Influence of micromechanical models on the bending response of bidirectional FG beams under linear, uniform, exponential and sinusoidal distributed loading

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

Abstract

This paper investigates the effect of micromechanical models on the bending behavior of bidirectional functionally graded (BDFG) beams subjected to different mechanical loading. The material properties of the beam are considered to be graded in both axial and thickness directions according to a power law. The beam's behavior is modeled by the mean of quasi 3D displacement field that contain undetermined integral terms and involves a reduced unknown functions. Navier's method is employed to determine and compute the displacements and stress for a simply supported beam. Different homogenization schemes such as Voigt, Reus, and Mori-Tanaka are employed to analyze the response of the BDFG beam subjected to linear, uniform, exponential and sinusoidal distributed loading. The results obtained by the present method are compared with available results in the literature and a good agreement was found. Several numerical results are presented in tabular form and in figures to examine the effects of the material gradation, micromechanical models and types of loading on the bending response of BDFG beams. It can be concluded that the present theory is not only accurate but also simple in predicting the bending response of BDFG beam subjected to different static loads.

Key Words

BDFG beams; quasi-3D model; bending; micromechanical models; different loading; displacements; stress

Address

Abdeljalil Meksi — Departement of Civil engineering, Faculty of architecture and civil engineering, University of sciences and technology Mohamed Boudiaf, Oran, Algeria
Samir Benyoucef and Mohamed Sekkal — Material and Hydrology Laboratory, University of SidiBel Abbes, Faculty of Technology, Algeria
Rabbab Bachir Bouiadjra — Material and Hydrology Laboratory, University of SidiBel Abbes, Faculty of Technology, Algeria; Departement of Civil Engineering, University Mustapha Stambouli of Mascara, Algeria
Mahmoud M. Selim — 4Department 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 SidiBel Abbes, Faculty of Technology, 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
Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

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