A hybrid finite element strategy for the simulation of MEMS structures

This work describes the development of a hybrid finite element strategy for modeling the nonlinear, strongly coupled electromechanical equations governing micro-electro-mechanical systems (MEMS) structures in general and the phenomena of static and dynamic pull-in exhibited by such structures in particular. It is known that conventional finite elements lock' severely for thin plate or shell-type structures (which is typical of geometries that occur in microsystems). The developed hybrid finite element formulation is based on a two-field variational formulation and involves an independent interpolation of the displacement and stress fields. In a conventional structural analysis, it is known that hybrid finite elements are much more immune to volumetric, shear, and membrane locking compared with conventional elements. This work extends the hybrid finite element method to the analysis of MEMS structures. Such an extension is not straightforward due to the strong coupling with the electric field variables. The formulation is based on a total Lagrangian description and is monolithic. This combination of the hybrid strategy and the monolithic scheme results in very good coarse-mesh accuracy and quadratic convergence both within the context of the static and transient formulations that have been developed. Numerous examples from the literature are considered to demonstrate the high efficacy of the developed method. Copyright (c) 2015 John Wiley & Sons, Ltd.

[1]  S. Chaterjee,et al.  A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams , 2009 .

[2]  C. S. Jog,et al.  Energy-momentum conserving algorithm for nonlinear transient analysis within the framework of hybrid elements , 2009 .

[3]  C. S. Jog,et al.  A 27-node hybrid brick and a 21-node hybrid wedge element for structural analysis , 2005 .

[4]  Jacob K. White,et al.  An efficient numerical technique for electrochemical simulation of complicated microelectromechanical structures , 1997 .

[5]  Daniel Rixen,et al.  Non-conforming element for accurate modelling of MEMS , 2007 .

[6]  Narayana R Aluru,et al.  A reproducing kernel particle method for meshless analysis of microelectromechanical systems , 1999 .

[7]  Gang Li,et al.  Efficient mixed-domain analysis of electrostatic MEMS , 2003, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[8]  Daniel Rixen,et al.  Monolithic modelling of electro‐mechanical coupling in micro‐structures , 2006 .

[9]  Han Yan,et al.  Electrostatic pull-in instability in MEMS/NEMS: A review , 2014 .

[10]  Jacob K. White,et al.  A multilevel Newton method for mixed-energy domain simulation of MEMS , 1999 .

[11]  Ray W. Ogden,et al.  Nonlinear Electroelastic Deformations , 2006 .

[12]  Anshul Gupta,et al.  WSMP: Watson Sparse Matrix Package Part II - direct solution of general systems Version 15.01 , 2015 .

[13]  Ole Sigmund,et al.  A monolithic approach for topology optimization of electrostatically actuated devices , 2008 .

[14]  D. Rixen,et al.  Electrostatic coupling of MEMS structures: transient simulations and dynamic pull-in , 2005 .

[15]  Jacob K. White,et al.  A relaxation/multipole-accelerated scheme for self-consistent electromechanical analysis of complex 3-D microelectromechanical structures , 1993, Proceedings of 1993 International Conference on Computer Aided Design (ICCAD).

[16]  S. Senturia,et al.  Self-consistent simulation and modelling of electrostatically deformed diaphragms , 1994, Proceedings IEEE Micro Electro Mechanical Systems An Investigation of Micro Structures, Sensors, Actuators, Machines and Robotic Systems.

[17]  C. S. Jog,et al.  Non‐linear analysis of structures using high performance hybrid elements , 2006 .

[18]  M. Rahman and S. Chowdhury.  A Highly Accurate Closed-Form Model for Pull-in Voltage of Circular Diaphragms under Large Deflection , 2009 .

[19]  P. A. Voltairas,et al.  A theoretical study of the hyperelasticity of electro‐gels , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[20]  Paul Steinmann,et al.  On 3-D coupled BEM–FEM simulation of nonlinear electro-elastostatics , 2012 .

[21]  C. S. Jog,et al.  Improved hybrid elements for structural analysis , 2010 .

[22]  J. Funk,et al.  New convergence scheme for self-consistent electromechanical analysis of iMEMS , 1995, Proceedings of International Electron Devices Meeting.

[23]  J. C. Nadeau,et al.  Invariant Tensor-to-Matrix Mappings for Evaluation of Tensorial Expressions , 1998 .

[24]  S.K. De,et al.  Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS , 2004, Journal of Microelectromechanical Systems.

[25]  Raj K. Gupta,et al.  Electrostatic pull-in test structure design for in-situ mechanical property measurements of microelectromechanical systems (MEMS) , 1997 .