Numerical and analytical approximations to large post-buckling deformation of MEMS

This paper analyzes the electromechanical post-buckling response of an axially stressed clamped–clamped beam actuator subjected to a symmetric electrostatic field. Numerical solutions of the nonlinear integral–differential governing equation are first obtained by constructing the extended systems and applying the shooting method. The corresponding analytical approximate solutions are then established by combining Newtonʹs linearization with Galerkinʹs method. In contrast to the classical Galerkinʹs method, the linearization is performed prior to its application. This yields a set of linear algebraic equations instead of nonlinear algebraic equations, and hence analytical approximate solutions are established. These analytical approximate solutions show excellent agreement with numerical solutions from the shooting method, and they are valid for a wide range of beam-center deflection. The analytical approximate method presented here is simple in principle and it is easy to be implemented with the help of any symbolic computational software.