A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions

Mohamed Rabhi , Kouider Halim Benrahou , Abdelhakim Kaci , Mohammed Sid Ahmed Houari , Fouad Bourada , Abdelmoumen Anis Bousahla , Abdeldjebbar Tounsi , E.A. Adda Bedia , S.R. Mahmoud , Abdelouahed Tounsi

Abstract

In this study a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions. The key feature of this theoretical formulation is that, in addition to considering shear deformation effect, it has only three unknowns in the displacement field as in the case of the classical plate theory (CPT), contrary to five as in the first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Material characteristics of the sandwich plate faces are considered to vary within the thickness direction via an exponential law distribution as a function of the volume fractions of the constituents. Equations of motion are obtained by employing Hamilton\'s principle. Numerical results for buckling and free vibration analysis of exponentially graded sandwich plates under various boundary conditions are obtained and discussed. Verification studies confirmed that the present three -unknown shear deformation theory is comparable with higher-order shear deformation theories which contain a greater number of unknowns.

Key Words

functionally graded materials; sandwich plates; a 3-unknown theory; various boundary conditions; elastic; foundations; free vibration; buckling loads

Address

Mohamed Rabhi, Kouider Halim Benrahou and Abdeldjebbar Tounsi — Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria
Abdelhakim Kaci — 1.)Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria 2.) Department of Civil and Hydraulic Engineering, Dr Tahar Moulay University, Faculty of Technology, BP 138 Cite En-Nasr 20000, Saida, Algeria
Mohammed Sid Ahmed Houari — Faculty of Science and Technology, Mascara University, Mascara 29000, Algeria
Fouad Bourada — 1.) Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria 2.) Department of Science and Technology, Tissemsilt University Center, BP 38004 Ben Hamouda, Algeria
Abdelmoumen Anis Bousahla — Multi-scale Modeling and Simulation Laboratory, University of Sidi Bel Abbes, Algeria
E.A. Adda Bedia — Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
S.R. Mahmoud — GRC Department, Jeddah Community College, King Abdulaziz University, Jeddah, Saudi Arabia
Abdelouahed Tounsi — 1.) Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria 2.) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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