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http://dx.doi.org/10.12989/scs.2020.36.2.143

Bending behavior of squared cutout nanobeams incorporating surface stress effects  

Eltaher, Mohamed A (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University)
Abdelrahman, Alaa A. (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University)
Publication Information
Steel and Composite Structures / v.36, no.2, 2020 , pp. 143-161 More about this Journal
Abstract
In nanosized structures as the surface area to the bulk volume ratio increases the classical continuum mechanics approaches fails to investigate the mechanical behavior of such structures. In perforated nanobeam structures, more decrease in the bulk volume is obtained due to perforation process thus nonclassical continuum approaches should be employed for reliable investigation of the mechanical behavior these structures. This article introduces an analytical methodology to investigate the size dependent, surface energy, and perforation impacts on the nonclassical bending behavior of regularly squared cutout nanobeam structures for the first time. To do this, geometrical model for both bulk and surface characteristics is developed for regularly squared perforated nanobeams. Based on the proposed geometrical model, the nonclassical Gurtin-Murdoch surface elasticity model is adopted and modified to incorporate the surface energy effects in perforated nanobeams. To investigate the effect of shear deformation associated with cutout process, both Euler-Bernoulli and Timoshenko beams theories are developed. Mathematical model for perforated nanobeam structure including surface energy effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Closed forms for the nonclassical bending and rotational displacements are derived for both theories considering all classical and nonclassical kinematics and kinetics boundary conditions. Additionally, both uniformly distributed and concentrated loads are considered. The developed methodology is verified and compared with the available results and an excellent agreement is noticed. Both classical and nonclassical bending profiles for both thin and thick perforated nanobeams are investigated. Numerical results are obtained to illustrate effects of beam filling ratio, the number of hole rows through the cross section, surface material characteristics, beam slenderness ratio as well as the boundary and loading conditions on the non-classical bending behavior of perforated nanobeams in the presence of surface effects. It is found that, the surface residual stress has more significant effect on the bending deflection compared with the corresponding effect of the surface elasticity, Es. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams.
Keywords
surface stress effects; squared cutout nanobeams; filling ratio; shear deformation; nonclassical bending; closed forms;
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Times Cited By KSCI : 64  (Citation Analysis)
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87 Vinyas, M. and Kattimani, S.C. (2017e), "Static studies of stepped functionally graded magneto-electro-elastic beam subjected to different thermal loads", Compos. Struct., 163, 216-237. https://doi.org/10.1016/j.compstruct.2016.12.040.   DOI
88 Phung-Van, P., Tran, L.V., Ferreira, A.J.M., Nguyen-Xuan, H. and Abdel-Wahab, M. (2017a), "Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads", Nonlinear Dynam., 87(2), 879-894. https://doi.org/10.1007/s11071-016-3085-6.   DOI
89 Phung-Van, P., Ferreira, A.J.M., Nguyen-Xuan, H. and Wahab, M. A. (2017b), "An isogeometric approach for size-dependent geometrically nonlinear transient analysis of functionally graded nanoplates", Compos. Part B: Eng., 118, 125-134. https://doi.org/10.1016/j.compositesb.2017.03.012.   DOI
90 Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F. and Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. https://doi.org/10.12989/scs.2020.34.5.643.   DOI
91 Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695   DOI
92 Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457.   DOI
93 Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res, 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.   DOI
94 Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Bedia, E.A. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concrete, 25(2), 155-166. https://doi.org/10.12989/cac.2020.25.2.155.   DOI
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96 Romano, G., Barretta, R., Diaco, M. and de Sciarra, F.M. (2017), "Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams", Int. J. Mech. Sci., 121, 151-156. https://doi.org/10.1016/j.ijmecsci.2016.10.036.   DOI
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98 Vinyas, M. and Kattimani, S.C. (2018b), "Investigation of the effect of BaTiO3/CoFe2O4 particle arrangement on the static response of magneto-electro-thermo-elastic plates", Compos. Struct., 185, 51-64. https://doi.org/10.1016/j.compstruct.2017.10.073.   DOI
99 Phung-Van, P., Thai, C.H., Nguyen-Xuan, H. and Wahab, M.A. (2019), "Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis", Compos. Part B: Eng., 164, 215-225. https://doi.org/10.1016/j.compositesb.2018.11.036.   DOI
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