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Imperfection sensitivity of the size-dependent postbuckling response of pressurized FGM nanoshells in thermal environments

Sahmani S., Aghdam M. M.

Archives of Civil and Mechanical Engineering

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2017

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Vol. 17, no. 3

623--638

EN

The purpose of the current study is to address the nonlinear buckling and postbuckling response of nanoscaled cylindrical shells made of functionally graded material (FGM) under hydrostatic pressure aiming to investigate the sensitivity to the initial geometric imperfection in the presence of surface effects and thermal environments. According to a power law distribution, the material properties of the FGM nanoshell are considered change through the shell thickness. Also, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account to eliminate the stretching-bending coupling terms. In order to acquire the size effect qualitatively, the well-known Gurtin-Murdoch elasticity theory is incorporated within the framework of the classical shell theory. Using the variational approach, the non-classical governing equations are displayed and deduced to boundary layer type ones. Afterwards, explicit expressions for the size-dependent radial postbuckling equilibrium paths of imperfect FGM nanoshells are proposed with the aid of a perturbation-based solution methodology. It is displayed that by moving from the ceramic phase to the metal one, the critical buckling pressure decreases, but the postbuckling stiffness increases, because in contrast to the ceramic phase, the surface modulus and residual surface stress associated with the metal phase have the same sign.

2

A mode-III crack with variable surface effects

Wang X., Schiavone P.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 4

1319--1327

EN

We study the contribution of variable surface effects to the antiplane deformation of a linearly elastic material with a mode-III crack. The surface elasticity is incorporated using a modified version of the continuum based surface/interface model of Gurtin and Murdoch. In our discussion, the surface moduli are not constant but vary along the crack surfaces. Using Green’s function method, the problem is reduced to a single first-order Cauchy singular integro-differential equation, which is solved numerically using Chebyshev polynomials and a collocation method. Our results indicate that the gradient of the surface shear modulus exerts a significant influence on the crack opening displacement and on the singular stress field at the crack tips.

3

The effect of surface elasticity on a Mode-III interface crack

Kim C. I., Schiavone P., Ru C.-Q.

Archives of Mechanics

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2011

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Vol. 63, nr 3

267-267

EN

We study the contribution of surface elasticity to the anti-plane deformations of a linearly elastic bi-material with Mode-III interface crack. The surface elasticity is incorporated using a version of the continuum-based surface/interface model of Gurtin and Murdoch. We obtain a complete semi-analytic solution valid throughout the solid (including the crack tips) via a Cauchy singular, integro-differential equation of the first kind. Our solution demonstrates that the surface elasticity on the crack face leads to finite stresses at the crack tips and stress discontinuities across the material interface.