Open Access

ARTICLE

A Three-Dimensional Meshless Scheme with Background Grid for Electrostatic-Structural Analysis

Ming-Hsiao Lee, Wen-Hwa Chen

Computers, Materials & Continua 2009, 11(1), 59-78. https://doi.org/10.3970/cmc.2009.011.059

Abstract

On the analysis of electrostatic-structural coupled problems as encountered in many electrostatic driven MEMS devices, the electrostatic analysis domain is often extremely distorted due to the deflection of the structure. This kind of problem is difficult to be dealt with by almost all kinds of available numerical methods. A new three-dimensional meshless scheme with background grid is thus proposed herein. By this scheme, a three-dimensional fixed background grid with regularly-distributed nodes is utilized. Another set of discretized boundary grid is employed to describe the boundary surfaces of both the structure and the electrostatic field. The analysis electrostatic/structural domains are modeled by the nodes which are from the boundary grid and the background grid enclosed by the boundary surfaces. During the solution process, when the boundary surfaces of the structure move, those boundary nodes remain the same, while the internal nodes may be re-selected from the fixed background grid according to the new positions of the boundary surfaces. Hence, no matter how large the boundary surfaces deflect, regularly distributed internal nodes from the fixed background grid are obtained and the distortion of the analysis model is minimized. Therefore, the whole solution process can be automatically handled by the scheme proposed without the need of intervening, e.g. remeshing or rezoning. Several cases of electrostatic-structural coupled problems are tackled in this work to demonstrate the effectiveness and advantages of the novel meshless scheme.

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Keywords

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