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A size-dependent finite element (FE) formulation including surface free energy effect is developed in this article to study the post-buckling behavior of nanofilms under the action of thermal loads. The Gurtin-Murdoch surface elasticity theory is utilized to consider the surface effects. Moreover, the principle of virtual work is used so as to derive the equilibrium equations. The proposed FE formulation is based on the first-order shear deformation theory (FSDT). The von Kármán nonlinear relations are also employed to take the geometric nonlinearity into account. After deriving the FE equations, the resulting set of parameterized non-linear equations is solved using the pseudo arc-length continuation algorithm, and bifurcation diagrams of nanofilms are obtained. Selected numerical results are presented for the influences of surface stress on the thermal post-buckling characteristics of nanofilms subject to different types of boundary conditions. [ABSTRACT FROM PUBLISHER]

The present study presents the effect of deformation and stress due to preloading on vibration of circular plates. The preloadings may be applied in the radial direction on edge or in the transverse direction on plate surface. The research features that, first, a unified displacement field for circular plates is employed; second, the formulation is based on elasticity and has fewer approximations or assumptions than plate theories; third and most noticeable, the analysis takes into account the deformation due to preloading, in addition to the stresses and shows that such deformation has significant effect on vibration of circular plates for some cases. [ABSTRACT FROM AUTHOR]