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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2016014205
pages 65-80

SIZE-DEPENDENT POSTBUCKLING OF ANNULAR NANOPLATES WITH DIFFERENT BOUNDARY CONDITIONS SUBJECTED TO THE AXISYMMETRIC RADIAL LOADING INCORPORATING SURFACE STRESS EFFECTS

R. Ansari
Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
V. Mohammadi
Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
M. Faghih Shojaei
Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
R. Gholami
Department of Mechanical Engineering, Lahijan Branch, Islamic Azad University, P.O. Box 1616, Lahijan, Iran

ABSTRACT

This paper addresses the problem of size-dependent axisymmetric postbuckling behavior of annular shear deformable nanoplates by taking into consideration surface effects. A size-dependent continuum plate model is developed based on the Gurtin−Murdoch elasticity theory, the first-order shear deformation theory, and the von Karman geometrically nonlinear relations. It is assumed that the annular nanoplate is subjected to compressive axisymmetric radial loads. By using the Gurtin−Murdoch theory, the influences of surface stress and residual surface stress are incorporated into the formulation. Afterward, according to the virtual work principle, the size-dependent geometrically nonlinear governing equations and associated boundary conditions of first-order shear deformable nanoplates are obtained. The obtained set of nonlinear equations is discretized and solved via the generalized differential quadrature method and pseudo-arc-length continuation method. Then, the postbuckling behavior of nanoplates made of silicon and aluminum with different boundary conditions is carefully studied. The results obtained from classical and non-classical theories are compared for the first three postbuckling modes. In addition, the effects of the surface elastic modulus, residual surface stress, thickness, and radius ratio on the postbuckling response of annular nanoplates are examined.


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