The geometrically nonlinear analysis of microswitches using the local meshfree method

Abstract

In the modelling and simulation of the microelectromechanical systems (MEMS) devices, for example the microswitch, the large deformation or the geometrical nonlinearity should be considered. Due to the issue of the mesh distortion, the finite element method (FEM) is not effective for this large deformation analysis. In this paper, a local meshfree formulation is developed for the geometrically nonlinear analysis of MEMS devices. The moving least square approximation (MLSA) is employed to construct the meshfree shape functions based on the arbitrary distributed field nodes and the spline weight function. The discrete system of equations for two-dimensional MEMS analysis is obtained using the weighted local weak-form, and based on the total Lagrangian (TL) approach, which refers all variables to the initial configuration. The Newton-Raphson iteration technique is used to get final results. Several typical microswitches are simulated by the developed nonlinear local meshfree method. Some important parameters of these microswitches, e.g., the pull-in voltage, are studied. Comparing with the experimental results and results obtained by the linear analysis, the nonlinear meshfree analysis of microswitches is accurate and efficient. It has demonstrated that the present nonlinear local meshfree formulation is very effective for the geometrically nonlinear analysis of the MEMS devices, because it totally avoids the issue of mesh distortion in FEM.