Advanced shear deformation theory for bending analysis of porous multidirectional functionally graded nanobeams
Ali Alnujaie,Ahmed A. Daikh,Amin Sami Hamdi,Azza M. Abdraboh,Amr E. Assie,Mohamed A Eltaher,Alaa A. Abdelrhmaan
Abstract
This study presents a comprehensive analytical investigation of the static bending behavior of functionally graded (FG) porous nanobeams incorporating size-dependent effects based on nonlocal strain gradient elasticity theory. A unified quasi-3D formulation with three displacement variables is developed, accounting for thickness stretching and higher-order shear deformation effects. The material properties are assumed to vary smoothly in both axial and transverse directions following power-law distributions, while different porosity patterns (even, uneven I, and uneven II) are considered to capture realistic material degradation. Three grading configurations, namely FG-2D, FG-T, and FG-A, are examined under various loading conditions (sinusoidal, uniform, and linear) and boundary constraints. The governing equations are derived using Hamilton's principle and solved via Galerkin's method. The influence of nonlocal parameter, length-scale parameter, porosity coefficient, and gradation indices on deflection and stress responses is systematically analyzed. The results reveal strong size-dependent behavior, where nonlocal effects tend to soften the structure while strain gradient effects introduce stiffness enhancement. Moreover, porosity significantly increases deflection and stress levels, while FG-A and FG-T configurations exhibit distinct stiffness characteristics compared to FG-2D. The proposed model demonstrates high accuracy, efficiency, and versatility in capturing the mechanical response of porous FG nanobeams.
Ali Alnujaie — Department of Mechanical Engineering, College of Engineering and Copmuter Sciences, Jazan University, Jazan, Saudi Arabia/ Engineering and Technology Research Center, P.O. Box 114, Jazan 82817, Saudi Arabia
Ahmed A. Daikh — Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, University Centre of Naama, Naama 45000, Algeria
Amin Sami Hamdi — Department of Civil Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
Azza M. Abdraboh — Physics Department, Faculty of Science, Benha University, Benha, Egypt
Amr E. Assie — Department of Mechanical Engineering, College of Engineering and Copmuter Sciences, Jazan University, Jazan, Saudi Arabia
Mohamed A Eltaher — Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia/ Mechanical Design & Production Department, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt
Alaa A. Abdelrhmaan — Mechanical Design & Production Department, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt/ Jeddah International College (JIC), Jeddah, Saudi Arabia
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