Static analysis of functionally graded beams using higher order shear deformation theory

Abstract Displacement field based on higher order shear deformation theory is implemented to study the static behavior of functionally graded metal–ceramic (FGM) beams under ambient temperature. FGM beams with variation of volume fraction of metal or ceramic based on power law exponent are considered. Using the principle of stationary potential energy, the finite element form of static equilibrium equation for FGM beam is presented. Two stiffness matrices are thus derived so that one among them will reflect the influence of rotation of the normal and the other shear rotation. Numerical results on the transverse deflection, axial and shear stresses in a moderately thick FGM beam under uniform distributed load for clamped–clamped and simply supported boundary conditions are discussed in depth. The effect of power law exponent for various combination of metal–ceramic FGM beam on the deflection and stresses are also commented. The studies reveal that, depending on whether the loading is on the ceramic rich face or metal rich face of the beam, the static deflection and the static stresses in the beam do not remain the same.

[1]  J. N. Reddy,et al.  A new beam finite element for the analysis of functionally graded materials , 2003 .

[2]  D. Haojiang,et al.  The analytical solutions for orthotropic cantilever beams (I): Subjected to surface forces , 2005 .

[3]  Jerome T. Tzeng,et al.  Thermal Stresses in Functionally Graded Beams , 2002 .

[4]  H. Ding,et al.  Elasticity solutions for plane anisotropic functionally graded beams , 2007 .

[5]  G. Venkateswara Rao,et al.  Thermal buckling of cross-ply composite laminates , 1992 .

[6]  Grant P. Steven,et al.  A mixed model for composite beams with piezoelectric actuators and sensors , 1999 .

[7]  Ohseop Song,et al.  Spinning thin-walled beams made of functionally graded materials: modeling, vibration and instability , 2004 .

[8]  J. N. Reddy,et al.  THERMOMECHANICAL ANALYSIS OF FUNCTIONALLY GRADED CYLINDERS AND PLATES , 1998 .

[9]  Ivo Caliò,et al.  Closed-form solutions for axially graded beam-columns , 2005 .

[10]  H. Ding,et al.  Analytical solution for fixed-end beam subjected to uniform load , 2005 .

[11]  M. Koizumi.  FGM activities in Japan , 1997 .

[12]  Isaac Elishakoff,et al.  Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode , 2005 .

[13]  Ohseop Song,et al.  Thermoelastic Modeling and Vibration of Functionally Graded Thin-Walled Rotating Blades , 2003 .

[14]  Bhavani V. Sankar,et al.  AN ELASTICITY SOLUTION FOR FUNCTIONALLY GRADED BEAMS , 2001 .

[15]  Rakesh K. Kapania,et al.  Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling. , 1989 .

[16]  P. Venini,et al.  Finite elements for functionally graded Reissner–Mindlin plates , 2004 .

[17]  Ohseop Song,et al.  Thin-Walled Beams Made of Functionally Graded Materials and Operating in a High Temperature Environment: Vibration and Stability , 2005 .

[18]  J. Reddy,et al.  A higher order beam finite element for bending and vibration problems , 1988 .

[19]  A. Zenkour.  Generalized shear deformation theory for bending analysis of functionally graded plates , 2006 .

[20]  K. Y. Lam,et al.  On efficient finite element modeling of composite beams and plates using higher-order theories and an accurate composite beam element , 1998 .

[21]  Zheng Zhong,et al.  Analytical solution of a cantilever functionally graded beam , 2007 .