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Shape design of a MEMS device by Schwarz‐Christoffel numerical inversion and Pareto optimality

Shape design of a MEMS device by Schwarz‐Christoffel numerical inversion and Pareto optimality Purpose – This paper sets out to provide a numerical procedure for field analysis and shape design for a class of MEMS devices. Design/methodology/approach – The proposed numerical procedure for field analysis relies on numerical inversion of Schwarz‐Christoffel (SC) transformations for doubly‐connected regions: the geometry of a given micromotor is mapped into an annulus, where the non‐radial field excited by the transformed electrodes is computed. In turn, the shape design relies on the definition of non‐dominated solution according to the Pareto optimality conditions. Findings – The SC approach proposed here allows the designer to evaluate both driving torque and radial force characteristics of the device with suitable accuracy within short CPU times. In turn, this allows one to perform repeated field analyses for a large number of feasible geometries and to use enumerative approaches to design optimization. By this means, a 3D objective space is investigated to identify the optimal shape of an electrostatic micromotor, subject to prescribed constraints. Originality/value – To the best of one's knowledge, the combination of SC transformations and Pareto optimality is an unprecedented method for MEMS design. In particular, it is expected that the proposed SC tools will supply a fast and accurate computation to compare or supplement results from FEM tools, when a large number of geometries should be analysed. This could be particularly useful in the preliminary steps of a design procedure for a given class of devices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

Shape design of a MEMS device by Schwarz‐Christoffel numerical inversion and Pareto optimality

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References (6)

Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0332-1649
DOI
10.1108/03321640810878162
Publisher site
See Article on Publisher Site

Abstract

Purpose – This paper sets out to provide a numerical procedure for field analysis and shape design for a class of MEMS devices. Design/methodology/approach – The proposed numerical procedure for field analysis relies on numerical inversion of Schwarz‐Christoffel (SC) transformations for doubly‐connected regions: the geometry of a given micromotor is mapped into an annulus, where the non‐radial field excited by the transformed electrodes is computed. In turn, the shape design relies on the definition of non‐dominated solution according to the Pareto optimality conditions. Findings – The SC approach proposed here allows the designer to evaluate both driving torque and radial force characteristics of the device with suitable accuracy within short CPU times. In turn, this allows one to perform repeated field analyses for a large number of feasible geometries and to use enumerative approaches to design optimization. By this means, a 3D objective space is investigated to identify the optimal shape of an electrostatic micromotor, subject to prescribed constraints. Originality/value – To the best of one's knowledge, the combination of SC transformations and Pareto optimality is an unprecedented method for MEMS design. In particular, it is expected that the proposed SC tools will supply a fast and accurate computation to compare or supplement results from FEM tools, when a large number of geometries should be analysed. This could be particularly useful in the preliminary steps of a design procedure for a given class of devices.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering – Emerald Publishing

Published: Jul 11, 2008

Keywords: Optimization techniques; MEMS; Numerical analysis

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