Application of Generalized Finite Difference Method for Nonlinear Analysis of the Electrothermal Micro-Actuator.

In this work, the generalized finite difference method (GFDM), a popular meshless numerical method, is employed for predicting the thermal and mechanical behavior of an electrothermal micro-actuator. Based on the concept of GFDM and discretization on the computational domain, the discrete forms of the thermal and mechanical governing equations are derived, respectively. With the help of the incremental load method, the discrete form from the electrothermal analysis is solved precisely and the temperature distribution is obtained. Meanwhile, combining this approach with the discrete control equation derived from the natural boundary condition, its displacement is also evaluated. The convergence of the temperature by different iterative methods is tested and compared. The computational stability and efficiency (CPU time) in these two analyses are also given in this study. To further investigate the accuracy of the solutions, experiments to capture temperature and FEM analysis are conducted. Regardless of the imperfect boundary condition, the temperature distribution calculated by the GFDM shows great agreement with that obtained by experiment and FEM. A similar phenomenon can be also found in the comparison between the displacements evaluated by the GFDM and FEM, respectively.