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Failure Analysis of Anisotropic Plates by the Boundary Element Method

Published online by Cambridge University Press:  21 October 2014

A. Sahli ,
S. Boufeldja ,
S. Kebdani  and
O. Rahmani
A. Sahli*
Affiliation:
Faculté de Génie Mécanique, Université des Sciences et de la Technologie d'Oran, Oran, Algérie
S. Boufeldja
Affiliation:
Faculté de Génie Mécanique, Université des Sciences et de la Technologie d'Oran, Oran, Algérie
S. Kebdani
Affiliation:
Faculté de Génie Mécanique, Université des Sciences et de la Technologie d'Oran, Oran, Algérie
O. Rahmani
Affiliation:
Faculté de Génie Mécanique, Université des Sciences et de la Technologie d'Oran, Oran, Algérie
*
*[email protected]
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Abstract

This paper presents a dynamic formulation of the boundary element method for stress and failure criterion analyses of anisotropic thin plates. The elastostatic fundamental solutions are used in the formulations and inertia terms are treated as body forces. The radial integration method (RIM) is used to obtain a boundary element formulationithout any domain integral for general anisotropic plate problems. In the RIM, the augmented thin plate spline is used as the approximation function. A formulation for transient analysis is implemented. The time integration is carried out using the Houbolt method. Integral equations for the second derivatives of deflection are developed and all derivatives of fundamental solutions are computed analytically. Only the boundary is discretized in the formulation. Numerical results show good agreement with results available in literature as well as finite element results.

Keywords

Boundary element methodRadial integration method, PlatesComposite materialsDynamic of platesStress analyses and failure criterion
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 6 , December 2014 , pp. 561 - 570
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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References

1.Lakshminarayana, H. V. and Murthy, S. S. A., “Shear-Flexible Triangular Finite Element Model for Laminated Composite Plates,” International Journal for Numerical Methods in Engineering, 20, pp. 591–623 (1984).CrossRefGoogle Scholar
2.Luo, R. K., Green, E. R. and Morrison, C. J., “Impact Damage Analysis of Composite Plates,” International Journal of Impact Engineering, 22, pp. 435–447 (1999).CrossRefGoogle Scholar
3.Zhao, G. P. and Cho, C. D., “Damage Initiation and Propagation in Composite Shells Subjected to Impact,” Composite Structures, 78, pp. 91–100 (2007).CrossRefGoogle Scholar
4.Ganapathy, S. and Rao, K. P., “Failure Analysis of Laminated Composite Cylindrical/Spherical Shell Panels Subjected to Low-Velocity Impact,” Computers and Structures, 68, pp. 627–641 (1998).CrossRefGoogle Scholar
5.Li, C. F., Hu, N., Yin, Y. J., et al., “Low-Velocity Impact-Induced Damage of Continuous Fiber-Reinforced Composite Laminates. Part I: An Fem Numerical Model,” Composites Part A-Applied Science and Manufacturing, 33, pp. 1055–1062 (2002).Google Scholar
6.Li, C. F., Hu, N., Cheng, J. G., et al., “Low-Velocity Impact-Induced Damage of Continuous Fiber-Reinforced Composite Laminates. Part II: Verification and Numerical Investigation,” Composites Part A: Applied Science and Manufacturing, 33, pp. 1063–1072 (2002).Google Scholar
7.Shi, G. and Bezine, G., “Buckling Analysis of Ortho-tropic Plates by Boundary Element Method,” Mechanics Research Communications, 26, pp. 1351–1370 (1990).Google Scholar
8.Wu, B. C. and Altiero, N. J., “A New Numerical Method for the Analysis of Anisotropic Thin Plate Bending Problems,” Computer Methods in Applied Mechanics and Engineering, 25, pp. 343–353 (1981).Google Scholar
9.Rajamohan, C. and Raamachandran, J., “Bending of Anisotropic Plates by Charge Simulation Method,” Advances in Engineering Software, 30, pp. 369–373 (1999).Google Scholar
10.Paiva, W. P., Sollero, P. and Albuquerque, E. L., “Treatment of Hypersingularities in Boundary Element Anisotropic Plate Bending Problems,” Latin American Journal of Solids and Structures, 1, pp. 49–73 (2003).Google Scholar
11.Wang, J. and Schweizerhof, K., “Fundamental Solutions and Boundary Integral Equations of Moderately Thick Symmetrically Laminated Anisotropic Plates,” Communications in Numerical Methods in Engineering, 12, pp. 383–394 (1996).3.0.CO;2-4>CrossRefGoogle Scholar
12.Wang, J. and Schweizerhof, K., “Free Vibration of Laminated Anisotropic Shallow Shells Including Transverse Shear Deformation by the Boundary-Domain Element Method,” Computers and Structures, 62, pp. 151–156 (1997).CrossRefGoogle Scholar
13.Wang, J. and Schweizerhof, K., “The Fundamental Solution of Moderately Thick Laminated Aniso-tropic Shallow Shells,” International Journal of Engineering Science, 33, pp. 995–1004 (1995).Google Scholar
14.Venturini, W. S., “A Study of Boundary Element Method and Its Application on Engineering Problems,” Ph.D. Dissertation, Sao Carlos School of Engineering, University of Sao Paulo, Brazil (1988) (in Portuguese).Google Scholar
15.Gao, X., “The Radial Integration Method for Evaluation of Domain Integrals with Boundary Only Discretization,” Engineering Analysis with Boundary Elements, 26, pp. 905–916 (2002).CrossRefGoogle Scholar
16.Albuquerque, E. L.et al., “Boundary Element Analysis of Anisotropic Kirchhoff Plates,” International Journal of Solids and Structures, 43, pp. 4029–4046 (2006).Google Scholar
17.Tsai, S. W. and Wu, E. M., “A General Theory of Strength Test for Anisotropic Materials,” Journal of Composite Materials, 5, pp. 58–80 (1971).Google Scholar
18.Hill, R., “A Theory of the Yelding and Plastic Flow of Anisotropic Metals,” Proceedings of the Royal Socety, 193, pp. 281–297 (1950).Google Scholar
19.Tsai, S. W., Strength Theories of Filamentary Structures, in Fundamental Aspects of Fiber Reinforced Plastic Composites, Schwartz, R.T. and Schwartz, H.T. Eds., Wiley Interscience, New York, US, pp. 3–11 (1968).Google Scholar
20.Lekhnitskii, S. G., Anisotropic Plates, Gordon and Breach, New York, US (1968).Google Scholar
21.Shi, G. and Bezine, G. A., “General Boundary Integral Formulation for the Anisotropic Plate Bending Problems,” Journal of Composite Materials, 22, pp. 694–716 (1988).CrossRefGoogle Scholar
22.Paiva, J. B., “Boundary Element Formulation for Plate Bending and its Aplication in Engineering,” Ph.D. Dissertation, Sao Carlos School of Engineering, University of Sao Paulo, Brazil (1987) [Text in Portuguese].Google Scholar
23.Albuquerque, E. L. and Aliabadi, M. H., “A Boundary Element Analysis of Symmetric Laminated Composite Shallow Shells,” Computer Methods in Applied Mechanics and Engineering, 199, pp. 2663–2668 (2010).Google Scholar
24.Houbolt, J. C., “A Reccurrence Matrix Solution for the Dynamic Response of Elastic Aircraft,” Journal of Aeronautical and Science, 17, pp. 540–550 (1950).CrossRefGoogle Scholar
25.Loeffler, C. F. and Mansur, W. J., Analysis of Time Integration Schemes for Boundary Element Applications to Transient Wave Propagation Problems, in Boundary Element Techniques: Applications in Stress Analysis and Heat Transfer, Brebbia, C. A. and Venturini, W. S. Eds., Computational Mechanics Publications, Southampton, Boston, US, pp. 105–122 (1987).Google Scholar
26.Albuquerque, E. L., Sollero, P. and Aliabadi, M. H., “The Boundary Element Method Applied to Time Dependent Problems in Anisotropic Materials,” International Journal of Solids and Structures, 39, pp. 1405-22 (2002).Google Scholar
27.Fedelinsk, P., Aliabadi, M. H. and Rooke, D. P., “Boundary Element Formulations for the Dynamic Analysis of Cracked Structures,” Engineering Analysis with Boundary Elements, 17, pp. 45–56 (1996).Google Scholar
28.Chirino, F., Gallego, R. and Saez, A., et al., “A Comparative Study of Three Boundary Element Approaches to Transient Dynamic Crack Problems,” Engineering Analysis with Boundary Elements, 13, pp. 11–19 (1994).Google Scholar
29.Sladek, J., et al., “Local Boundary Integral Equations for Orthotropic Shallow Shells,” International Journal of Solids and Structures, 44, pp. 2285–2303 (2007).Google Scholar