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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

2017

Vol. 17, no. 3

623--638

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.

Nonlinear interfacial instability of two electrified miscible fluids

Mahmoud Y. D., Moatimid G. M., El-Dib Y. O.

Mechanics and Mechanical Engineering

2000

Vol. 4, nr 2

225--249

In a previews paper [1], a simplified formulation was presented to deal with the intcrfacial linear stability problem with mass and heat transfer, considering the presence of a periodic electric field. The present paper treats the same problem with a nonlinear approach. This approach is achieved by considering the multiple time scale method. The analysis reveals the existence of both resonant and non - resonant cases. Three types of nonlinear Schődinger equations are derived . The necessary and sufficient stability of conditions in obtained and the results are confirmed numerically. Graphs are drawn to illustrate the stability regions.