Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T13:59:58.737Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 April 2015

Y.-C. Shiah
Y.-C. Shiah*
Affiliation:
Department of Aeronautics and Astronautics National Cheng Kung University Tainan, Taiwan
*
* Corresponding author (ycshiah@mail.ncku.edu.tw)
Get access

Abstract

This 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.

Keywords

Boundary element methodIntegral regularizationIntegration by parts3D elastostatic analysis
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 5 , October 2015 , pp. 533 - 543
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Zozulya, V. V., “Divergent Integrals in Elastostatics: Regularization in 3-D Case,” Computer Modeling in Engineering & Sciences, 70, pp. 253–349 (2010).Google Scholar
2.Chen, J. T. and Hong, H.-K., “Review of Dual Boundary Element Methods with Emphasis on Hypersingular Integrals and Divergent Series,” Applied Mechanics Reviews, 52, pp. 17–33 (1999).Google Scholar
3.Guz, A. N. and Zozulya, V. V., “Fracture Dynamics with Allowance for a Crack Edges Contact Interaction,” International Journal of Nonlinear Sciences and Numerical Simulation, 2, pp. 173–233 (2001).CrossRefGoogle Scholar
4.Tanaka, M., Sladek, V. and Sladek, J., “Regularization Techniques Applied to Boundary Element Methods,” Applied Mechanics Reviews, 47, pp. 457–499 (1994).CrossRefGoogle Scholar
5.Granados, J. J. and Gallego, R., “Regularization of Nearly Hypersingular Integrals in the Boundary Element Method,” Engineering Analysis with Boundary Elements, 25, pp. 165–184 (2001).CrossRefGoogle Scholar
6.Tomioka, , Satoshi, and Nishiyama, Shusuke, “Analytical Regularization of Hypersingular Integral for Helmholtz Equation in Boundary Element Method,” Engineering Analysis with Boundary Elements, 34, pp. 393–404 (2010).Google Scholar
7.de Lacerda, L. A. and Wrobel, L. C., “Hypersingular Boundary Integral Equation for Axisymmetric Elasticity,” International Journal for Numerical Methods in Engineering, 52, pp. 1337–1354 (2001).CrossRefGoogle Scholar
8.Shiah, Y. C. and Shi, Y.-X., “Heat Conduction across Thermal Barrier Coatings of Anisotropic Substrates,” International Communications in Heat and Mass Transfer, 33, pp. 827–835 (2006).CrossRefGoogle Scholar
9.Shiah, Y. C., Chen, Y. H. and Kuo, W. S., “Analysis for the Interlaminar Stresses of Thin Layered Composites Subjected to Thermal Loads,” Composites Science and Technology, 67, pp. 2485–2492 (2007).CrossRefGoogle Scholar
10.Shiah, Y. C., Hematiyan, M. R. and Chen, Y. H., “Regularization of the Boundary Integrals in the BEM Analysis of 3D Potential Problems,” Journal of Mechanics, 29, pp. 385–401 (2013).CrossRefGoogle Scholar
11. Wikipedia online, https://en.wikipedia.org/wiki/Quartic_functionGoogle Scholar