Optimal design of an electrostatically actuated microbeam for maximum pull-in voltage

Abdalla, Mostafa; Reddy, C. K.; Faris, Waleed Fekry; Gürdal, Zafer

doi:10.1016/j.compstruc.2004.07.010

Cited by 42 publications

(20 citation statements)

References 6 publications

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“…This expression is highly useful since it provides an efficient way to compute numerically consistent sensitivities. The sensitivities equation can be established starting from the equilibrium equation by using a similar approach to references [11,17]. At first, the equilibrium equation (3) is derived with respect to the pseudo-density µ i ,…”

Section: Pull-in Voltage Sensitivity Analysismentioning

confidence: 99%

“…Particular homotopy methods are characterized by the additional constraint chosen. In this paper, we use the normal flow method (see references [11,23]) which imposes that the correction has to be perpendicular to the set of curves defined by perturbing the equilibrium equation (3), r (q, V ) = δ where δ is any perturbation vector. This set of curves is called the Davidenko flow.…”

Section: Normal Flow Algorithmmentioning

confidence: 99%

“…Moreover, topology optimization of electrostatic force inverters has also been studied very recently by Yoon and Sigmund [10] using the classical density distribution formulation and a monolithic analysis. Another interesting contribution in this field is the one from Abdalla et al [11]. Using a simplified modeling based on a beam model, they have established a sizing method to adjust the thickness or width evolution along an electromechanical microbeam in order to maximize its pull-in voltage.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Microbeam pull-in voltage topology optimization including material deposition constraint

Lemaire¹,

Rochus²,

Golinval³

et al. 2008

Computer Methods in Applied Mechanics and Engineering

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Because of the strong coupling between mechanical and electrical phenomenon existing in electromechanical microdevices, some of them experience, above a given driving voltage, an unstable behavior called pull-in effect. The present paper investigates the application of topology optimization to electromechanical microdevices for the purpose of delaying the unstable behavior by maximizing their pull-in voltage. Within the framework of this preliminary study, the pull-in voltage maximization procedure is developed on the basis of electromechanical microbeams reinforcement topology design problem. The proposed sensitivity analysis requires only the knowledge of the microdevice pull-in state and of the first eigenmode of the tangent stiffness matrix. As the pull-in point research is a highly non-linear problem, the analysis is based on a monolithic finite element formulation combined with a normal flow algorithm (homotopy method). An application of the developed method is proposed and the result is compared to the one obtained using a linear compliance optimization. Moreover, as, the results provided by the developed method do not comply with manufacturing constraints, a deposition process constraint is added to the optimization problem and its effect on the final design is also tested.

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Section: Pull-in Voltage Sensitivity Analysismentioning

confidence: 99%

Section: Normal Flow Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Microbeam pull-in voltage topology optimization including material deposition constraint

Lemaire¹,

Rochus²,

Golinval³

et al. 2008

Computer Methods in Applied Mechanics and Engineering

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show abstract

“…al. 13 for microbeams, and Bochobza-Degani and Nemirovsky 14 for torsional actuators. There have also been many investigations into the use of a combination of higher and lower fidelity solution techniques.…”

Section: A Electro-mechanical Analysismentioning

confidence: 99%

Topology Optimization of Electrostatic MEMS

Raulli¹,

Maute²

2004

10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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“…The beam must contact these structures as deflection occurs, which may not be possible or desirable. Other designs with variable geometry have been presented [7,8], but not with the intention of finding specific shapes to reduce the pull-in voltage for a given required displacement.…”

Section: Introductionmentioning

confidence: 99%

Reducing Pull-In Voltage by Adjusting Gap Shape in Electrostatically Actuated Cantilever and Fixed-Fixed Beams

et al. 2010

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A gap with variable geometry is presented for both cantilever beam and fixed-fixed beam actuators as a method to reduce the pull-in voltage while maintaining a required displacement. The method is applicable to beams oriented either in a plane parallel to or perpendicular to a substrate, but is most suitable for vertically oriented (lateral) beams fabricated with a high aspect ratio process where variable gap geometry can be implemented directly in the layout. Finite element simulations are used to determine the pull-in voltages of these modified structures. The simulator is verified against theoretical pull-in voltage equations as well as previously published finite element simulations. By simply varying the gap in a linear fashion the pull-in voltage can be reduced by 37.2% in the cantilever beam case and 29.6% in the fixed-fixed beam case over a structure with a constant gap. This can be reduced a further 4.8% by using a polynomial gap shape (n = 4/3) for the cantilever beam and 1.2% for the fixed-fixed beam by flattening the bottom of the linearly varying gap.

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Optimal design of an electrostatically actuated microbeam for maximum pull-in voltage

Cited by 42 publications

References 6 publications

Microbeam pull-in voltage topology optimization including material deposition constraint

Microbeam pull-in voltage topology optimization including material deposition constraint

Topology Optimization of Electrostatic MEMS

Reducing Pull-In Voltage by Adjusting Gap Shape in Electrostatically Actuated Cantilever and Fixed-Fixed Beams

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