Three-dimensional elastic analysis by the boundary element method with analytical integrations over triangular leaf elements

Kuriyama, Ken; Mizuta, Yoshiaki; Mozumi, Hiroshi; Watanabe, Tomohiko

doi:10.1016/0148-9062(94)00021-t

Cited by 20 publications

(17 citation statements)

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“…This is particularly attractive as the amount of data required to describe the problem is greatly reduced as compared with FEM. Due to the BEMs advantage in reducing model dimensions, three-dimensional application using the displacement discontinuity method for (Demuth et al 1996) stress analysis has become efficient (Kuriyama and Mizuta 1993;Kuriyama et al 1995;Cayol and Cornet 1997).…”

Section: Boundary Element Methodsmentioning

confidence: 99%

Superiority of neural networks for pillar stress prediction in bord and pillar method

2009

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Estimation of pillar stress is a crucial task in underground mining. This is used to determine pillar dimensions, room width, roof conditions, and general mine layout. There are several methods for estimating induced stresses due to underground excavations, i.e., empirical methods, numerical solutions, and currently artificial intelligence (AI). AI based techniques are gradually gaining popularity especially for problems involving uncertainty. In this paper, an attempt has been made to predict stresses developed in the pillars of bord and pillar mining using artificial neural network. A comparison has also been done to compare the obtained results with the boundary element method as well as measured field values. For this purpose, a multilayer perceptron neural network model was developed. A number of architectures with different hidden layers and neurons were tried to get the best solution, and the architecture 5-20-8-1 was found to be an optimum solution. Sensitivity analysis was also carried out to understand the influence of important input parameters on pillar stress concentration.

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Section: Boundary Element Methodsmentioning

confidence: 99%

Superiority of neural networks for pillar stress prediction in bord and pillar method

2009

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“…(12). By contrast, the total number of linear equations and variables both equal to the number of triangular in constant triangular element [9,10].…”

Section: Basic Equations In 3d-ddmmentioning

confidence: 92%

“…(11) was given by Kuriyama et al [9,10], which is not listed in this paper. When x 1 ¼y 1 ¼ y 2 ¼0, the analytical expression of g(x,y,z) and h(x,y,z) in Eq.…”

Section: Three-dimensional Displacement Discontinuity Elementmentioning

confidence: 96%

“…Hence, D i ξ; η ð Þ is not related to the coordinates (ξ, η, 0) in the element, i.e., constant displacement element, then the Eq. (4) can be expressed by [9,10,26].…”

Section: Three-dimensional Displacement Discontinuity Elementmentioning

confidence: 99%

“…Even though the strong singularities in boundary integral equation [7,29,1,21,22], the 3D DDM on the triangular element is improved from constant element to higher order element. Kuriyama et al [9,10] proposed the 3D DDM with the boundary surface division into constant triangular elements and briefly presented the solution procedure. Davey and Hinduja [8] established the integral solutions for triangular elements applied to potential problems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A novel linear triangular element of a three-dimensional displacement discontinuity method

Wan

Jin

et al. 2015

Engineering Analysis with Boundary Elements

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Efficient solution of 3-D geomechanical problems by indirect BEM using iterative methods

Kayupov

Bulgakov

Kühn

1998

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYThe research herein primarily addresses to geomechanical problems of underground constructions in Mining and Civil Engineering. The problems are solved using the Indirect Boundary Element Method (IBEM). Although the geometry of the constructions themselves is usually very complicated, it will become much more complicated if we were to draw the existing joints. The computational problem therefore is how to deal with huge amount of equations and find out efficient methods of their formation and solution keeping in mind restraints of the computer memory and calculation time. Several approaches are used to enhance the performance of the Indirect Boundary Element Method. One of them deals with application of efficient equation solvers. It is shown that Krylov-type methods like CGS and GMRES with simple Jacoby preconditioning appear to be efficient and robust. In addition, adaptive integration on the boundary elements, together with diagonal dominance of equations make it possible to accelerate convergence of the iterative procedure. Some of the problems discussed allow a substantial reduction of matrix entries that leads to a very cheap iterative solution keeping reasonable accuracy of the results.1998 John Wiley & Sons, Ltd.

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Three-dimensional elastic analysis by the boundary element method with analytical integrations over triangular leaf elements

Cited by 20 publications

References 1 publication

Superiority of neural networks for pillar stress prediction in bord and pillar method

Superiority of neural networks for pillar stress prediction in bord and pillar method

A novel linear triangular element of a three-dimensional displacement discontinuity method

Efficient solution of 3-D geomechanical problems by indirect BEM using iterative methods

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