Combined effects of partial loading and partial elastic foundation on the bending response of functionally graded structures

Abderrahmane Menasria , Nabil Himeur , Abdelhakim Bouhadra , Messaoud Bazzouzi , Abdelouahed Tounsi

Abstract

This study uniquely investigates functionally graded nanoplates under combined partial loading and nonuniform elastic support, developing a quasi-3D model, a unified analytical framework for complex foundations, and novel closed-form solutions, thereby addressing a critical yet underexplored area in structural mechanics. A simplified quasi-3D high-order shear deformation theory incorporating integral terms is used. The governing equilibrium equations consider the interaction between the loading type and the variation of Winkler-Pasternak and Kerr foundation parameters. The numerical results for non-dimensional stresses and displacements are obtained using the virtual displacement principle and Navier's solution technique. The accuracy of the non-dimensional formulas is validated against existing literature, demonstrating excellent agreement. Additionally, several parametric studies examine the effects of various geometric and material factors. This analytical model is well suited for analyzing the bending behaviour of simply supported FG plates in specific engineering applications.

Key Words

elastic bending; FG nanoplates; Navier solution; partial foundation; partial loads; quasi-3D theory

Address

Abderrahmane Menasria — Civil Engineering Department, Faculty of Sciences and Technology, University of Khenchela, BP 1252 Road of Batna, Khenchela 40000, Algeria; Materials and Hydrology Laboratory, University of Sidi Bel Abbes, BP 89, Sidi Bel Abbes, 22000, Algeria
Nabil Himeur — Mechanical Engineering Department, Faculty of Sciences and Technology, University of Khenchela, BP 1252 Road of Batna, Khenchela 40000, Algeria; Laboratory of Engineering and Sciences of Advanced Materials, BP 1252 Road of Batna, Khenchela 40000, Algeria
Abdelhakim Bouhadra — Civil Engineering Department, Faculty of Sciences and Technology, University of Khenchela, BP 1252 Road of Batna, Khenchela 40000, Algeria; Materials and Hydrology Laboratory, University of Sidi Bel Abbes, BP 89, Sidi Bel Abbes, 22000, Algeria
Messaoud Bazzouzi — Civil Engineering Department, Faculty of Sciences and Technology, University of Khenchela, BP 1252 Road of Batna, Khenchela 40000, Algeria; Laboratory of Research in Civil Engineering (LRGC), University of Biskra, BP14507000 Biskra, Algeria
Abdelouahed Tounsi — Laboratory of Engineering and Sciences of Advanced Materials, BP 1252 Road of Batna, Khenchela 40000, Algeria; Laboratory of Research in Civil Engineering (LRGC), University of Biskra, BP14507000 Biskra, Algeria

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