A double-layer interpolation method for implementation of BEM analysis of problems in potential theory

Zhang, Jianming; Lin, Weicheng; Dong, Yunqiao; Ju, Chuanming

doi:10.1016/j.apm.2017.06.044

Cited by 47 publications

(14 citation statements)

References 21 publications

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“…However, compared to the direct algorithm, the more complex the model, the more time our algorithm saves. In addition, the qualities of meshes conforming to curves discretization results are given to illustrate that meshes are suitable for subsequent numerical analysis, such as FEM (Nayroles et al , 1992) and BEM (Qin et al , 2010; Brebbia et al , 1984; Zhang et al , 2017).…”

Section: Results and Comparisonsmentioning

confidence: 99%

“…The quad-tree and triangular grid are commonly used as background grid in two-dimensional (Owen and Saigal, 2015), and the octree and tetrahedral grid are popularly applied in three-dimensional (Borouchaki et al , 2015; Zhang et al , 2017). In this paper, we use octree as three-dimensional background grid.…”

Section: Basic Concepts Of Geometry and Nodal Spacing Functionmentioning

confidence: 99%

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A fast algorithm for the adaptive discretization of 3D parametric curves

Zhang

Chi

2019

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Purpose The purpose of this paper is to present a fast algorithm for the adaptive discretization of three-dimensional parametric curves. Design/methodology/approach The proposed algorithm computes the parametric increments of all segments to obtain the parametric coordinates of all discrete nodes. This process is recursively applied until the optimal discretization of curves is obtained. The parametric increment of a segment is inversely proportional to the number of sub-segments, which can be subdivided, and the sum of parametric increments of all segments is constant. Thus, a new expression for parametric increment of a segment can be obtained. In addition, the number of sub-segments, which a segment can be subdivided is calculated approximately, thus avoiding Gaussian integration. Findings The proposed method can use less CPU time to perform the optimal discretization of three-dimensional curves. The results of curves discretization can also meet requirements for mesh generation used in the preprocessing of numerical simulation. Originality/value Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the algorithm saves in the process of curve discretization.

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Section: Results and Comparisonsmentioning

confidence: 99%

Section: Basic Concepts Of Geometry and Nodal Spacing Functionmentioning

confidence: 99%

A fast algorithm for the adaptive discretization of 3D parametric curves

Zhang

Chi

2019

Self Cite

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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%

“…Firstly, we compute the distance r P 1 � P 1 P ′ , r P 2 � P 2 P ′ , and r P 3 � P 3 P ′ . en, we calculate the SIFs using equation (27) through the CODs of P 1 , P 2 , and P 3 . We denote the results as K p 1 , K p 2 , and K p 3 .…”

Section: Calculation Of Sifsmentioning

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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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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“…The boundary element method [1 -6] has been applied in many areas [7][8][9][10][11][12] because of its high accuracy and boundary-only discretization. Compared with the finite element method (FEM), BEM can obtain very high accuracy with much fewer elements on the boundary.…”

Section: Introductionmentioning

confidence: 99%

The boundary element method for elasticity problems with concentrated loads based on displacement singular elements

Zhou

Wang

et al. 2019

Engineering Analysis with Boundary Elements

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The boundary element method (BEM) has been implemented in elasticity problems very successfully because of its high accuracy. However, there are very few investigations about BEM with concentrated loads. The displacement at the concentrated load point is infinite and traditional elements will lead inaccurate results near the concentrated load point. This paper proposes two types of displacement singular elements to approximate the displacement near concentrated load point, and high accuracy can be obtained without refinement. The second type of displacement singular element is a general element type, which can work well for both problems with or without boundary concentrated loads. Numerical examples have been studied and compared with results obtained by traditional BEM and finite element method (FEM) to show the necessary of the proposed methods.

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A double-layer interpolation method for implementation of BEM analysis of problems in potential theory

Cited by 47 publications

References 21 publications

A fast algorithm for the adaptive discretization of 3D parametric curves

A fast algorithm for the adaptive discretization of 3D parametric curves

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

The boundary element method for elasticity problems with concentrated loads based on displacement singular elements

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