Bending analysis of porous microbeams based on the modified strain gradient theory including stretching effect

Lemya Hanifi Hachemi Amar, Abdelhakim Kaci, Aicha Bessaim, Mohammed Sid Ahmed Houari and Abdelouahed Tounsi

Abstract

In this paper, a quasi-3D hyperbolic shear deformation theory for the bending responses of a functionally graded (FG) porous micro-beam is based on a modified couple stress theory requiring only one material length scale parameter that can capture the size influence. The model proposed accounts for both shear and normal deformation effects through an illustrative variation of all displacements across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-beam. The effective material properties of the functionally graded micro-beam are assumed to vary in the thickness direction and are estimated using the homogenization method of power law distribution, which is modified to approximate the porous material properties with even and uneven distributions of porosity phases. The equilibrium equations are obtained using the virtual work principle and solved using Navier's technique. The validity of the derived formulation is established by comparing it with the ones available in the literature. Numerical examples are presented to investigate the influences of the power law index, material length scale parameter, beam thickness, and shear and normal deformation effects on the mechanical characteristics of the FG micro-beam. The results demonstrate that the inclusion of the size effects increases the microbeams stiffness, which consequently leads to a reduction in deflections. In contrast, the shear and normal deformation effects are just the opposite.

Key Words

functionally graded micro-beam; material length scale parameter; modified couple stress theory; porosity; shear and normal deformation effects

Address

Lemya Hanifi Hachemi Amar: Ecole Nationale Supérieure d'Ingénieurs de Bretagne Sud, Institut de Recherche Dupuy de Lôme (IRDL), UMR CNRS 6027, Centre de Recherche, Rue de Saint Maudé-BP 92116, 56321 Lorient Cedex, France; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria Abdelhakim Kaci: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria; Faculté de Technologie, Département de Génie Civil et Hydraulique, Université de Saida Dr. Tahar Moulay, BP 138 Cité En-Nasr 20000 Saida, 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 29000, Algérie 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 29000, Algérie Abdelouahed Tounsi: Faculté de Technologie, Département de Génie Civil et Hydraulique, Université de Saida Dr. Tahar Moulay, BP 138 Cité En-Nasr 20000 Saida, Algérie; YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Eastern Province, Saudi Arabia

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