A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations

Kheira Soltani, Aicha Bessaim, Mohammed Sid Ahmed Houari, Abdelhakim Kaci, Mohamed Benguediab, Abdelouahed Tounsi and Mohammed Sh Alhodaly

Abstract

This work presents the buckling investigation of functionally graded plates resting on two parameter elastic foundations by using a new hyperbolic plate theory. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only four unknowns and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. The governing equations are derived using Hamilton's principle and solved using Navier's steps. The validation of the proposed theoretical model is performed to demonstrate the efficacy of the model. The effects of various parameters like the Winkler and Pasternak modulus coefficients, inhomogeneity parameter, aspect ratio and thickness ratio on the behaviour of the functionally graded plates are studied. It can be concluded that the present theory is not only accurate but also simple in predicting the critical buckling loads of functionally graded plates on elastic foundation.

Key Words

functionally graded material; Winkler-Pasternak elastic foundation; new plate theory; buckling analysis; analytical modeling

Address

(1) Kheira Soltani, Mohamed Benguediab: Department of Mechanical Engineering, Faculty of Technology, University of Sidi Bel Abbes, Algeria; (2) Aicha Bessaim, Mohammed Sid Ahmed Houari: University Mustapha Stambouli of Mascara, Faculty of Sciences and Technology, Civil Engineering Department, Mascara, Algeria; (3) Mohammed Sid Ahmed Houari: Centre of Excellence for Advanced Materials Research, King Abdulaziz University, Jeddah, 21589, Saudi Arabia; (4) Kheira Soltani, Mohamed Benguediab: Faculty of Technology, Laboratory of Materials and Reactive Systems (LMRS), University of Sidi Bel-Abbes, Algeria; (5) Abdelhakim Kaci: Universite Dr Taher Moulay Saida - Algeria, Département de Génie Civil et Hydraulique, Algeria; (6) Aicha Bessaim, Mohammed Sid Ahmed Houari, Abdelhakim Kaci, Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; (7) Abdelouahed Tounsi: Laboratoire de Modélisation et Simulation Multi-échelle, Faculté des Sciences, Département de Physique, Université de Sidi Bel Abbes, Algeria; (8) Mohammed Sh Alhodaly: Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.

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