Advanced Boundary Element Analysis of Three-Dimensional Elastic Solids with Fiber Reinforcements
Publication: Journal of Engineering Mechanics
Volume 134, Issue 9
Abstract
An advanced boundary element methodology for the analysis of three-dimensional fiber-reinforced elastic solids using the concept of fiber elements has been presented in this paper as an extension of the earlier work of Banerjee and co-workers. The previous simplified formulation was based on the assumption that the Poisson ratios of the matrix and the fiber are equal. However, this may not be a valid assumption for all values of elastic stiffness ratios and fiber to matrix volume ratios. Moreover, such restrictions do not allow for any future extensions to nonlinear analysis. Also, because of limiting computing power available at that time, their implementation was restricted to only a small number of fiber elements in a given analysis. The new algorithm proposed in this work does not make any such assumptions. In this algorithm, the fibers are semianalytically integrated and the resulting equations are back-substituted into the equations for the composite matrix without any further approximation. The present work has been implemented in a general purpose multiregion boundary element computer program and is capable of handling very large numbers of fiber elements in a given analysis. Several numerical examples are presented to validate the proposed method of fiber composite analysis and its applicability is demonstrated via practical engineering problems.
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Acknowledgments
The writers are deeply indebted to Boundary Element Software Technology Corporation (GPBEST) of Getzville, N.Y. for making available several blocks of the General Purpose GPBEST system for this development.
References
Abramowitz, M., and Stegun, I. A. (1974). Handbook of mathematical functions, Dover, New York.
American Concrete Institute (ACI). (2002). Building code requirements for structural concrete, ACI 318-02, Farmington Hills, Mich.
Banerjee, P. K. (1994). The boundary element methods in engineering, McGraw-Hill, London.
Banerjee, P. K., Ahmad, S., and Manolis, G. D. (1986). “Transient elastodynamic analysis of three-dimensional problems by boundary element method.” Earthquake Eng. Struct. Dyn., 14, 933–949.
Banerjee, P. K., and Butterfield, R. (1981). Boundary element methods in engineering science, McGraw-Hill, London.
Banerjee, P. K., and Henry, D. P. (1992). “Elastic analysis of three-dimensional solids with fiber inclusions by BEM.” Int. J. Solids Struct., 29, 2423–2440.
Banerjee, P. K., Henry, D. P., and Dargush, G. F. (1991). “Micromechanical studies of composites by BEM: Enhancing analysis techniques for composite materials.” Proc., ASME Winter Annual Meeting, Atlanta, American Society of Mechanical Engineers, New York.
Banerjee, P. K., Henry, D. P., Dargush, G. F., Hopkins, D., and Goldberg, R. K. (1994). BEST-CMS user’s manual, National Aeronautics and Space Administration, Washington, D.C.
Byrd, P. F., and Friedman, M. D. (1954). Handbook of elliptical integrals for engineers and physicists, Springer, Berlin.
Cruse, T. A. (1974). “An improved boundary integral equation method for three-dimensional elastic stress analysis.” Comput. Struct., 4, 741–754.
Henry, D. P., and Banerjee, P. K. (1991). “Elastic analysis of three-dimensional solids with small holes by BEM.” Int. J. Numer. Methods Eng., 31, 369–384.
Liu, Y. J., Nishimura, N., and Otani, Y. (2005a). “Large-scale modeling of carbon-nanotube composites by the boundary element method based on a rigid-inclusion model.” Comput. Mater. Sci., 34, 173–187.
Liu, Y. J., Nishimura, N., Otani, Y., Takahashi, T., Chen, X. L., and Munakata, H. (2005b). “A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model.” J. Appl. Mech., 72, 115–128.
Mukherjee, S. (1982). Boundary element method in creep and fracture, Applied Science Publishers, London.
Rizzo, F. J., and Shippy, D. J. (1979). “A boundary integral approach to potential and elasticity problems for axisymmetric bodies with arbitrary boundary conditions.” Mech. Res. Commun., 6, 99–103.
Wang, H. C. (1989). “A general purpose development of BEM for axisymmetric solids.” Ph.D. dissertation, State Univ. of New York at Buffalo, Buffalo, N.Y.
Wang, H. C., and Banerjee, P. K. (1989). “Multi-domain general axisymmetric stress analysis by BEM.” Int. J. Numer. Methods Eng., 28, 2065–2083.
Watson, J. O. (1979). “Advanced implementation of the BEM for two and three-dimensional elastostatics.” Developments in BEM, Vol. 1, P. K. Banerjee and R. Butterfield, eds., Elsevier Applied Science, London, 31–63.
Zia, P. (1968). “Torsion theories for concrete members: Torsion of structural concrete.” ACI Publication SP-18, Detroit, 103–132.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 9 • September 2008
Pages: 739 - 749
Copyright
© 2008 ASCE.
History
Received: May 25, 2006
Accepted: Sep 24, 2007
Published online: Sep 1, 2008
Published in print: Sep 2008
Notes
Note. Associate Editor: Dinesh R. Katti
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