Mechanical Buckling of Functionally Graded Engesser-Timoshenko Beams Located on a Continuous Elastic Foundation

This paper studies mechanical buckling of functionally graded beams subjected to axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. Applying the Hamilton's principle, the equilibrium equation is established. The influences of dimensionless geometrical parameter, functionally graded index and foundation coefficient on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Authors:

• M. Karami Khorramabadi
• A. R. Nezamabadi

Keywords:

• Mechanical Buckling
• Functionally graded beam- Engesser-Timoshenko beam theory

References:

[1] O. Rabin BH, Shiota I. Functionally gradient materials. Mater Res Soc
Bull 1995;20:14-8.
[2] Koizumi M. FGM activities in Japan. Compos Part B: Eng 1997;28:1-4.
[3] Ichinose N, Miyamoto N, Takahashi S. Ultrasonic transducers with
functionally graded piezoelectric ceramics. J Eur Ceram Soc
2004;24:1681-5
[4] Wu CCM, Kahn M, Moy W. Piezoelectric ceramics with functional
gradients: a new application in material design. J Am Ceram Soc
1996;79:809-12.
[5] Li CY, Weng GJ. Antiplane crack problem in functionally graded
piezoelectric materials. J Appl Mech 2002;69:481-8.
[6] Chen WQ, Ye GR, Cai JB. Thermoelastic stresses in a uniformly heated
functionally graded isotropic hollow cylinder. J Zhejiang Univ (Science)2002;3:1-5.
[7] Cheng ZQ, Lim CW, Kitipornchai S. Three-dimensional asymptotic
approach to inhomogeneous and laminated piezoelectric plates. Int J Solids Struct 2000;37:3153-75.
[8] Lim CW, He LH. Exact solution of a compositionally graded piezoelectric layer under uniform stretch, bending and twisting.Int J
Mech Sci 2001;43:2479-92.
[9] Lim CW, He LH, Soh AK. Three dimensional electromechanical
responses of a parallel piezoelectric bimorph. Int J Solids Struct
2001;38:2833-49.
[10] Chen WQ, Ding HJ, Hou PF. Exact solution of an external circular crack
in a piezoelectric solid subjected to shear loading. J Zhejiang Univ
(Science) 2001;2:9-14.
[11] Hou PF, Ding HJ, Guan FL. A penny-shaped crack in an infinite
piezoelectric body under antisymmetric point loads. J Zhejiang Univ
(Science) 2001;2:146-51.
[12] Zhang W, Hong T. Adaptive Lagrange finite element methods for high
precision vibrations and piezoelectric acoustic wave computations in
SMT structures and plates with nano interfaces. J Zhejiang Univ
(Science) 2002;3:6-12.
[13] Wang Y, Xu RQ, Ding HJ. Free vibration of piezoelectric annular plate.
J Zhejiang Univ (Science) 2003;4:379-87.
[14] Lim CW, Lau CWH. A new two-dimensional model for
electromechanical response of thick laminated piezoelectric actuator. Int
J Solids Struct, in press.
[15] Ootao Y, Tanigawa Y. Three-dimensional transient
piezothermoelasticity in functionally graded rectangular plate bonded to
a piezoelectric plate. Int J Solids Struct 2000;37:4377-401.
[16] Pagano NJ. Exact solutions for composite laminates in cylindrical
bending. J Compos Mater 1969;3:398-411.
[17] He XQ, Ng TY, Sivashanker S, Liew KM. Active control of FGM plates
with integrated piezoelectric sensors and actuators. Int J Solids Struct
2001;38:1641-55.
[18] Liew KM, He XQ, Ng TY, Sivashanker S. Active control of FGM plates
subjected to a temperature gradient: modelling via finite element method
based on FSDT. Int J Numer Meth Eng 2001;52:1253-71.
[19] Reddy J.N. and Praveen G.N., Nonlinear Transient Thermoelastic
Analysis of Functionally Graded Ceramic-metal Plates, International
Journal of. Solids and Structures, Vol. 35, 1998, pp. 4467-4476
[20] Wang C.M., Reddy J.N., 2000, "Shear Deformable Beams and Plates",
Oxford, Elsevier.
[21] Reddy J.N., 2004, " Mechanics of Laminated Composite Plates and
Shells Theory and Analysis", New York, CRC.
World Academy of Science, Engineering and Technology 58 2011