Buckling of Doubly Clamped Nano-Actuators in General form Through Spectral Meshless Radial Point Interpolation (SMRPI)

Abstract

The present paper is devoted to the development of a kind of spectral meshless radial point interpolation (SMRPI) technique in order to obtain a reliable approximate solution for buckling of nano-actuators subject to different nonlinear forces. To end this aim, a general type of the governing equation for nano-actuators, containing integro-differential terms and nonlinear forces is considered. This general type for the nano-actuators is a non-linear fourth-order Fredholm integro-differential boundary value problem. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. In the current work, the thin plate splines (TPSs) are used as radial basis functions. This numerical based technique enables us to overcome all kind of nonlinearities in the mentioned boundary value problem and then to obtain fast convergent solution. Thus, it can facilitate the design of nano-actuators.