Strongly Coupled Finite Element Formulation of Electromechanical Systems with Integrated Mesh Morphing using Radial Basis Functions

Authors: D. Kriebel, J. E. Mehner

Abstract:

The paper introduces a method to efficiently simulate nonlinear changing electrostatic fields occurring in micro-electromechanical systems (MEMS). Large deflections of the capacitor electrodes usually introduce nonlinear electromechanical forces on the mechanical system. Traditional finite element methods require a time-consuming remeshing process to capture exact results for this physical domain interaction. In order to accelerate the simulation process and eliminate the remeshing process, a formulation of a strongly coupled electromechanical transducer element will be introduced which uses a combination of finite-element with an advanced mesh morphing technique using radial basis functions (RBF). The RBF allows large geometrical changes of the electric field domain while retain high element quality of the deformed mesh. Coupling effects between mechanical and electrical domains are directly included within the element formulation. Fringing field effects are described accurate by using traditional arbitrary shape functions.

Keywords: electromechanical, electric field, transducer, simulation, modeling, finite-element, mesh morphing, radial basis function

References:

[1] M. Kaltenbacher, Numerical Simulation of Mechatronic Sensors and Actuators: Finite Elements for Computational Multiphysics, 3rd ed. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015.
[Online]. Available: http://ebooks.ciando.com/book/index.cfm/bok_id/1868085
[2] S Mukhopadhyay and N. Majumdar, Use of the neBEM solver to Compute the 3D Electrostatic Properties of Comb Drives, 2007.
[Online]. Available: https://www.researchgate.net/publication/2177896_Use_of_the_neBEM_solver_to_Compute_the_3D_Electrostatic_Properties_of_Comb_Drives
[3] V. Rochus, D. J. Rixen, and J.-C. Golinval, “Monolithic modelling of electro-mechanical coupling in micro-structures,” Int. J. Numer. Meth. Engng., vol. 65, no. 4, pp. 461–493, 2006, doi: 10.1002/nme.1450.
[4] M. Gyimesi, I. Avdeev, and D. Ostergaard, “Finite-Element Simulation of Micro-Electromechanical Systems (MEMS) by Strongly Coupled Electromechanical Transducers,” IEEE Trans. Magn., vol. 40, no. 2, pp. 557–560, 2004, doi: 10.1109/TMAG.2004.824592.
[5] L. R. Herrmann, “Laplacian-Isoparametric Grid Generation Scheme,” J. Engrg. Mech. Div., vol. 102, no. 5, pp. 749–756, 1976, doi: 10.1061/JMCEA3.0002158.
[6] A. de Boer, M. S. van der Schoot, and H. Bijl, “Mesh deformation based on radial basis function interpolation,” Computers & Structures, vol. 85, 11-14, pp. 784–795, 2007, doi: 10.1016/j.compstruc.2007.01.013.
[7] M. E. Biancolini, “Mesh Morphing and Smoothing by Means of Radial Basis Functions (RBF),” in Advances in Computer and Electrical Engineering, Handbook of Research on Computational Science and Engineering, S. Patnaik, J. Leng, and W. Sharrock, Eds.: IGI Global, 2012, pp. 347–380.
[8] A. Beckert and H. Wendland, “Multivariate interpolation for fluid-structure-interaction problems using radial basis functions,” Aerospace Science and Technology, vol. 5, no. 2, pp. 125–134, 2001, doi: 10.1016/S1270-9638(00)01087-7.
[9] M. E. Biancolini, Ed., Fast Radial Basis Functions for Engineering Applications. Cham: Springer, 2018.