Document Type : Research Paper


Department of Mechanical Engineering, University of Jordan, Amman-11942, Jordan.


Detailed formulation and coding of exact finite element is carried out to study the static behavior of a layered beam structure. The beam element is modelled based on the first-order shear deformation theory and it is assumed to be composed of three layers whereas the middle layer is made of functionally graded material (FGM), i.e. with variable elastic properties in the thickness direction. The shape of the FGM mechanical properties variation in the thickness direction takes the form of exponential or power-law. The governing equations and boundary conditions are derived by applying the virtual work principle. Variations of displacements along the beam and stresses across the depth due to mechanical loadings are investigated. Comparative examples are carried out to highlight the static behavior difference between FGM layered beams and pure metal-ceramic beams.


Main Subjects

[1]  Koizumi, M. F. G. M. (1997). FGM activities in Japan. Composites part B: Engineering28(1-2), 1-4.
[2]  Chakraborty, A., Mahapatra, D. R., & Gopalakrishnan, S. (2002). Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities. Composite structures55(1), 23-36.
[3] Chakraborty, A., Gopalakrishnan, S., & Reddy, J. N. (2003). A new beam finite element for the analysis of functionally graded materials. International journal of mechanical sciences45(3), 519-539.
[4]  García-Vallejo, D., Mikkola, A. M., & Escalona, J. L. (2007). A new locking-free shear deformable finite element based on absolute nodal coordinates. Nonlinear dynamics50(1), 249-264.
[5] Kadoli, R., Akhtar, K., & Ganesan, N. (2008). Static analysis of functionally graded beams using higher order shear deformation theory. Applied mathematical modelling32(12), 2509-2525.
[6] Roy, A., & Khan, K. (2013). Static response analysis of a FGM Timoshenko’s Beam subjected to Uniformly Distributed Loading Condition. MIT international journal of mechanical engineering, 3(2), 80–85.
[7]  Khan, A. A., Naushad Alam, M., & Wajid, M. (2016). Finite element modelling for static and free vibration response of functionally graded beam. Latin American journal of solids and structures13(4), 690-714.
[8]  El-Ashmawy, A. M., Kamel, M. A., & Elshafei, M. A. (2016). Thermo-mechanical analysis of axially and transversally Function Graded Beam. Composites part B: Engineering102, 134-149.
[9]  Ugural, A. (1999). Stresses in plates and shells. McGraw-Hill.