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Article
Publication date: 12 July 2013

Sascha Duczek and Ulrich Gabbert

Piezoelectric actuators and sensors are an invaluable part of lightweight designs for several reasons. They can either be used in noise cancellation devices as thin‐walled…

Abstract

Purpose

Piezoelectric actuators and sensors are an invaluable part of lightweight designs for several reasons. They can either be used in noise cancellation devices as thin‐walled structures are prone to acoustic emissions, or in shape control approaches to suppress unwanted vibrations. Also in Lamb wave based health monitoring systems piezoelectric patches are applied to excite and to receive ultrasonic waves. The purpose of this paper is to develop a higher order finite element with piezoelectric capabilities in order to simulate smart structures efficiently.

Design/methodology/approach

In the paper the development of a new fully three‐dimensional piezoelectric hexahedral finite element based on the p‐version of the finite element method (FEM) is presented. Hierarchic Legendre polynomials in combination with an anisotropic ansatz space are utilized to derive an electro‐mechanically coupled element. This results in a reduced numerical effort. The suitability of the proposed element is demonstrated using various static and dynamic test examples.

Findings

In the current contribution it is shown that higher order coupled‐field finite elements hold several advantages for smart structure applications. All numerical examples have been found to agree well with previously published results. Furthermore, it is demonstrated that accurate results can be obtained with far fewer degrees of freedom compared to conventional low order finite element approaches. Thus, the proposed finite element can lead to a significant reduction in the overall numerical costs.

Originality/value

To the best of the author's knowledge, no piezoelectric finite element based on the hierarchical‐finiteelementmethod has yet been published in the literature. Thus, the proposed finite element is a step towards a holistic numerical treatment of structural health monitoring (SHM) related problems using p‐version finite elements.

Details

Engineering Computations, vol. 30 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 3 May 2013

Pavel Karban, František Mach and Ivo Doležel

The paper presents the principal elements of automatic adaptivity built in our 2D software for monolithic solution of multiphysics problems based on a fully adaptive finite

Abstract

Purpose

The paper presents the principal elements of automatic adaptivity built in our 2D software for monolithic solution of multiphysics problems based on a fully adaptive finite element method of higher order of accuracy. The adaptive techniques are illustrated by appropriate examples.

Design/methodology/approach

Presented are algorithms for realization of the h‐adaptivity, p‐adaptivity, hp‐adaptivity, creation of curvilinear elements for modelling general boundaries and interfaces. Indicated also is the possibility of combining triangular and quadrilateral elements (both classical and curved).

Findings

The presented higher‐order adaptive processes are reliable, robust and lead to a substantial reduction of the degrees of freedom in comparison with the techniques used in low‐order finite element methods. They allow solving examples that are by classical approaches either unsolvable or solvable at a cost of high memory and time of computation.

Research limitations/implications

The adaptive processes described in the paper are still limited to 2D computations. Their computer implementation is highly nontrivial (every physical field in a multiphysics task is generally solved on a different mesh satisfying its specific features) and in 3D the number of possible adaptive steps is many times higher.

Practical implications

The described adaptive techniques may represent a powerful tool for the monolithic solution of complex multiphysics problems.

Originality/value

The presented higher‐order adaptive approach of solution is shown to provide better results than the schemes implemented in professional codes based on low‐order finite element methods. Obtaining the results, moreover, requires less time and computer memory.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 32 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 13 September 2011

Pavel Karban, František Mach, Ivo Dolezel and Jerzy Barglik

The purpose of this paper is to present a methodology of high‐precision finite element modeling of induction heating of rotating nonferromagnetic cylindrical billets in…

Abstract

Purpose

The purpose of this paper is to present a methodology of high‐precision finite element modeling of induction heating of rotating nonferromagnetic cylindrical billets in static magnetic field produced by appropriately arranged permanent magnets.

Design/methodology/approach

The mathematical model consisting of two partial differential equations describing the distribution of the magnetic and temperature fields are solved by a fully adaptive higher‐order finite element method in the monolithic formulation and selected results are validated experimentally.

Findings

The method of solution realized by own code is very fast, robust and exhibits much more powerful features when compared with classical low‐order numerical methods implemented in existing commercial codes.

Research limitations/implications

For sufficiently long arrangements the method provides good results even for 2D model. The principal limitation consists in problems with determining correct boundary conditions for the temperature field (generalized coefficient of convective heat transfer as a function of the temperature and revolutions).

Practical implications

The methodology can successfully be used for design of devices for induction heating of cylindrical nonmagnetic bodies by rotation and determination of their operation parameters.

Originality/value

The paper is a presentation of the fully adaptive higher‐order finite element and its utilization for a monolithic numerical solution of a relatively complicated coupled problem.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 9 September 2013

Andreas Hauck, Michael Ertl, Joachim Schöberl and Manfred Kaltenbacher

The purpose of this paper is to propose a solution strategy for both accurate and efficient simulation of nonlinear magnetostatic problems in thin structures using higher

Abstract

Purpose

The purpose of this paper is to propose a solution strategy for both accurate and efficient simulation of nonlinear magnetostatic problems in thin structures using higher order finite element methods. Special interest is put in the investigation of the step-lap joints of transformer cores, with a focus on the spatial resolution of the field quantities.

Design/methodology/approach

The usage of hierarchical finite elements of higher order makes it possible to adapt the local accuracy in different spatial directions in thin steel sheets. Due to explicit representation of gradients in the basis functions, a simple Schwarz-type block preconditioner with a conjugate gradient solver can efficiently solve the arising algebraic system. By adapting the block size automatically according to the aspect ratio, deterioration of convergence in case of thin elements can be prevented. The resulting Newton scheme is accelerated utilizing the hierarchical splitting in a two-level scheme, where an initial guess is computed on a coarse sub-space.

Findings

Compared to an isotropic choice of polynomial order for the basis functions, significant runtime and memory can be saved in the simulation of thin structures without losing accuracy. The iterative solution scheme proves to be robust with respect to the polynomial order, even for aspect ratios of 1:1000 and anisotropies in two directions. An additional saving in runtime and Newton iterations can be achieved by solving the nonlinear problem initially on the lowest order basis functions only and projecting the solution to the complete space as starting value, analogous to a full multigrid scheme.

Originality/value

Within the presented solution strategy, especially the anisotropic block preconditioner and the accelerated Newton scheme based on the two-level splitting constitute a novel contribution. They provide building blocks, which can be utilized for other types of magnetic field problems like transient nonlinear problems or hysteresis modeling as well.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 32 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 7 September 2012

Pavel Karban, František Mach and Ivo Dolezel

The purpose of this paper is to present a model of induction heating of aluminium billets rotating in a static magnetic field generated by permanent magnets. The model is…

Abstract

Purpose

The purpose of this paper is to present a model of induction heating of aluminium billets rotating in a static magnetic field generated by permanent magnets. The model is solved by the authors' own software and the results are verified experimentally.

Design/methodology/approach

The mathematical model of the problem given by two partial differential equations describing the distribution of the magnetic and temperature fields in the system is solved by a fully adaptive higher‐order finite element method in the hard‐coupled formulation. All material nonlinearities are taken into account.

Findings

The method of solution realized by the code is reliable and works faster in comparison with the existing low‐order finite element codes.

Research limitations/implications

The method works for 2D arrangements with an extremely high accuracy. Its limitations consist mainly in problems of determining the coefficients of convection and radiation for temperature field in the system (respecting both temperature and revolutions).

Practical implications

The methodology can successfully be used for design of devices for induction heating of cylindrical nonmagnetic bodies by rotation and anticipation of their operation parameters.

Originality/value

The paper presents a fully adaptive higher‐order finite element and its utilization for a hard‐coupled numerical solution of the problem of induction heating.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 31 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 20 September 2018

Don Liu, Hui-Li Han and Yong-Lai Zheng

This paper aims to present a high-order algorithm implemented with the modal spectral element method and simulations of three-dimensional thermal convective flows by using…

Abstract

Purpose

This paper aims to present a high-order algorithm implemented with the modal spectral element method and simulations of three-dimensional thermal convective flows by using the full viscous dissipation function in the energy equation. Three benchmark problems were solved to validate the algorithm with exact or theoretical solutions. The heated rotating sphere at different temperatures inside a cold planar Poiseuille flow was simulated parametrically at varied angular velocities with positive and negative rotations.

Design/methodology/approach

The fourth-order stiffly stable schemes were implemented and tested for time integration. To provide the hp-refinement and spatial resolution enhancement, a modal spectral element method using hierarchical basis functions was used to solve governing equations in a three-dimensional space.

Findings

It was found that the direction of rotation of the heated sphere has totally different effects on drag, lateral force and torque evaluated on surfaces of the sphere and walls. It was further concluded that the angular velocity of the heated sphere has more influence on the wall normal velocity gradient than on the wall normal temperature gradients and therefore, more influence on the viscous dissipation than on the thermal dissipation.

Research limitations/implications

This paper concerns incompressible fluid flow at constant properties with up to medium temperature variations in the absence of thermal radiation and ignoring the pressure work.

Practical implications

This paper contributes a viable high-order algorithm in time and space for modeling convective heat transfer involving an internal heated rotating sphere with the effect of viscous heating.

Social implications

Results of this paper could provide reference for related topics such as enhanced heat transfer forced convection involving rotating spheres and viscous thermal effect.

Originality/value

The merits include resolving viscous dissipation and thermal diffusion in stationary and rotating boundary layers with both h- and p-type refinements, visualizing the viscous heating effect with the full viscous dissipation function in the energy equation and modeling the forced advection around a rotating sphere with varied positive and negative angular velocities subject to a shear flow.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 3 August 2015

André Jacomel Torii, Roberto Dalledone Machado and Marcos Arndt

– The purpose of this paper is to present an application of the Generalized Finite Element Method (GFEM) for modal analysis of 2D wave equation.

Abstract

Purpose

The purpose of this paper is to present an application of the Generalized Finite Element Method (GFEM) for modal analysis of 2D wave equation.

Design/methodology/approach

The GFEM can be viewed as an extension of the standard Finite Element Method (FEM) that allows non-polynomial enrichment of the approximation space. In this paper the authors enrich the approximation space with sine e cosine functions, since these functions frequently appear in the analytical solution of the problem under study. The results are compared with the ones obtained with the polynomial FEM using higher order elements.

Findings

The results indicate that the proposed approach is able to obtain more accurate results for higher vibration modes than standard polynomial FEM.

Originality/value

The examples studied in this paper indicate a strong potential of the GFEM for the approximation of higher vibration modes of structures, analysis of structures subject to high frequency excitations and other problems that concern high frequency oscillatory phenomena.

Details

Engineering Computations, vol. 32 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 3 May 2013

Liang Li, Stéphane Lanteri and Ronan Perrussel

This work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two‐dimensional…

Abstract

Purpose

This work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two‐dimensional time‐harmonic electromagnetic wave propagation problems.

Design/methodology/approach

The proposed HDG method for the discretization of the two‐dimensional transverse magnetic Maxwell equations relies on an arbitrary high order nodal interpolation of the electromagnetic field components and is formulated on triangular meshes. In the HDG method, an additional hybrid variable is introduced on the faces of the elements, with which the element‐wise (local) solutions can be defined. A so‐called conservativity condition is imposed on the numerical flux, which can be defined in terms of the hybrid variable, at the interface between neighbouring elements. The linear system of equations for the unknowns associated with the hybrid variable is solved here using a multifrontal sparse LU method. The formulation is given, and the relationship between the considered HDG method and a standard upwind flux‐based DG method is also examined.

Findings

The approximate solutions for both electric and magnetic fields converge with the optimal order of p+1 in L2 norm, when the interpolation order on every element and every interface is p and the sought solution is sufficiently regular. The presented numerical results show the effectiveness of the proposed HDG method, especially when compared with a classical upwind flux‐based DG method.

Originality/value

The work described here is a demonstration of the viability of a HDG formulation for solving the time‐harmonic Maxwell equations through a detailed numerical assessment of accuracy properties and computational performances.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 32 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 April 2006

O.M. Haddad and M.Q. Al‐Odat

This study seeks to focus on the annular flow between rectangular and equilateral‐triangular ducts under all possible arrangements. The aim of this work is to obtain…

Abstract

Purpose

This study seeks to focus on the annular flow between rectangular and equilateral‐triangular ducts under all possible arrangements. The aim of this work is to obtain accurate prediction of the friction factor of this flow using high‐order finite element method.

Design/methodology/approach

Steady and fully developed laminar flow of incompressible Newtonian fluid in an annulus of variable cross‐sectional geometry is investigated numerically. Accurate prediction of the friction factor of this flow was obtained using high‐order finite element method.

Findings

The results were in agreement with already published findings in the literature. It was found that a higher annular area ratio will lead to a monotonic increase in fRe value in the case of regular annuli, and will lead to an increase followed by a decrease in fRe value in the case of irregular annuli. Also, it was, found that irregular annuli have lower fRe value than regular annuli, and that the square‐in‐triangle case has the lowest fRe value, whereas the square‐in‐square case has the highest fRe value.

Originality/value

Accurate prediction of the friction factor of the laminar flow in irregular annuli was obtained. Also, the obtained results can be utilized to optimize the annular geometries under consideration. In addition, the obtained results can lead to the design of more efficient heat exchangers.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 16 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 11 July 2008

Pavel Kus, Pavel Solin and Ivo Dolezel

This paper seeks to describe the solution of a simple electrostatic problem using an adaptive hp‐FEM and to show the benefits of this approach. Numerical experiments are…

Abstract

Purpose

This paper seeks to describe the solution of a simple electrostatic problem using an adaptive hp‐FEM and to show the benefits of this approach. Numerical experiments are presented to demonstrate its superiority.

Design/methodology/approach

Adaptive hp‐FEM is used. In contrast with standard FEM, the automatic adaptivity procedure can choose from a variety of refinement candidates. An element with over estimated error can be refined in space, or its polynomial degree can be increased. Arbitrary level hanging nodes are allowed, so that no unnecessary refinements are performed in order to keep a mesh regular.

Findings

Numerical solution of a singular electrostatic problem is presented. From the comparison it can be seen that the hp‐FEM outperforms both the standard linear and quadratic elements significantly. The accuracy of an hp‐FEM solution would be hard to attain by standard means due to the limited capacity of the computer memory.

Originality/value

The paper describes results obtained from an original and innovative implementation of the adaptive hp‐FEM.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 27 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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