Some benchmark problems and basic ideas on the accuracy of boundary element analysis

Yao, Zhenhan; Wang, Haitao

doi:10.1016/j.enganabound.2013.10.001

Cited by 27 publications

(6 citation statements)

References 18 publications

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“…To achieve high computational accuracy, the integrals with singularity in the DBEM must be accurately computed [9,12,15,[19][20][21][22][23][24][25][26][27]. In this section, the singular integral is gradually computed through three steps.…”

Section: Regularization Of Singular Integralsmentioning

confidence: 99%

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A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

Xie

Zhou

2020

Mathematical Problems in Engineering

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This paper focuses on tackling the two drawbacks of the dual boundary element method (DBEM) when solving crack problems with a discontinuous triangular element: low accuracy of the calculation of integrals with singularity and crack front element must be utilized to model the square-root property of displacement. In order to calculate the integrals with higher order singularity, the triangular elements are segmented into several subregions which consist of subtriangles and subpolygons. The singular integrals in those subtriangles are handled by the singularity subtraction technique in the integration space and can be regularized and accurately calculated. For the nearly singular integrals in those subpolygons, the element subdivision technique is employed to improve the calculation accuracy. In addition, considering the location of the crack front in the element, special crack front elements are constructed based on a 6-node discontinuous triangular element, in which the displacement extrapolation method is introduced to obtain the stress intensity factors (SIFs) without consideration of orthogonalization of the crack front mesh. Several numerical results are investigated to fully verify the validation of the presented approach.

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Section: Regularization Of Singular Integralsmentioning

confidence: 99%

“…To cope with the singular integrals, the element subdivision is necessary in the 3D BEM [9,[19][20][21][22][23][24][25]. Moreover, a suitable integral area is of great importance to improving the accuracy of singular integral calculation, especially for Cauchy or Hadamard finite part integrals.…”

Section: Triangular Element Subdivision Techniquementioning

confidence: 99%

A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

Xie

Zhou

2020

Mathematical Problems in Engineering

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“…Pham et al (2012) applied the Gallerkin fast multipole BEM with quadratic elements in the analysis of structures containing pores and cracks. Yao and Wang (2013) presented some studies on the accuracy of quadratic boundary elements. Novel techniques were developed for the efficient calculation of nearly singular integrals, by Zhang et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the FMBEM efficiency in the analysis of porous structures

Ptaszny

Hatłas²

2018

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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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“…[16,19,35]. However, constant and linear elements are not efficient in the analysis of bending problems due to slow convergence to the exact solution [18,34]. Many structures and constituents of microstructures may be subjected to bending, e.g.…”

Section: Introductionmentioning

confidence: 99%

Accuracy of the fast multipole boundary element method with quadratic elements in the analysis of 3D porous structures

Ptaszny

2015

Comput Mech

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In this work, a fast multipole boundary element method for 3D elasticity problem was developed by the application of the fast multipole algorithm and isoparametric 8-node boundary elements with quadratic shape functions. The problem is described by the boundary integral equation involving the Kelvin solutions. In order to keep the numerical integration error on appropriate level, an adaptive method with subdivision of boundary elements into subelements, described in the literature, was applied. An extension of the neighbour list of boundary element clusters, corresponding to near-field computations, was proposed in order to reduce the truncation error of expansions in problems with high stress concentration. Efficiency of the method is illustrated by numerical examples including a solid with single spherical cavity, solids with two interacting spherical cavities, and numerical homogenization of solids with cubic arrangement of spherical cavities. All results agree with analytical models available in the literature. The examples show that the method can be applied to the analysis of porous structures.

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Some benchmark problems and basic ideas on the accuracy of boundary element analysis

Cited by 27 publications

References 18 publications

A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

Evaluation of the FMBEM efficiency in the analysis of porous structures

Accuracy of the fast multipole boundary element method with quadratic elements in the analysis of 3D porous structures

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