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Boundary Element Calculation of Near-Boundary Solutions in 3D Generally Anisotropic Solids by the Self-Regularization Scheme

  • Y. C. Shiah (a1) and L. D. Chang (a1)

Abstract

This research targets investigation of the internal elastic field near the boundaries of 3D anisotropic bodies by the boundary element method (BEM). This analysis appears to be most important, especially for the interest in the internal solutions near corners or crack tips, where structural failure is most likely to occur. Although the BEM is very efficient for analyzing the problem, nearly singular integration will arise when the internal point of interest stays near the boundary. The present work is to show how the self-regularized boundary integral equation (BIE) can be applied to the interior analysis for 3D generally anisotropic bodies. So far, to the authors' best knowledge, no implementation work has been reported in the literature for successfully treating the near boundary solutions in 3D generally anisotropic solids. In the end, a few benchmark examples are presented to demonstrate the veracity of the present approach for the interior BEM analysis of 3D anisotropic elasticity.

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*Corresponding author (ycshiah@mail.ncku.edu.tw)

References

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1. 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. 1733 (1999).
2. 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. 173233 (2001).
3. Tanaka, M., Sladek, V. and Sladek, J., “Regularization Techniques Applied to Boundary Element Methods,” Applied Mechanics Reviews, 47, pp. 457499 (1994).
4. Zozulya, V. V., “Divergent Integrals in Elastostatics: Regularization in 3-D Case,” CMES- Computer Modeling in Engineering & Sciences, 70, pp. 253349 (2010).
5. Shiah, Y. C., Tan, C. L. and Li-Ding, Chan, “Boundary Element Analysis of Thin Anisotropic Structures by the Self-Regularization Scheme,” CMES – Computer Modeling in Engineering & Sciences, 109, pp. 1533 (2015).
6. Granados, J. J. and Gallego, R., “Regularization of Nearly Hypersingular Integrals in the Boundary Element Method,” Engineering Analysis with Boundary Elements, 25, pp. 165184 (2001).
7. Tomioka, S. and Nishiyama, S., “Analytical Regularization of Hypersingular Integral for Helmholtz Equation in Boundary Element Method,” Engineering Analysis with Boundary Elements, 34, pp. 393404 (2010).
8. Lacerda, L. A. de and Wrobel, L. C., “Hypersingular Boundary Integral Equation for Axisymmetric Elasticity,” International Journal for Numerical Methods in Engineering, 52, pp. 13371354 (2001).
9. Shiah, Y. C. and Shi, Yi-Xiao, “Heat Conduction Across Thermal Barrier Coatings of Anisotropic Substrates,” International Communications in Heat and Mass Transfer, 33, pp. 827835 (2006).
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. 385401 (2013).
11. Shiah, Y. C, “3D Elastostatic Boundary Element Analysis of Thin Bodies by Integral Regularizations,” Journal of Mechanics, 31, pp. 533543 (2015).
12. Cruse, T. A. and Richardson, J. D., “Non-Singular Somigliana Stress Identities in Elasticity,” International Journal for Numerical Methods in Engineering, 39, pp. 32733304 (1996).
13. Richardson, J. D. and Cruse, T. A., “Weakly Singular Stress-BEM for 2-D Elastostatics,” International Journal for Numerical Methods in Engineering, 45, pp. 1335 (1999).
14. He, M. G. and Tan, C. L., “A Self-Regularization Technique in Boundary Rlement Method for 3-D Stress Analysis,” CMES - Computer Modeling in Engineering and Sciences, 95, pp. 317349 (2013).
15. Ting, T. C. T. and Lee, V. G., “The Three-Dimensional Elastostatic Green's Function for General Anisotropic Linear Elastic Solid,” The Quarterly Journal of Mechanics and Applied Mathematics, 50, pp. 407426 (1997).
16. Shiah, Y. C., Tan, C. L. and Wang, C. Y., “Efficient Computation of the Green's Function and Its Derivatives for Three-Dimensional Anisotropic Elasticity in BEM Analysis,” Engineering Analysis with Boundary Elements, 36, pp. 17461755 (2012).
17. Shiah, Y. C., Tan, C. L. and Lee, V. G., “Evaluation of Explicit-Form Fundamental Solutions for Displacements and Stresses in 3D Anisotropic Elastic Solids,” CMES - Computer Modeling in Engineering & Sciences, 34, pp. 205226 (2008).
18. Huntington, H. B., The Elastic Constants of Crystal, Academic Press, New York (1958).

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