Large Deflection of Various Functionally Graded Beam Using Shooting Method


Article Preview

The equation of large deflection of functionally graded beam subjected to arbitrary loading condition is derived. In this work assumed that the elastic modulus varies by exponential and power function in longitudinal direction. The nonlinear derived equation has not exact solution so shooting method has been proposed to solve the nonlinear equation of large deflection. Results are validated with finite element solutions. The method will be useful toward the design of compliant mechanisms driven by smart actuators. Finally the effect of different elastic modulus functions and loading conditions are investigated and discussed.



Edited by:

Wu Fan






A. Soleimani "Large Deflection of Various Functionally Graded Beam Using Shooting Method", Applied Mechanics and Materials, Vols. 110-116, pp. 4705-4711, 2012

Online since:

October 2011





[1] K.E. Bisshop, D.C. Drucker, Large deflection cantilever beams, Q. Appl. Math., vol. 3, p.272–275, (1945).

[2] L.L. Howell, A. Midha, Parametric deflection approximations for endloaded large deflection beams in compliant mechanisms, ASME J. Mech. Des., vol. 117, p.156–165, (1995).

DOI: 10.1115/1.2826101

[3] A. Saxena, S.N. Kramer, A simple and accurate method for determining large deflections in compliant mechanisms subjected to end forces and moments, ASME J. Mech. Des., vol. 120, p.392–400, (1998).

DOI: 10.1115/1.2829164

[4] C. Kimball, L. -W. Tsai, Modeling of flexural beams subjected to arbitrary end loads, ASME J. Mech. Des., vol. 124, p.223–234, (2002).

DOI: 10.1115/1.1455031

[5] A. Banerjee, B. Bhattacharya, A.K. Mallik, Large deflection of cantilever beams with geometric non-linearity: Analytical and numerical approaches, International Journal of Non-Linear Mechanics, vol. 43, p.366 – 376, (2008).

DOI: 10.1016/j.ijnonlinmec.2007.12.020

[6] M. Koizumi, FGM activities in Japan, Composites Part B: Engineering, vol. 28, pp.1-4, (1997).

[7] S. Suresh and A. Mortensen, Fundamentals of functionally graded materials, IOM Communications, London, (1998).

[8] F. Delale and F. Erdogan, The crack problem for nonhomogeneous plane, Journal of Applied Mechanics, vol. 50, no. 3, pp.609-614, (1983).

DOI: 10.1115/1.3167098

[9] N. Noda and Z.H. Jin, Thermal stress intensity factors for a crack in a strip of a functionally gradient material, International Journal of Solids and Structures, vol. 30, no. 8, pp.1039-1056, (1993).

DOI: 10.1016/0020-7683(93)90002-o

[10] Z.H. Jin and R.C. Batra, Stress intensity relaxation at the tip of an edge crack in a functionally graded material subjected to a thermal shock, " Journal of Thermal Stress, vol. 19, no. 4, pp.317-339, (1996).

DOI: 10.1080/01495739608946178

[11] A. Stanoyevitch, Introduction to Numerical Ordinary and Partial Differential Equations Using Matlab, Wiley, NJ, (2005).

DOI: 10.1002/9781118033326

[12] P.B. Bailey, L.F. Shampine, P.E. Waltman, Non-linear Two Point Boundary Value Problems, Academic Press, New York, London, (1968).

In order to see related information, you need to Login.