Numerical evaluation of nearly hyper-singular integrals in the boundary element analysis

2016 ◽  
Vol 167 ◽  
pp. 15-23 ◽  
Author(s):  
Yan Gu ◽  
Qingsong Hua ◽  
Wen Chen ◽  
Chuanzeng Zhang
Keyword(s):  
Boundary Element ◽  
Numerical Evaluation ◽  
Singular Integrals ◽  
Element Analysis ◽  
Boundary Element Analysis

3D Elastostatic Boundary Element Analysis of thin bodies by Integral Regularizations

2015 ◽  
Vol 31 (5) ◽  
pp. 533-543 ◽  
Author(s):  
Y.-C. Shiah
Keyword(s):  
Boundary Element ◽  
Singular Integrals ◽  
Successful Implementation ◽  
Distance Ratio ◽  
Element Analysis ◽  
Quadrature Scheme ◽  
Ansys Analysis ◽  
Usual Manner ◽  
Nearly Singular Integrals ◽  
Boundary Element Analysis

AbstractThis paper presents a regularization scheme for the nearly singular integrals used for 3D elastostatic boundary element analysis. For the regularization process, the local projection coordinates of the source point are first located via an iteration procedure. For planar elements, the boundary integrals are analytically integrated by parts to smooth the drastic fluctuations of their integrands so that the regularized forms can be numerically integrated by any conventional schemes in an usual manner. The validity of the formulations is numerically tested using the Gauss Quadrature scheme. The test shows the accuracy is satisfactory for the distance ratio (distance: Element characteristic length) falling below micro-scale. To further demonstrate our successful implementation, a numerical example is studied with verifications compared with ANSYS analysis.

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