Analysis of electrostatic MEMS using meshless local Petrov-Galerkin (MLPG) method

Romesh C. Batra, Maurizio Porfiri, Davide Spinello

Research output: Contribution to journalArticle

Abstract

We analyze electrostatic deformations of rectangular, annular circular, solid circular, and elliptic micro-electromechanical systems (MEMS) by modeling them as elastic membranes. The nonlinear Poisson equation governing their deformations is solved numerically by the meshless local Petrov-Galerkin (MLPG) method. A local symmetric augmented weak formulation of the problem is introduced, and essential boundary conditions are enforced by introducing a set of Lagrange multipliers. The trial functions are constructed by using the moving least-squares approximation, and the test functions are chosen from a space of functions different from the space of trial solutions. The resulting nonlinear system of equations is solved by using the pseudoarclength continuation method. Presently computed values of the pull-in voltage and the maximum pull-in deflection for the rectangular and the circular MEMS are found to agree very well with those available in the literature; results for the elliptic MEMS are new.

Original languageEnglish (US)
Pages (from-to)949-962
Number of pages14
JournalEngineering Analysis with Boundary Elements
Volume30
Issue number11
DOIs
StatePublished - Nov 2006

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Meshless Local Petrov-Galerkin Method
Galerkin methods
Micro-electro-mechanical Systems
Electrostatics
MEMS
Elliptic Systems
Least squares approximations
Moving Least-squares Approximation
Nonlinear Systems of Equations
Continuation Method
Weak Formulation
Lagrange multipliers
Poisson equation
Test function
Set theory
Poisson's equation
Deflection
Nonlinear systems
Nonlinear Equations
Membrane

Keywords

  • Meshless method
  • Micro-electromechanical systems
  • Pseudoarclength continuation method
  • Pull-in instability

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

Cite this

Analysis of electrostatic MEMS using meshless local Petrov-Galerkin (MLPG) method. / Batra, Romesh C.; Porfiri, Maurizio; Spinello, Davide.

In: Engineering Analysis with Boundary Elements, Vol. 30, No. 11, 11.2006, p. 949-962.

Research output: Contribution to journalArticle

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N2 - We analyze electrostatic deformations of rectangular, annular circular, solid circular, and elliptic micro-electromechanical systems (MEMS) by modeling them as elastic membranes. The nonlinear Poisson equation governing their deformations is solved numerically by the meshless local Petrov-Galerkin (MLPG) method. A local symmetric augmented weak formulation of the problem is introduced, and essential boundary conditions are enforced by introducing a set of Lagrange multipliers. The trial functions are constructed by using the moving least-squares approximation, and the test functions are chosen from a space of functions different from the space of trial solutions. The resulting nonlinear system of equations is solved by using the pseudoarclength continuation method. Presently computed values of the pull-in voltage and the maximum pull-in deflection for the rectangular and the circular MEMS are found to agree very well with those available in the literature; results for the elliptic MEMS are new.

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