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Nonlocal strain gradient finite element analysis of nanobeams using two-variable trigonometric shear deformation theory |
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| Authors: | Merzouki Tarek Houari Mohammed Sid Ahmed Haboussi Mohamed Bessaim Aicha Ganapathi Manickam |
| Affiliation: | 1.LISV, University of Versailles Saint-Quentin, 10-12 Avenue de l’Europe, 78140, Vélizy-Villacoublay, France ;2.Laboratoire d’Etude des Structures et de Mécanique des Matériaux, University Mustapha Stambouli of Mascara, Mascara, Algeria ;3.Laboratoire des Sciences des Procédés et des Matériaux (LSPM), CNRS UPR 3407, Université Paris 13, Sorbonne-Paris-Cité, 93430, Villetaneuse, France ;4.School of Mechanical Engineering, VIT University, Vellore, 632 014, India ; |
| Abstract: | In the present paper, a new trigonometric two-variable shear deformation beam nonlocal strain gradient theory is developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending, buckling and free vibration analysis of nanobeams. The model introduces a nonlocal stress field parameter and a length scale parameter to capture the size effect. The governing equations derived are solved employing finite element method using a 3-nodes beam element, developed for this purpose. The predictive capability of the proposed model is shown through illustrative examples for bending, buckling and free vibration of nanobeams. Comparisons with other higher-order shear deformation beam theory are also performed to validate its numerical implementation and assess its accuracy within the nonlocal context. |
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