Dynamic Response of Strain Rate Dependent Glass/Epoxy Composite Beams Using Finite Difference Method

This paper deals with a numerical analysis of the transient response of composite beams with strain rate dependent mechanical properties by use of a finite difference method. The equations of motion based on Timoshenko beam theory are derived. The geometric nonlinearity effects are taken into account with von Kármán large deflection theory. The finite difference method in conjunction with Newmark average acceleration method is applied to solve the differential equations. A modified progressive damage model which accounts for strain rate effects is developed based on the material property degradation rules and modified Hashin-type failure criteria and added to the finite difference model. The components of the model are implemented into a computer code in Mathematica 6. Glass/epoxy laminated composite beams with constant and strain rate dependent mechanical properties under dynamic load are analyzed. Effects of strain rate on dynamic response of the beam for various stacking sequences, load and boundary conditions are investigated.

Authors:

• M. M. Shokrieh
• A. Karamnejad

Keywords:

• Composite beam
• Finite difference method
• Progressive damage modeling
• Strain rate.

References:

[1] K. P. Soldatos and I. Elishakoff, "A transverse shear and normal
deformable orthotropic beam theory", Journal of Sound and Vibration,
vol. 154, no. 3, pp. 528-33, June 1992.
[2] A. W. Obst and R. K. Kapania, "Nonlinear static and transient finite
element analysis of laminated beams", Composite Engineering, vol. 2,
no. 5-7, pp. 375-389, Feb. 1992.
[3] S. R. Marur and T. Kant, "On the performance of higher order theories
for transient dynamic analysis of sandwich and composite beams",
Composites & Structures, vol. 65, no. 5, pp. 741-759, Dec. 1997.
[4] A. A. Khedeir, "Dynamic response of antisymmetric cross-ply laminated
composite beams with arbitrary boundary conditions", International
Journal of Engineering Science, vol. 34, no. 1, pp. 9-19, Jan. 1996.
[5] T. Kant, S. R. Marur and G. S. Rao, "Analytical solution to the dynamic
analysis of laminated beams using higher order refined theory",
Composite Structures, vol. 40, no.1, pp. 1-9, Dec. 1997.
[6] S. W. Gong and K. Y. Lam, "Analysis of layered composite beam to
underwater shock including structural damping and stiffness effects ",
Shock and Vibration, vol. 9, no. 6, pp. 283-291, 2002.
[7] J. N. Reddy, Mechanics of Laminated Composite Plates and Shells:
Theory and Analysis), second ed., CRC Press, Boca Raton, FL, 2004, pp.
109-197.
[8] LS-DYNA 971 Keyword User-s Manual, Livermore Software
Technology Corporation, California, USA, 2006, pp.1840-1841.
[9] M. M. Shokrieh, "Progressive Fatigue Damage Modeling of Composite
Materials", Ph.D. thesis, Dept. Mech. Eng., McGill Univ., Montreal,
Canada, 1996.
[10] M. M. Shokrieh and M. J. Omidi, "Tension behavior of unidirectional
glass/epoxy composites under different strain rates", Composite
Structures, vol. 88, no. 4, pp. 595-601, May 2009.
[11] M. M. Shokrieh and M. J. Omidi, "Compressive response of glass-fiber
reinforced polymeric composites to increasing compressive strain rates",
Composite Structures, vol. 89, no. 4, pp. 517-523, Aug. 2009.
[12] M. M. Shokrieh and M. J. Omidi, "Investigation of strain rate effects on
in-plane shear properties of glass/epoxy composites", Composite
Structures, vol. 91, no. 1, pp. 95-102, Nov. 2009.
[13] M. R. Karim, "Constitutive Modeling and Failure Criteria of Carbon-
Fiber Reinforced Polymers under High Strain rates", Ph.D. thesis, The
Graduate Faculty of The University of Akron, USA, 2005.
[14] W. Wang, G. Makarov and R. A. Shenoi, "An analytical model for
assessing strain rate sensitivity of unidirectional composite laminates",
Composite Structures, vol.69, no.1, pp. 45-54, June 2005.
[15] O. I. Okoli and G. F. Smith, "High strain rate characterization of a
glass/epoxy composite", Journal of Composites Technology & Research,
vol. 22, no. 1, pp. 3-11, Jan. 2000.