Free vibration analysis of Bi-Directional Functionally Graded Beams using a simple and efficient finite element model

Zakaria Belabed, Abdeldjebbar Tounsi, Abdelmoumen Anis Bousahla, Abdelouahed Tounsi, Mohamed Bourada and Mohammed A. Al-Osta

Abstract

This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

Key Words

bi-directional functionally graded beam; exponential power-law; finite element formulation; free vibration; higher-order shear deformation theory

Address

Zakaria Belabed: Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, Institute of Technology, University Center of Naama, BP 66, 45000 Naama, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Abdeldjebbar Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Industrial Engineering and Sustainable Development Laboratory, University of Rélizane, Algeria Abdelmoumen Anis Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, Faculty of Science & Technology, Mechanical Engineering Department, Université de Sidi Bel Abbés, Algeria Abdelouahed Tounsi: Department of Civil and Environmental Engineering, Lebanese American University, 309 Bassil Building, Byblos, Lebanon; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia Mohamed Bourada: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Mohammed A. Al-Osta: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia; Interdisciplinary Research Center for Construction and Building Materials, KFUPM, 31261 Dhahran, Saudi Arabia

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