The effect of transverse shear deformation on the post-buckling behavior of functionally graded beams

Ali Meksi , Hadj Youzera , Mohamed Sadoun , Ali Abbache , Sid Ahmed Meftah , Abdelouahed Tounsi , Muzamal Hussain

Abstract

The purposes of the present work it to study the effect of shear deformation on the static post-buckling response of simply supported functionally graded (FGM) axisymmetric beams based on classical, first-order, and higher-order shear deformation theories. The behavior of postbuckling is introduced based on geometric nonlinearity. The material properties of functionally graded materials (FGM) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The equations of motion and the boundary conditions derived using Hamilton's principle. This article compares and addresses the efficiency, the applicability, and the limits of classical models, higher order models (CLT, FSDT, and HSDT) for the static post-buckling response of an asymmetrically simply supported FGM beam. The amplitude of the static post-buckling obtained a solving the nonlinear governing equations. The results showing the variation of the maximum post-buckling amplitude with the applied axial load presented, for different theory and different parameters of material and geometry. In conclusion: The shear effect found to have a significant contribution to the post-buckling behaviors of axisymmetric beams. As well as the classical beam theory CBT, underestimate the shear effect compared to higher order shear deformation theories HSDT.

Key Words

amplitude; axisymmetric beams; buckling; classical theory; functionally graded beams; post buckling

Address

Ali Meksi — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P. 29000 Mascara, Algérie
Hadj Youzera — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P. 29000 Mascara, Algérie
Mohamed Sadoun — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P. 29000 Mascara, Algérie
Ali Abbache — Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbes, Alegria
Sid Ahmed Meftah — Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbes, Alegria
Abdelouahed Tounsi — YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea 4Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Eastern Province, Saudi Arabia 5Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 6Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

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