a nonlinear finite element analysis software to enhance its performance.

Details

Engineering Computations, vol. 24 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 27 August 2019

Maliheh Tavoosi, Mehrdad Sharifian and Mehrzad Sharifian

The purpose of this paper is to suggest a robust hybrid method for updating the stress and plastic internal variables in plasticity considering damage mechanics.

Abstract

Purpose

The purpose of this paper is to suggest a robust hybrid method for updating the stress and plastic internal variables in plasticity considering damage mechanics.

Design/methodology/approach

By benefiting the properties of the well-known explicit and implicit integrations, a new mixed method is derived. In fact, the advantages of the mentioned techniques are used to achieve an efficient integration.

Findings

The numerical studies demonstrate the high precision and robustness of the suggested algorithm.

Research limitations

The perfect von-Mises plasticity together with Lemaitre damage model is considered within the realm of small deformations.

Practical implications

Updating stress and plastic internal variables are of utmost importance in elastoplastic analyses of structures. The accuracy and efficiency of stress-updating methods significantly affect the final outcomes of nonlinear analyses.

Originality/value

The idea which is used to derive the hybrid method leads to an efficient integration method for updating the constitutive equations of the damage mechanics.

Details

Engineering Computations, vol. 37 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 14 November 2008

Marissa Condon, Emira Dautbegovic and Tao Xu

The paper aims to propose several new approaches for the discrete‐time integration of stiff non‐linear differential equations.

Abstract

Purpose

The paper aims to propose several new approaches for the discrete‐time integration of stiff non‐linear differential equations.

Design/methodology/approach

The proposed approaches build on a method developed by the authors involving Padé approximates about each function sample. Both single‐ and multi‐step methods are suggested. The use of Richardson extrapolation is recommended for increasing efficiency.

Findings

The efficacy of the methods is shown using two examples and results are compared to a standard integration technique.

Originality/value

The paper shows that the methods are suitable for application in any field of science requiring efficient and accurate numerical solution of stiff differential equations.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 27 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

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