Modeling of Electro-Mechanical Coupling Problem using the Finite Element Formulation

Véronique Rochus, Daniel Rixen, Jean Claude Golinval

Research output: Contribution to journalConference articlepeer-review

9 Scopus citations


A modeling procedure is proposed to handle the strong electro-mechanical coupling appearing in micro-electro-mechanical systems (MEMS). The finite element method is used to discretize simultaneously the electrostatic and mechanical fields. The formulation is consistently derived from variational principles based on the electro-mechanical free energy. In classical weakly coupled formulations staggered iteration is used between the electrostatic and the mechanical domain. Therefore, in those approaches, linear stiffness is evaluated by finite differences and equilibrium is reached typically by relaxation techniques. The strong coupling formulation presented here allows to derive exact tangent matrices of the electro-mechanical system. Thus it allows to compute non-linear equilibrium positions using Newton-Raphson type of iterations combined with adaptive meshing in case of large displacements. Furthermore, the tangent matrix obtained in the method exposed in this paper greatly simplifies the computation of vibration modes and frequencies of the coupled system around equilibrium configurations. The non-linear variation of frequencies with respect to voltage and stiffness can be then be investigated until pull-in appears. In order to illustrate the effectiveness of the proposed formulation numerical results are shown first for the reference problem of a simple flexible capacitor, then for the model of a micro-bridge.

Original languageEnglish
Pages (from-to)349-360
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2003
Externally publishedYes
EventPROCEEDINGS OF SPIE SPIE - The International Society for Optical Engineering: Smart Structures and Materials 2003 Modeling, Signal Processing, and Control - San Diego, CA, United States
Duration: 3 Mar 20036 Mar 2003


  • Finite Element Method (FEM)
  • Micro-Electro-Mechanical Systems (MEMS)
  • Non-Linearity
  • Strong Electro-Mechanical Coupling


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