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Article
Publication date: 1 September 1998

K. Bouranta, G.A. Malegiannakis and B. Kröplin

Coupled problems are of great interest in the area of technical applications. In the current paper we present the theory of thermo‐electro‐mechanical coupling and provide a…

Abstract

Coupled problems are of great interest in the area of technical applications. In the current paper we present the theory of thermo‐electro‐mechanical coupling and provide a discretization by using the method of finite elements. The thermo‐electro‐mechanical effect presents a physical interaction between the fundamental quantities of the sub‐domains elastomechanics, electrostatics and heat balance. Throughout thermodynamic analysis we derive the constitutive equations which describe the above behaviour and relate the main quantities which describe the three fields. From the principal equations of elastomechanics, electrostatics and heat balance separately, we derive the weak formulation of the load equilibrium, the electrostatic equilibrium and the heat balance individually. Furthermore a FE‐formulation leads the weak formulations of the coupled problem to a system of three coupling differential equations. This system is non‐linear with respect to the temperature and we solve it using an incremental solution. The numerical result is to be shown on a one‐dimensional test example.

Details

Engineering Computations, vol. 15 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 9 July 2020

Dominique Giraud, Baptiste Ristagno, Denis Netter, Julien Fontchastagner, Nicolas Labbe and Vincent Lanfranchi

This paper aims to propose a method to evaluate the information obtained on harmonics calculations and to estimate the precision of results using finite element method for an…

89

Abstract

Purpose

This paper aims to propose a method to evaluate the information obtained on harmonics calculations and to estimate the precision of results using finite element method for an innovative motor topology in which some well-known meshing rules are difficult to apply.

Design/methodology/approach

The same magnetostatic problem is solved with several mesh sizes using both scalar and vector potentials magnetics formulations on a complex topology, an axial claw pole motor (ACPM). The proposed method lies in a comparison between the two weak formulations to determine what information is obtained on harmonics calculations and to estimate its precision. Moreover, an original mesh method is applied in the air gap to improve the numerical results.

Findings

The precision on harmonics calculations using finite element method on an ACPM is estimated. For the proposed motor and mesh, only the mean value (even with large mesh) and the first harmonic (with fine mesh) of torque are calculated with a good accuracy. This results confirm that the non-respect of the meshing rules have a strong impact on the results and that scalar and vector potentials magnetics formulations do not give exactly the same results. Before using torque harmonics values in vibration calculations, a finite element model has to be validated by using both fomulations.

Research limitations/implications

This method is time-consuming and only applied on an ACPM in this work.

Originality/value

The axial claw pole motor, for which the classic meshing rules cannot be applied, is a complex topology very under-studied. To improve the calculation of space harmonics, the authors proposed to split the airgap into four parts. Then in the two central parts, the meshing step of the structured mesh is equal to the rotating step.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 December 1999

P. Dular, J. Gyselinck, F. Henrotte, W. Legros and J. Melkebeek

Two complementary 3D finite element formulations, with either the magnetic field or the magnetic vector potential as unknowns, are developed to deal with the modeling of eddy…

Abstract

Two complementary 3D finite element formulations, with either the magnetic field or the magnetic vector potential as unknowns, are developed to deal with the modeling of eddy currents in electrical steel laminations. The magnetic flux through the flux gates of the conducting region is imposed via the boundary terms of the weak formulations, in a natural way thanks to the use of edge finite elements. The two formulations are applied to a simple 1D eddy current problem with analytical solution. As a practical 3D application example, a T‐joint region of an electrical steel lamination is considered.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 18 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 3 May 2016

Israel Tuval, Dan Givoli and Ehud Behar

The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a…

Abstract

Purpose

The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a zero-thickness interface. The advantage of the new model is that it saves the need to construct and use a fine mesh inside the layer and in regions adjacent to it, and thus leads to a reduction in the computational effort associated with implicit or explicit finite element schemes.

Design/methodology/approach

Special asymptotic models have been proposed for linear heat transfer and linear elasticity, to handle thin layers. In these models the thin layer is replaced by an interface with zero thickness, and specific jump conditions are imposed on this interface in order to represent the special effect of the layer. One such asymptotic interface model is the first-order Bövik-Benveniste model. In a paper by Sussmann et al., this model was incorporated in a FE formulation for linear steady-state heat conduction problems, and was shown to yield an accurate and efficient computational scheme. Here, this work is extended to the time-dependent case.

Findings

As shown here, and demonstrated by numerical examples, the new model offers a cost-effective way of handling thin layers in linear time-dependent heat conduction problems. The hybrid asymptotic-FE scheme can be used with either implicit or explicit time stepping. Since the formulation can easily be symmetrized by one of several techniques, the lack of self-adjointness of the original formulation does not hinder an accurate and efficient solution.

Originality/value

Most of the literature on asymptotic models for thin layers, replacing the layer by an interface, is analytic in nature. The proposed model is presented in a computational context, fitting naturally into a finite element framework, with both implicit and explicit time stepping, while saving the need for expensive mesh construction inside the layer and in its vicinity.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 July 2006

Patrick Dular, Ruth V. Sabariego and Patrick Kuo‐Peng

The paper seeks to develop dual 3D finite element (FE) formulations for modeling both inductive and capacitive effects in massive inductors, in particular micro‐coils. The paper…

Abstract

Purpose

The paper seeks to develop dual 3D finite element (FE) formulations for modeling both inductive and capacitive effects in massive inductors, in particular micro‐coils. The paper aims to build circuit relations relating the voltages and the currents in such inductors to be used in circuit coupling.

Design/methodology/approach

A circuit relation involving a unique voltage and complementary inductive and capacitive currents is defined for each inductor. The inductive circuit relation is first classically obtained by a FE magnetodynamic model. Then, the capacitive relation is obtained through a FE electric model, using sources evaluated from the first model. The conformity is defined on one hand for the magnetic flux density and the electric field, and on the other hand for the magnetic field and the electric flux density. Mixed FE, i.e. nodal, edge and face elements, are used to satisfy each chosen conformity level for the unknown fields and to naturally define the involved global quantities, i.e. the voltages, currents and charges.

Findings

This contribution points out the interest of satisfying conformity properties for the coupled magnetic and electric problems. An accurate computation of these effects is obtained in the critical frequency range of their strong interaction. In addition, the complementarity of dual solutions gives the possibility to estimate the discretisation error.

Originality/value

The mathematical and discretisation tools for any wished conformity level are unified for naturally coupling magnetic and electric problems. The global quantities basis functions involved in the FE circuit relations benefit from a significant support reduction, which facilitates their evaluation and gives them direct physical interpretations.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 13 August 2018

Sebastian Grabmaier, Matthias Jüttner and Wolfgang Rucker

Considering the vector Helmholtz equation in three dimensions, this paper aims to present a novel approach for coupling the finite element method and a boundary integral…

Abstract

Purpose

Considering the vector Helmholtz equation in three dimensions, this paper aims to present a novel approach for coupling the finite element method and a boundary integral formulation. It is demonstrated that the method is well-suited for many realistic three-dimensional problems in high-frequency engineering.

Design/methodology/approach

The formulation is based on partial solutions fulfilling the global boundary conditions and the iterative interaction between them. In comparison to other coupling formulation, this approach avoids the typical singularity in the integral kernels. The approach applies ideas from domain decomposition techniques and is implemented for a parallel calculation.

Findings

Using confirming elements for the trace space and default techniques to realize the infinite domain, no additional loss in accuracy is introduced compared to a monolithic finite element method approach. Furthermore, the degree of coupling between the finite element method and the integral formulation is reduced. The accuracy and convergence rate are demonstrated on a three-dimensional antenna model.

Research limitations/implications

This approach introduces additional degrees of freedom compared to the classical coupling approach. The benefit is a noticeable reduction in the number of iterations when the arising linear equation systems are solved separately.

Practical implications

This paper focuses on multiple heterogeneous objects surrounded by a homogeneous medium. Hence, the method is suited for a wide range of applications.

Originality/value

The novelty of the paper is the proposed formulation for the coupling of both methods.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 7 August 2017

Julio Marti, Ernesto Ortega and Sergio Idelsohn

The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems containing weak discontinuities.

Abstract

Purpose

The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems containing weak discontinuities.

Design/methodology/approach

The enrichment is introduced in the elements cut by the materials interface by means of adding additional shape functions. The weak form of the problem is obtained using Galerkin approach and subsequently integrating the diffusion term by parts. To enforce the continuity of the fluxes in the “cut” elements, a contour integral must be added. These contour integrals named here the “inter-elemental heat fluxes” are usually neglected in the existing enrichment approaches. The proposed approach takes these fluxes into account.

Findings

It has been shown that the inter-elemental heat fluxes cannot be generally neglected and must be included. The corresponding method can be easily implemented in any existing finite element method (FEM) code, as the new degrees of freedom corresponding to the enrichment are local to the elements. This allows for their static condensation, thus not affecting the size and structure of the global system of governing equations. The resulting elements have exactly the same number of unknowns as the non-enriched finite element (FE).

Originality/value

It is the first work where the necessity of including inter-elemental heat fluxes has been demonstrated. Moreover, numerical tests solved have proven the importance of these findings. It has been shown that the proposed enrichment leads to an improved accuracy in comparison with the former approaches where inter-elemental heat fluxes were neglected.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 19 March 2020

Behrooz Yousefi, Mohammad Reza Esfahani and Mohammadreza Tavakkolizadeh

This paper aims to develop a new multi-fiber element for predicting the structural behavior of planar-reinforced concrete (RC) members.

Abstract

Purpose

This paper aims to develop a new multi-fiber element for predicting the structural behavior of planar-reinforced concrete (RC) members.

Design/methodology/approach

In this work, an exact multi-directional stiffness matrix is analytically derived based on the post-cracking bond-slip interaction between concrete and steel bars. The approach is also extended for large displacement analysis using Green–Lagrange finite strain tensor. In the proposed formulation, the weak form of governed differential equations is approximated by a trial-function expansion based on a finite strain-description and an additional degree of freedom for steel bars.

Findings

The findings provide a realistic description of cracking in the concrete structure. Numerical studies are conducted to examine the accuracy of the suggested approach and its capability to predict fairly complex responses of RC models. The findings prove that the proposed element can evaluate local and global responses of RC members, and it can be used as a reliable tool to reflect bond-slip effects in large displacement level. This leads to a robust and precise model for non-linear analysis of RC structures.

Originality/value

The methodology is capable of simulating coupled inelastic shear-flexural behavior of RC members through local stress field theory and Timoshenko beam model.

Open Access
Article
Publication date: 18 January 2022

Valentin Hanser, Markus Schöbinger and Karl Hollaus

This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis.

Abstract

Purpose

This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis.

Design/methodology/approach

The mixed multiscale finite element method based on the based on the T,Φ-Φ formulation, with the current vector potential T and the magnetic scalar potential Φ allows the laminated core to be modelled as a single homogeneous block. This means that the individual sheets do not have to be resolved, which saves a lot of computing time and reduces the demands on the computer system enormously.

Findings

As a representative numerical example, a single-phase transformer with 4, 20 and 184 sheets is simulated with great success. The eddy current losses of the simulation using the standard finite element method and the simulation using the mixed multiscale finite element method agree very well and the required simulation time is tremendously reduced.

Originality/value

The vector Preisach model is used to account for vector hysteresis and is integrated into the mixed multiscale finite element method for the first time.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 14 August 2007

Patrick Dular, Ruth V. Sabariego, Johan Gyselinck and Laurent Krähenbühl

This paper seeks to develop a sub‐domain perturbation technique to efficiently calculate strong skin and proximity effects in conductors within frequency and time domain finite…

Abstract

Purpose

This paper seeks to develop a sub‐domain perturbation technique to efficiently calculate strong skin and proximity effects in conductors within frequency and time domain finite element (FE) analyses.

Design/methodology/approach

A reference eddy current FE problem is first solved by considering perfect conductors. This is done via appropriate boundary conditions (BCs) on the conductors. Next the solution of the reference problem gives the source for eddy current FE perturbation sub‐problems in each conductor then considered with a finite conductivity. Each of these problems requires an appropriate volume mesh of the associated conductor and its surrounding region.

Findings

The skin and proximity effects in both active and passive conductors can be accurately determined in a wide frequency range, allowing for precise losses calculations in inductors as well as in external conducting pieces.

Originality/value

The developed method allows one to accurately determine the current density distributions and ensuing losses in conductors of any shape, not only in the frequency domain but also in the time domain. Therefore, it extends the domain of validity and applicability of impedance‐type BC techniques. It also offers an original way to uncouple FE regions that allows the solution process to be lightened, as well as efficient parameterized analyses on the signal form and the conductor characteristics.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 26 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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