Research PaperNo Access

Surface Effect on Static Bending of Functionally Graded Porous Nanobeams Based on Reddy’s Beam Theory

Jie Su

School of Mechanical Engineering, Tianjin University, Tianjin 300350, P. R. China

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Yang Xiang

School of Computing, Engineering and Mathematics, Western Sydney University, Penrith, NSW 2751, Australia

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Liao-Liang Ke

School of Mechanical Engineering, Tianjin University, Tianjin 300350, P. R. China

E-mail Address: llke@tju.edu.cn

Corresponding author.

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, and

Yue-Sheng Wang

School of Mechanical Engineering, Tianjin University, Tianjin 300350, P. R. China

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https://doi.org/10.1142/S0219455419500627Cited by:24 (Source: Crossref)

Abstract

In this paper, the surface effect on the static bending behavior of functionally graded porous (FGP) nanobeams subjected to a concentrated transverse load is studied by using Reddy’s higher-order beam theory. Three types of porosity distributions are considered for the nanobeam, i.e. uniform porosity distribution, symmetric and asymmetric non-uniform porosity distributions. With the consideration of the surface effect, the nanobeams can be abstracted as a composite beam composed of a surface layer and a bulk volume. According to the generalized Young–Laplace equation, the normal stress discontinuity across a surface due to the effect of surface stress is taken into consideration. The analytical solutions of the static bending problem of FGP nanobeams are obtained for the beams with hinged-hinged, clamped-clamped and clamped-free boundary conditions. The effects of the residual surface stress, porosity distribution type, porosity coefficient and length-to-thickness ratio on the transverse displacement of the FGP beams are discussed.

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