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Proceedings Paper

Nonlinear analysis of beams under electrostatic loads
Author(s): A. Gugliotta; Aurelio Soma; S. Di Mauro; F. De Bona; F. Roccaforte
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Paper Abstract

The aim of this work is that of evaluating the relative contribution of the different non-linearities in the simple case of slender cantilever beams and plates under electrostatic loads. This case not allows analytical solution to be achieved and therefore a numerical approach must be followed. Multipurpose commercial software do not feature simultaneous solution of electrostatic and structural problems. In this work a solution algorithm for the coupled electro-mechanical system to be implemented in a finite element commercial software is prosed. The solution follows a Newton iterative method in which the solution of the linear system is obtained through the biconjugate gradient stabilized method. This approach is compared with the already proposed relaxation scheme. The 2D case was firstly considered taking into account the contribution of the fringing field on the tip of the beam. In order of evaluate the accuracy of such a model a 3D model has also been developed taking into account the fringing field on the lateral surface, the anticlastic curvature of the beam and the lateral effect of the constraint. The result obtained emphasizes the coupling between electrical and mechanical solution as an error around 30 percent is obtained if the mechanical solution is calculated on the base of the undeformed electric field On the other hand the 2D mode gives a suitable model of the structure as an error of the order of 2.5 percent with respect to the 3D case has been obtained.

Paper Details

Date Published: 10 April 2000
PDF: 9 pages
Proc. SPIE 4019, Design, Test, Integration, and Packaging of MEMS/MOEMS, (10 April 2000); doi: 10.1117/12.382265
Show Author Affiliations
A. Gugliotta, Politecnico di Torino (Italy)
Aurelio Soma, Politecnico di Torino (Italy)
S. Di Mauro, Politecnico di Torino (Italy)
F. De Bona, Univ. di Udine (Italy)
F. Roccaforte, Univ. di Udine (Italy)


Published in SPIE Proceedings Vol. 4019:
Design, Test, Integration, and Packaging of MEMS/MOEMS
Bernard Courtois; Selden B. Crary; Kaigham J. Gabriel; Jean Michel Karam; Karen W. Markus; Andrew A. O. Tay, Editor(s)

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