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Structural Engineering and Mechanics Volume 86, Number 3, May10 2023 , pages 291-309 DOI: https://doi.org/10.12989/sem.2023.86.3.291 |
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Formulation and evaluation a finite element model for free vibration and buckling behaviours of functionally graded porous (FGP) beams |
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Abdelhak Mesbah, Zakaria Belabed, Khaled Amara, Abdelouahed Tounsi, Abdelmoumen A. Bousahla and Fouad Bourada
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| Abstract | ||
| This paper addresses the finite element modeling of functionally graded porous (FGP) beams for free vibration and buckling behaviour cases. The formulated finite element is based on simple and efficient higher order shear deformation theory. The key feature of this formulation is that it deals with Euler-Bernoulli beam theory with only three unknowns without requiring any shear correction factor. In fact, the presented two-noded beam element has three degrees of freedom per node, and the discrete model guarantees the interelement continuity by using both C0 and C1 continuities for the displacement field and its first derivative shape functions, respectively. The weak form of the governing equations is obtained from the Hamilton principle of FGP beams to generate the elementary stiffness, geometric, and mass matrices. By deploying the isoparametric coordinate system, the derived elementary matrices are computed using the Gauss quadrature rule. To overcome the shear-locking phenomenon, the reduced integration technique is used for the shear strain energy. Furthermore, the effect of porosity distribution patterns on the free vibration and buckling behaviours of porous functionally graded beams in various parameters is investigated. The obtained results extend and improve those predicted previously by alternative existing theories, in which significant parameters such as material distribution, geometrical configuration, boundary conditions, and porosity distributions are considered and discussed in detailed numerical comparisons. Determining the impacts of these parameters on natural frequencies and critical buckling loads play an essential role in the manufacturing process of such materials and their related mechanical modeling in aerospace, nuclear, civil, and other structures. | ||
| Key Words | ||
| buckling; finite element method; free vibration; functionally graded porous (FGP) beams; shear deformation beam theory; two-noded isoparametric finite element | ||
| Address | ||
| Abdelhak Mesbah: Smart Structures Laboratory, Faculty of Science & Technology, Civil Engineering Department, University of Ain Témouchent, Po Box 284, 46000 Ain-Temouchent, Algeria Zakaria Belabed: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Technology, Institute of Science and Technology, Naama University Center, BP 66, 45000 Naama, Algeria Khaled Amara: Engineering and Sustainable Development Laboratory, University of Ain Temouchent, Ain Temouchent 46000, Algeria Abdelouahed Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabi; YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea Abdelmoumen A. Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, University of Sidi Bel Abbés, Algeria Fouad Bourada: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Département des Sciences et de la Technologie, Université de Tissemsilt, BP 38004 Ben Hamouda, Algérie | ||