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

Published online by Cambridge University Press:  10 May 2018

Y. C. Shiah  and
M. R. Hematiyan
Y. C. Shiah*
Affiliation:
Department of Aeronautics and AstronauticsNational Cheng Kung UniversityTainan, Taiwan
M. R. Hematiyan
Affiliation:
Department of Mechanical EngineeringShiraz UniversityShiraz, Iran
*
*Corresponding author (ycshiah@mail.ncku.edu.tw)
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Abstract

In 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.

Keywords

Composite laminatesInterlaminar stressesBoundary element method

Information

Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 6 , December 2018 , pp. 829 - 837
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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References

1. González-Cantero, J. M., Graciani, E., Blázquez, A. and París, F., “A New Analytical Model for Evaluating Interlaminar Stresses in the Unfolding Failure of Composite Laminates,” Composite Structures, 147, pp. 260–273 (2016).Google Scholar
2. Tahani, M. and Andakhshideh, A., “Interlaminar Stresses in Thick Rectangular Laminated Plates with Arbitrary Laminations and Boundary Conditions under Transverse Loads,” Composite Structures, 94, pp. 1793–1804 (2012).Google Scholar
3. Tahani, M., Andakhshideh, A. and Maleki, S., “Interlaminar Stresses in Thick Cylindrical Shell with Arbitrary Laminations and Boundary Conditions under Transverse Loads,” Composites Part B-Engineering, 98, pp. 151–165 (2016).Google Scholar
4. Fi, Y., Li, S. and Mao, Y., “The Analysis of Interlaminar Stresses for Composite Laminated Shallow Shells with Interfacial Damage,” Acta Mechanica Solida Sinica, 24, pp. 539–555 (2011).Google Scholar
5. Libersky, L. and Petschek, A., “Smooth Particle Hydrodynamics with Strength of Materials,” Proceedings of the Next Free-Lagrange Conference, Jackson Lake Lodge, Moran, Wyoming (1990).Google Scholar
6. Barbieri, E. and Meo, M., “A Meshfree Penalty-Based Approach to Delamination in Composites,” Composites Science and Technology, 69, pp. 2169–2177 (2009).Google Scholar
7. Ma, H. and Kamiya, N., “A General Algorithm for Accurate Computation of Field Variables and Its Derivatives Near the Boundary in BEM,” Engineering Analysis with Boundary Element Method, 25, pp. 833–841 (2001).Google Scholar
8. Niu, Z., Wendland, W. L., Wang, X. and Zhou, H., “A Semi-Analytical Algorithm for the Evaluation of the Nearly Singular Integrals in Three-Dimensional Boundary Element Methods,” Computer Methods in Applied Mechanics and Engineering, 194, pp. 1057–1074 (2005).Google Scholar
9. Zhou, H. L., Niu, Z. R., Cheng, C. Z. and Guan, Z. W., “Analytical Integral Algorithm Applied to Boundary Layer Effect and Thin Body Effect in BEM for Anisotropic Potential Problems,” Composite Structures, 86, pp. 1656–1671 (2008).Google Scholar
10. Shiah, Y. C., “3D Elastostatic Boundary Element Analysis of Thin Bodies by Integral Regularizations,” Journal of Mechanics, 31, pp. 533–543 (2014).Google Scholar
11. Ye, T. Q. and Liu, Y. J., “Finite Deflection Analysis of Elastic Plate by the Boundary Element Method,” Applied Mathematical Modelling, 9, pp. 183–188 (1985).Google Scholar
12. Liu, Y. J., “Elastic Stability Analysis of Thin Plate by the Boundary Element Method – A New Formulation,” Engineering Analysis with Boundary Element Method, 4, pp. 160–164 (1987).Google Scholar
13. Krishnasamy, G., Rizzo, F. J. and Li, Y. J., “Boundary Integral Equations for Thin Bodies,” International Journal for Numerical Methods in Engineering, 37, pp. 107–121 (1994).Google Scholar
14. Liu, Y. J., “Analysis of Shell-Like Structures by the Boundary Element Method Based on 3-D Elasticity: Formulation and Verification,” International Journal for Numerical Methods in Engineering, 41, pp. 541–558 (1998).Google Scholar
15. Cruse, T. A. and Aithal, R., “Non-Singular Boundary Integral Equation Implementation,” International Journal for Numerical Methods in Engineering, 36, pp. 237–254 (1993).Google Scholar
16. Rudolphi, T. J., “The Use of Simple Solutions in the Regularization of Hypersingular Boundary Integral Equations,” Mathematical and Computer Modeling, 15, pp. 269–278 (1991).Google Scholar
17. Sladek, V., Sladek, J. and Tanaka, M., “Regularization of Hypersingular and Nearly Singular Integrals in Potential Theory and Elasticity,” International Journal for Numerical Methods in Engineering, 36, pp. 1609–1628 (1993).Google Scholar
18. Matsumoto, T. and Tanaka, M., “Boundary Stress Calculation Using Regularized Boundary Integral Equation for Displacement Gradients,” International Journal for Numerical Methods in Engineering, 36, pp. 783–797 (1993).Google Scholar
19. Cruse, T. A. and Richardson, J. D., “Non-Singular Somigliana Stress Identities in Elasticity,” International Journal for Numerical Methods in Engineering, 39, pp. 3273–3304 (1996).Google Scholar
20. He, M. G. and Tan, C. L., “A Self-Regularization Technique in Boundary Element Method for 3-D Stress Analysis,” CMES-Computer Modeling in Engineering & Sciences, 95, pp. 317–349 (2013).Google Scholar
21. Shiah, Y. C., Tan, C. L. and Chan, L. D., “Boundary Element Analysis of Thin Anisotropic Structures by the Self-Regularization Scheme,” CMES-Computer Modeling In Engineering & Sciences, 109, pp. 15–33 (2015).Google Scholar
22. Shiah, Y. C. and Chang, L. D., “Boundary Element Calculation of Near-Boundary Solutions in 3D Generally Anisotropic Solids by the Self-Regularization Scheme,” Journal of Mechanics DOI: 10.1017/jmech.2017.75 (2017).Google Scholar
23. Lifshitz, I. M. and Rozenzweig, L. N., “Construction of the Green Tensor for the Fundamental Equation of Elasticity Theory in the Case of Unbounded Elastically Anisotropic Medium,” Zhurnal Eksperimental noi I Teioretical Fiziki, 17, pp. 783–791 (1947).Google Scholar
24. 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. 205–226 (2008).Google Scholar
25. Tan, C. L., Shiah, Y. C. and Lin, C. W., “Stress Analysis of 3D Generally Anisotropic Solids Using the Boundary Element Method,” CMES-Computer Modeling in Engineering & Sciences, 41, pp. 195–214 (2009).Google Scholar
26. 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. 407–426 (1997).Google Scholar
27. Tan, C. L., Shiah, Y. C. and Wang, C. Y., “Boundary Element Elastic Stress Analysis of 3D Generally Anisotropic Solids Using Fundamental Solutions Based on Fourier Series,” International Journal of Solids And Structures, 50, pp. 2701–2711 (2013).Google Scholar
28. Shiah, Y. C., Tan, C. L. and Wang, C. Y., “An Improved Numerical Evaluation Scheme of the Fundamental Solution and Its Derivatives for 3D Anisotropic Elasticity Based on Fourier Series,” CMES-Computer Modeling in Engineering & Sciences, 87, pp. 1–22 (2012).Google Scholar
29. Hwu, C. B. and Chang, H. W., “Coupled Stretching– Bending Analysis of Laminated Plates with Corners via Boundary Elements,” Composite Structures, 120, pp. 300–314 (2015).Google Scholar