Analytic solution for the hygro-thermo-mechanical bending behaviour of FG nanoplates on nonlinear elastic foundations using a nonlocal Quasi-3D HSDT

Madiha Boussalem, Abdelhakim Bouhadra, Abderrahmane Menasria, Belgacem Mamen, Salah Refrafi, Abdelouahed Tounsi, Abdelmoumen Anis Bousahla and S.R. Mahmoud

Abstract

This study examines the hygro-thermo-mechanical bending of FG nanoplates supported by varying elastic foundations. It is expected that the thickness of the materials will change, and the formulation will take into account the effects of numerous power law distributions. To minimize the number of unknowns and account for the effects of stretching, the analyses employ a quasi-3D theory. By merging Eringen's theory for nonlocal integral elasticity with a quasi-3D high-order plate theory, the equilibrium equations are obtained while accounting for the nano-size effect. Two variable factors, each represented by multiple functions, are used to model the elastic basis on which the nanoplates rest. Navier's technique is used to solve the equations for the problem of a simply supported nanoplate, and the results are obtained. The FG nano-plate's bending response is thoroughly examined in relation to the volume fraction index k, geometric attributes, elastic foundation nano size coefficient, and various temperature rise profiles. The results are compared to those reported in the academic literature.

Key Words

bending; Eringen's theory; FG nanoplates; hygro-thermo-mechanical loads; nonlinear foundation

Address

Madiha Boussalem: Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela, Algeria; Laboratoire d'Ingénierie et Sciences des Matériaux Avancés, Abbes Laghrour University, Khenchela, Algeria Abdelhakim Bouhadra: Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Abderrahmane Menasria: Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Belgacem Mamen: Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Salah Refrafi: Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Abdelouahed Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia Abdelmoumen Anis Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria S.R. Mahmoud: GRC Department, Applied College, King Abdulaziz University, Jeddah 21589, Saudi Arabia

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