A semi-analytical algorithm for the evaluation of the nearly singular integrals in three-dimensional boundary element methods

2005 ◽  
Vol 194 (9-11) ◽  
pp. 1057-1074 ◽  
Author(s):  
Zhongrong Niu ◽  
W.L. Wendland ◽  
Xiuxi Wang ◽  
Huanlin Zhou
Keyword(s):  
Boundary Element ◽  
Singular Integrals ◽  
Three Dimensional ◽  
Boundary Element Methods ◽  
Analytical Algorithm ◽  
Dimensional Boundary ◽  
Nearly Singular Integrals

Modelling ground vibration from railways using wavenumber finite- and boundary-element methods

2005 ◽  
Vol 461 (2059) ◽  
pp. 2043-2070 ◽  
Author(s):  
X Sheng ◽  
C.J.C Jones ◽  
D.J Thompson
Keyword(s):  
Boundary Element ◽  
Singular Integrals ◽  
Moving Load ◽  
Three Dimensional ◽  
Ground Surface ◽  
Ground Vibration ◽  
Element Model ◽  
Boundary Element Methods ◽  
Element Discretization ◽  
Environmental Vibration

A mathematical model is presented for ground vibration induced by trains, which uses wavenumber finite- and boundary-element methods. The track, tunnel and ground are assumed homogeneous and infinitely long in the track direction ( x -direction). The models are formulated in terms of the wavenumber in the x -direction and discretization in the yz -plane. The effect of load motion in the x -direction is included. Compared with a conventional, three-dimensional finite- or boundary-element model, this is computationally faster and requires far less memory, even though calculations must be performed for a series of discrete wavenumbers. Thus it becomes practicable to carry out investigative study of train-induced ground vibration. The boundary-element implementation uses a variable transformation to solve the well-known problem of strongly singular integrals in the formulation. A ‘boundary truncation element’ greatly improves accuracy where the infinite surface of the ground is truncated in the boundary-element discretization. Predictions of vibration response on the ground surface due to a unit force applied at the track are performed for two railway tunnels. The results show a substantial difference in the environmental vibration that could be expected from the alternative designs. The effect of a moving load is demonstrated in a surface vibration example in which vibration propagates from an embankment into layered ground.

scholarly journals Interlaminar Stresses Analysis of Three-Dimensional Composite Laminates by the Boundary Element Method

2018 ◽  
Vol 34 (6) ◽  
pp. 829-837
Author(s):  
Y. C. Shiah ◽  
M. R. Hematiyan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Composite Laminates ◽  
Singular Integrals ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Interlaminar Stresses ◽  
Composite Layers ◽  
Nearly Singular Integrals ◽  
Element Method

AbstractIn engineering industries, composite laminates have been widely applied for various applications. This work presents an efficient analysis of the interlaminar stresses in three-dimensional thin layered anisotropic composites by the boundary element method (BEM). Due to the nearly singular integrals in the boundary integral equation, the conventional BEM approach cannot be applied to analyze the composite layers that are very thin. The present work employs the self-regularization scheme to analyze the interlaminar stresses in thin anisotropic composites. In the end, a few benchmark examples are presented to show the applicability of the present approach.

scholarly journals Closed Form Integration of Singular and Hypersingular Integrals in 3D BEM Formulations for Heat Conduction

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
A. Tadeu ◽  
J. Prata ◽  
N. Simões
Keyword(s):  
Closed Form ◽  
Boundary Element ◽  
Singular Integrals ◽  
Three Dimensional ◽  
Heat Diffusion ◽  
Integration Scheme ◽  
Hypersingular Integrals ◽  
Gaussian Integration ◽  
Integration Schemes ◽  
Dimensional Boundary

The evaluation of the singular and hypersingular integrals that appear in three-dimensional boundary element formulations for heat diffusion, in the frequency domain, is presented in analytical form. This improves computational efficiency and accuracy. Numerical integrations using existing techniques based on standard Gaussian integration schemes that incorporate an enormous amount of sampling points are used to verify the solutions of singular integrals. For the hypersingular integrals the comparison is evaluated by making use of an analytical solution that is valid for circular domains, combined with a standard Gaussian integration scheme for the remaining boundary element domain. Closed form solutions for cylindrical inclusions (with null temperatures and null heat fluxes prescribed on the boundary) are then derived and used to validate the three-dimensional boundary element formulations.

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