A quasi 3D solution for thermodynamic response of FG sandwich plates lying on variable elastic foundation with arbitrary boundary conditions

Rabbab Bachir Bouiadjra , Abdelkader Mahmoudi , Mohamed Sekkal , Samir Benyoucef , Mahmoud M. Selim , Abdelouahed Tounsi , Muzamal Hussain

Abstract

In this paper, an analytical solution for thermodynamic response of functionally graded (FG) sandwich plates resting on variable elastic foundation is performed by using a quasi 3D shear deformation plate theory. The displacement field used in the present study contains undetermined integral terms and involves only four unknown functions with including stretching effect. The FG sandwich plate is considered to be subject to a time harmonic sinusoidal temperature field across its thickness with any combined boundary conditions. Equations of motion are derived from Hamilton's principle. The numerical results are compared with the existing results of quasi-3D shear deformation theories and an excellent agreement is observed. Several numerical examples for fundamental frequency, deflection, stress and variable elastic foundation parameter's analysis of FG sandwich plates are presented and discussed considering different material gradients, layer thickness ratios, thickness-to-length ratios and boundary conditions. The results of the present study reveal that the nature of the elastic foundation, the boundary conditions and the thermodynamic loading affect the response of the FG plate especially in the case of a thick plate.

Key Words

different boundary conditions; FG thick sandwich plates; Quasi-3D solution; thermodynamic loading; variable elastic foundation

Address

Rabbab Bachir Bouiadjra — Department of Civil Engineering, University Mustapha Stambouli of Mascara, Algeria/ Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Abdelkader Mahmoudi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria/Department of Science and Technology, Faculty of Science and Technology, University of Adrar, Algeria
Mohamed Sekkal — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Samir Benyoucef — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Mahmoud M. Selim — Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Aflaj, 710-11912, Saudi Arabia
Abdelouahed Tounsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria/YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea/ Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia/ Interdisciplinary Research Center for Construction and Building Materials, KFUPM, Dhahran, Saudi Arabia
Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

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