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Article
Publication date: 1 June 1998

Ole da Silva Smith

Introducing the concept of a design domain to truss topology optimization, this paper presents an algorithm generating geometrically admissible ground structures on…

Abstract

Introducing the concept of a design domain to truss topology optimization, this paper presents an algorithm generating geometrically admissible ground structures on possibly concave (or even disconnected) 3D design domains. That is a set of connections between nodal points actually respecting the geometry of the design domain. Since ground structures may be applied in other contexts the presentation does not assume any specifics of truss topology optimization. However, in the example section an application of ground structures in a truss topology optimization problem may be found.

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Engineering Computations, vol. 15 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 1 February 1992

D. BEATOVIC, P.L. LEVIN, H. GAN, J.M. KOKERNAK and A.J. HANSEN

A hybrid formulation is proposed that incorporates finite element substructuring and Galerkin boundary elements in the numerical solution of Poisson's or Laplace's…

Abstract

A hybrid formulation is proposed that incorporates finite element substructuring and Galerkin boundary elements in the numerical solution of Poisson's or Laplace's equation with open boundaries. Substructuring the problem can dramatically decreases the size of matrix to be solved. It is shown that the boundary integration that results from application of Green's first theorem to the weighted residual statement can be used to advantage by imposing potential and flux continuity through the contour which separates the interior and exterior regions. In fact, the boundary integration is of exactly the same form as that found in Galerkin boundary elements.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 11 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 April 1982

Yukio KAGAWA, Tadakuni MURAI and Shinji KITAGAMI

A technique combining finite elements and boundary elements is promising for unbounded field problems. A hypothetical boundary is assumed in the unbounded domain, and the…

Abstract

A technique combining finite elements and boundary elements is promising for unbounded field problems. A hypothetical boundary is assumed in the unbounded domain, and the usual finite element method is applied to the inner region, while the boundary element method is applied to the outer infinite region. On the coupling boundary, therefore, both potential and flux must be compatible. In the finite element method, the flux is defined as the derivative of the potential for which a trial function is defined. In the boundary element method, on the other hand, the same polynomial function is chosen for the potential and the flux. Thus, the compatibility cannot be satisfied unless a special device is considered. In the present paper, several compatibility conditions are discussed concerning the total flux or energy flow continuity across the coupling boundary. Some numerical examples of Poisson and Helmholtz problems are demonstrated.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 1 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 7 August 2017

Qiao Wang, Wei Zhou, Yonggang Cheng, Gang Ma and Xiaolin Chang

Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous…

Abstract

Purpose

Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial differential equations. The purpose of this paper is to develop an accurate and reliable technique to effectively evaluate the volume potentials in 3D elasticity problems.

Design/methodology/approach

An adaptive background cell-based domain integration method is proposed for treatment of volume potentials in 3D elasticity problems. The background cells are constructed from the information of the boundary elements based on an oct-tree structure, and the domain integrals are evaluated over the cells rather than volume elements. The cells that contain the boundary elements can be subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements. The fast multipole method (FMM) is further applied in the proposed method to reduce the time complexity of large-scale computation.

Findings

The method is a boundary-only discretization method, and it can be applied in the BEM easily. Much computational time is saved by coupling with the FMM. Numerical examples demonstrate the accuracy and efficiency of the proposed method..

Originality/value

Boundary elements are used to create adaptive background cells, and domain integrals are evaluated over the cells rather than volume elements. Large-scale computation is made possible by coupling with the FMM.

Details

Engineering Computations, vol. 34 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 June 2000

A. Savini

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic…

Abstract

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 19 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 May 1999

Y.K. Lee and D.Y. Yang

An easy and robust grid‐based approach is proposed to construct the fully hexahedral mesh in three‐dimensional case and its application for the mesh regeneration or…

Abstract

An easy and robust grid‐based approach is proposed to construct the fully hexahedral mesh in three‐dimensional case and its application for the mesh regeneration or remeshing during the finite element simulation of a metal forming process is presented to show the validity and effectiveness of the scheme. The proposed scheme enables the construction of the provisional mesh by superimposing the regular cubical grid over the object to be meshed and removing the exterior grid points and cells. Because the constructed provisional mesh has the discrete rugged boundary that is quite different from the boundary geometry of the object to be meshed, the nodes on the boundary of the provisional mesh are projected onto the object boundary. The main disadvantage of the mesh constructed by grid‐based approaches is its severely distorted elements on the boundary owing to the projection of the rugged boundary onto the object boundary. In order to improve the quality of boundary elements, some layers of elements on the boundary surface are constructed and the nodes are repositioned by mesh smoothing. Consequently, the quality of boundary elements is effectively improved.

Details

Engineering Computations, vol. 16 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 14 November 2019

Jianming Zhang, Lei Han, Yudong Zhong, Yunqiao Dong and Weicheng Lin

This paper aims to propose a boundary element analysis of two-dimensional linear elasticity problems by a new expanding element interpolation method.

Abstract

Purpose

This paper aims to propose a boundary element analysis of two-dimensional linear elasticity problems by a new expanding element interpolation method.

Design/methodology/approach

The expanding element is made up based on a traditional discontinuous element by adding virtual nodes along the perimeter of the element. The internal nodes of the original discontinuous element are referred to as source nodes and its shape function as raw shape function. The shape functions of the expanding element constructed on both source nodes and virtual nodes are referred as fine shape functions. Boundary variables are interpolated by the fine shape functions, while the boundary integral equations are collocated on source nodes.

Findings

The expanding element inherits the advantages of both the continuous and discontinuous elements while overcomes their disadvantages. The polynomial order of fine shape functions of the expanding elements increases by two compared with their corresponding raw shape functions, while the expanding elements still keep independence to each other as the original discontinuous elements. This feature makes the expanding elements able to naturally and accurately interpolate both continuous and discontinuous fields.

Originality/value

Numerical examples are presented to verify the proposed method. Results have demonstrated that the accuracy, efficiency and convergence rate of the expanding element method.

Details

Engineering Computations, vol. 37 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 16 April 2018

Jacek Ptaszny and Marcin Hatłas

The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D…

Abstract

Purpose

The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear elastic structures with cavities. In particular, a comparison between the FMBEM and the finite element method (FEM) is performed in terms of accuracy, model size and computation time.

Design/methodology/approach

The developed FMBEM uses eight-node Serendipity boundary elements with numerical integration based on the adaptive subdivision of elements. Multipole and local expansions and translations involve solid harmonics. The proposed model is used to analyse a solid body with two interacting spherical cavities, and to predict the homogenized response of a porous material under linear displacement boundary condition. The FEM results are generated in commercial codes Ansys and MSC Patran/Nastran, and the results are compared in terms of accuracy, model size and execution time. Analytical solutions available in the literature are also considered.

Findings

FMBEM and FEM approximate the geometry with similar accuracy and provide similar results. However, FMBEM requires a model size that is smaller by an order of magnitude in terms of the number of degrees of freedom. The problems under consideration can be solved by using FMBEM within the time comparable to the FEM with an iterative solver.

Research limitations/implications

The present results are limited to linear elasticity.

Originality/value

This work is a step towards a comprehensive efficiency evaluation of the FMBEM applied to selected problems of micromechanics, by comparison with the commercial FEM codes.

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Article
Publication date: 1 April 1983

Y. KAGAWA, T. YAMABUCHI and S. KITAGAMI

The boundary element method is a useful method for the analysis of field problems involving unbounded regions. Therefore, the method can be used advantageously in…

Abstract

The boundary element method is a useful method for the analysis of field problems involving unbounded regions. Therefore, the method can be used advantageously in combination with the finite element method. This is sometimes called a combination method and it is suitable as a picture‐frame technique. Although this technique attains good accuracy, the matrix of the discretized equation is not banded, since it is a dense matrix. In this paper, we propose an infinite boundary element which divides the unbounded region radially. By the use of this element, the bandwidth of the discretized system matrix does not increase beyond that of the finite element region and its original matrix structure is maintained. The infinite boundary element can also be applied to homogeneous unbounded field problems, for which the Green's function of the mirror image is difficult to use. To illustrate the validity of the proposed technique, some numerical calculations are demonstrated and the results are compared with those of the usual combination method and the method using the hybrid‐type infinite element.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 2 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 January 1988

Thomas J. Rudolphi

The boundary element and finite element methods have been combined so as to allow for arbitrary intermixing of element types in modelling problems of axisymmetric…

Abstract

The boundary element and finite element methods have been combined so as to allow for arbitrary intermixing of element types in modelling problems of axisymmetric thermoelasticity, including body forces due to rotational inertia. The formulation for combining the methods is given, and a general purpose, finite element program has been generalized to accommodate both types of elements and to determine stresses within and on the boundary of boundary‐type elements after the primary solution for the displacements. Example problems demonstrate the validity and accuracy of the technique.

Details

Engineering Computations, vol. 5 no. 1
Type: Research Article
ISSN: 0264-4401

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