Universal Journal of Mechanical Engineering Vol. 8(2), pp. 105 - 113
DOI: 10.13189/ujme.2020.080205
Reprint (PDF) (748Kb)

A New Method of Resolution of the Bending of Thick FGM Beams Based on Refined Higher Order Shear Deformation Theory

Abderrahim Razouki ^*, Lhoucine Boutahar , Khalid El Bikri
Mohammed V University of Rabat, ENSET- Rabat, M2SM, B.P.6207, Rabat Instituts 10100, Rabat, Morocco

ABSTRACT

The aim of this work is to study the static bending of functionally graded beams accounting higher order of shear deformation theory. The governing equations, derived from the virtual work principle, are a set of ordinary differential equations describing a static bending of a thick beam. Thus, this paper presents the differential transform method used to solve the previous system of equations. The results obtained lay the foundation to determine the exact analytical solution for different boundary conditions and external loadings. The axial displacement and the bending and shear displacements, in the exact analytical form, of a thick clamped-clamped beam with functionally graded material under a uniform load will be fully developed. Moreover, normal and shear stresses will be analyzed. To confirm the efficiency of this work, a comparison with the numerical results provided by literature is performed. Through this work, the given analytical results provide engineers with an accurate tool to determine the analytical solution for the bending of plates and shells. In addition, the geometric and material parameters that appear clearly in the analytical results allow for a more optimized design of functionally graded material beams. This type of beams is frequently used in mechanical engineering fields such as aerospace engineering.

KEYWORDS
Differential Transformation Method, Exact Solution, Static Analysis, Clamped-Clamped Beam, Bending, Functionally Graded Beam

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Abderrahim Razouki , Lhoucine Boutahar , Khalid El Bikri , "A New Method of Resolution of the Bending of Thick FGM Beams Based on Refined Higher Order Shear Deformation Theory," Universal Journal of Mechanical Engineering, Vol. 8, No. 2, pp. 105 - 113, 2020. DOI: 10.13189/ujme.2020.080205.

(b). APA Format:
Abderrahim Razouki , Lhoucine Boutahar , Khalid El Bikri (2020). A New Method of Resolution of the Bending of Thick FGM Beams Based on Refined Higher Order Shear Deformation Theory. Universal Journal of Mechanical Engineering, 8(2), 105 - 113. DOI: 10.13189/ujme.2020.080205.