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Keywords:

  • micro beam;
  • finite element;
  • pull-in;
  • electrostatic

ABSTRACT

We establish the deflection functions of electrostatically actuated micro beams by an approximate finite element method (AFEM), in which the beam and the electrostatic load are discretized. The beam is replaced with a series of beam elements by traditional FEM. Using the total differential of the distributed electrostatic force, we represent such a force with the nodal forces on the beam elements. We calculate the deformation curve of the beam by gradually loading voltage in small increments, and pull-in behavior is identified when the convergence of the deflection iteration cannot be achieved after voltage increment. The proposed method considers the effect of deformation on stiffness by establishing a new equivalent stiffness matrix for each voltage step based on of the results of previous steps. Through this approach, we prevent the approximate errors of the stiffness matrix from accumulating. The AFEM results on micro beams with different geometries indicate good agreement with those obtained by other studies and those derived using commercial FE software. Copyright © 2013 John Wiley & Sons, Ltd.