A Novel Differential Quadrature Galerkin Method for Dynamic and Stability Behaviour of Bi-directional Functionally Graded Porous Micro Beams

Authors

  • Ahmed Saimi IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria https://orcid.org/0000-0002-3722-2526
  • Ismail Bensaid IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria https://orcid.org/0000-0003-4316-0648
  • Besma Khouani IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria
  • Med Yassin Mazari IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria
  • Ihab Eddine Houalef IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria
  • Abdelmadjid Cheikh IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria

DOI:

https://doi.org/10.13052/ejcm2642-2085.3244

Keywords:

DQGM, 2D-FG microbeam, porosity, couple stress, Vibration and buckling

Abstract

The free vibration and buckling behaviours of 2D-FG porous microbeams are explored in this paper utilizing the Quasi-3D beam deformation theory based on the modified couple stress theory and a Differential Quadrature Galerkin Method (DQGM) systematically, as a combination of the Differential Quadrature Method (DQM) and the semi-analytical Galerkin method, which has used to reduce computational cost for problems in dynamics. The governing equations are obtained using the Lagrange’s principle. The mass and stiffness matrices are calculated using the weighting coefficient matrices given by the differential quadrature (DQ) and Gauss-Lobatto quadrature rules. The matrices are expressed in a similar form to that of the Differential Quadrature Method by introducing an interpolation basis on the element boundary of the Galerkin method. The sampling points are determined by the Gauss-Lobatto node method. The influence of the thickness-to-material length scale parameter (MLSP) on the nondimensional natural frequencies and nondimensional critical buckling loads of 2D-FG porous microbeams are investigated, along with the effects of the boundary condition, aspect ratio and gradient index. The results are validated with literature to establish the accuracy of the procedure described. This work will provide a numerical basis for the design of FG microstructures in the field of micromechanics. These results can be applied to the engineering design of porous FG microstructures.

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Author Biographies

Ahmed Saimi, IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria

Ahmed Saimi obtained his Ph.D in Mechanics of Materials and Structures from the University of Tlemcen, Algeria, in 2017. He is currently a Senior Lecturer at the National High School of Hydraulics Blida, Algeria. A researcher member of Mechanical Systems and Structural Engineering Laboratory, IS2M/UABT. His research interests are: Finite element methods, Structural vibration, Structural dynamics, Dynamics of rotors, Dynamics of rotating machines, computational mechanics, FG materials, Composite materials.

Ismail Bensaid, IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria

Ismail Bensaid received his B.Sc, M.Sc and Ph.D degrees in Mechanical Engineering from Abou Beckr Belkaid University Tlemcen, Algeria. He is currently working in the level of the Mechanical engineering department at the same University. Dr. Bensaid does research in Mechanical and structural Engineering, Materials, Composite, Maintenance, Nanostructures and Dynamical Systems. He, as an author/co-author, has published more than 18 articles in various journals.

Besma Khouani, IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria

Besma Khouani, Ph.D student in Mechanical Engineering from Abou Beckr Belkaid University Tlemcen, Algeria. He is currently working in the level of the Mechanical engineering department at the same University. Mechanical and structural Engineering, Materials, Composite, Maintenance, Nanostructures and Dynamical Systems.

Med Yassin Mazari, IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria

Med Yassin Mazari, Ph.D student in Mechanical Engineering from Abou Beckr Belkaid University Tlemcen, Algeria. He is currently working in the level of the Mechanical engineering department at the same University. Mechanical and structural Engineering, Materials, Composite, Maintenance, Nanostructures and Dynamical Systems.

Ihab Eddine Houalef, IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria

Ihab Eddine Houalef, Ph.D student in Mechanical Engineering from Abou Beckr Belkaid University Tlemcen, Algeria. He is currently working in the level of the Mechanical engineering department at the same University. Mechanical and structural Engineering, Materials, Composite, Maintenance, Nanostructures and Dynamical Systems.

Abdelmadjid Cheikh, IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria

Abdelmadjid Cheikh obtained his PhD in production engineering and production management from the University of Nottingham, United Kingdom. He is currently a professor at the University of Tlemcen, Algeria (UABT). He also holds the position of Research Director in Mechanical Systems and Materials Engineering Laboratory (IS2M/UABT). His research interests are: Materials Engineering, Manufacturing Engineering, CAD/CAM, Computer Aided Tolerancing, Rapid Prototyping Processes, CNC Machining, 3D Printing, Optimization.

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Published

2023-11-04

How to Cite

Saimi, A. ., Bensaid, I. ., Khouani, B. ., Mazari, M. Y. ., Houalef, I. E. ., & Cheikh, A. . (2023). A Novel Differential Quadrature Galerkin Method for Dynamic and Stability Behaviour of Bi-directional Functionally Graded Porous Micro Beams. European Journal of Computational Mechanics, 32(04), 393–440. https://doi.org/10.13052/ejcm2642-2085.3244

Issue

2023: Vol 32 Iss 4

Section

Advanced Computational Modelling of Composite Materials