Shear correction factors of a new exponential functionally graded porous beams

Mohammed Sid Ahmed Houari, Aicha Bessaim, Tarek Merzouki, Ahmed Amine Daikh, Aman Garg, Abdelouahed Tounsi, Mohamed A. Eltaher and Mohamed-Ouejdi Belarbi

Abstract

This article introduces a novel analytical model for examining the impact of porosity on shear correction factors (SCFs) in functionally graded porous beams (FGPB). The study employs uneven and logarithmic-uneven modified porositydependent power-law functions, which are distributed throughout the thickness of the FGP beams. Additionally, a modified exponential-power law function is used to estimate the effective mechanical properties of functionally graded porous beams. The correction factor plays a crucial role in this analysis as it appears as a coefficient in the expression for the transverse shear stress resultant. It compensates for the assumption that the shear strain is uniform across the depth of the cross-section. By applying the energy equivalence principle, a general expression for static SCFs in FGPBs is derived. The resulting expression aligns with the findings obtained from Reissner's analysis, particularly when transitioning from the two-dimensional case (plate) to the onedimensional case (beam). The article presents a convenient algebraic form of the solution and provides new case studies to demonstrate the practicality of the proposed formulation. Numerical results are also presented to illustrate the influence of porosity distribution on SCFs for different types of FGPBs. Furthermore, the article validates the numerical consistency of the mechanical property changes in FG beams without porosity and the SCF by comparing them with available results.

Key Words

functionally graded beam; modified exponential-power law function; porosity; shear correction factor; transverse shear

Address

Mohammed Sid Ahmed Houari: Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, Mascara, Algérie Aicha Bessaim: Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, Mascara, Algérie Tarek Merzouki: LISV, University of Versailles Saint-Quentin, 10-12 Avenue de l'Europe, 78140 V'elizy, France Ahmed Amine Daikh: Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, Mascara, Algérie; Department of Technology, University Centre of Naama, P.O.Box 66, 45000 Naama, Algeria Aman Garg: State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria 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, P.O. Box 44519, Zagazig 44519, Egypt Mohamed-Ouejdi Belarbi: Laboratoire de Recherche en Génie Civil, LRGC, Université de Biskra, B.P. 145, R.P. 07000, Biskra, Algeria; School of Engineering, Lebanese American University, Byblos, Lebanon

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