A methodology for fast finite element modeling of electrostatically actuated MEMS

Sumant, Prasad S.; Aluru, N. R.; Cangellaris, A.C.

doi:10.1002/nme.2469

Cited by 4 publications

(2 citation statements)

References 19 publications

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“…While there have been significant advances in numerical simulation methods that allow better understanding of the underlying multiphasic (De and Aluru 2006;Li and Aluru 2003;Sumant et al 2009), they however, assume that the geometrical and physical properties of the device are known in a deterministic sense. Recently there have been efforts towards developing computational methods that can handle input uncertainties (Table 1).…”

Section: Introductionmentioning

confidence: 99%

MEMS stochastic model order reduction method based on polynomial chaos expansion

et al. 2015

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devices have some form of nonlinearity, either geometric nonlinearity due to large amplitude deflections or intrinsic nonlinearities due to governing equations, Multi-energy domain coupling effect of MEMS can hardly be described perfectly, because in a micron-scale or even in a Nanoscale working room, physical quantities of energy among the different domains interact with each other (Mounier 2012). Modeling and simulation is at the basis of the prediction of the device behavior and optimization of its performance. Modeling of MEMS devices is a very complex task. Their behavior involves multiple coupled energy domains. The electrical and the mechanical domains are the main ones, but also the fluidic and thermal domain may be of interest (Gong 2013). In addition, the devices have most of the time a three dimensional and geometrically complex structure. As a consequence, MEMS modelling is always a trade-off between accuracy and computational complexity (Binion and Chen 2010). An accurate device model can be achieved using the so called physical modelling. The partial differential equation governing the device behavior can be discretized on the device domain. The resulting system of ordinary differential equations gives a representation of the device. Several commercial tools are already available for device physical modelling and simulation, which make use of different discretization and solution techniques (Senturia 1998). However, proceeding this way, the afore-mentioned complexity factors lead to device physical models with a large number of degrees of freedom: 10-100 thousands of equations to solve represent a standard problem. The complexity of the simulation analysis adds to the complexity of the model. MEMS characterization often requires computationally expensive analysis such as transient analysis. Moreover, the derived models are often nonlinear. The primary source of nonlinearity is the electrostatic force, which couples the electrical and mechanical energy domains.Abstract Modeling and simulation of MEMS devices is a very complex task which involve the electrical, mechanical, fluidic and thermal domains, and there are still some uncertainties need to be accounted because of uncertain material and/or geometric parameters factors. According to these problems, we put forward to stochastic model order reduction method under random input conditions to facilitate fast time and frequency domain analyses, the method firstly process model order reduction by Structure Preserving Reduced-order Interconnect Macro Modeling method, then makes use of polynomial chaos expansions in terms of the random input and output variables for the matrices of a finite element model of the system; at last we give the expected values and standard deviations computing method to MEMS stochastic model. The simulation results verify the method is effective in large scale MEMS design process.

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Section: Introductionmentioning

confidence: 99%

MEMS stochastic model order reduction method based on polynomial chaos expansion

et al. 2015

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“…Variations during fabrication lead to uncertain material and/or geometric parameters causing a significant impact on MEMS device performance [4]. While there have been significant advances in numerical simulation methods that allow better understanding of the underlying multiphysics [5][6][7], they, however, assume that the geometrical and physical properties of the device are known in a deterministic sense. Recently there have been efforts towards developing computational methods that can handle input uncertainties.…”

Section: Introductionmentioning

confidence: 99%

A New MEMS Stochastic Model Order Reduction Method: Research and Application

et al. 2015

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Modeling and simulation of MEMS devices is a very complex tasks which involve the electrical, mechanical, fluidic, and thermal domains, and there are still some uncertainties that need to be accounted for during the robust design of MEMS actuators caused by uncertain material and/or geometric parameters. According to these problems, we put forward stochastic model order reduction method under random input conditions to facilitate fast time and frequency domain analyses; the method makes use of polynomial chaos expansions in terms of the random input variables for the matrices of a finite element model of the system and then uses its transformation matrix to reduce the model; the method is independent of the MOR algorithm, so it is seamlessly compatible with MOR method used in popular finite element solvers. The simulation results verify the method is effective in large scale MEMS design process.

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Multiscale, Multiphysics Modeling of Electromechanical Coupling in Surface‐Dominated Nanostructures

Park

Devel

2013

Multiscale Simulations and Mechanics of Biological Materials

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A methodology for fast finite element modeling of electrostatically actuated MEMS

Cited by 4 publications

References 19 publications

MEMS stochastic model order reduction method based on polynomial chaos expansion

MEMS stochastic model order reduction method based on polynomial chaos expansion

A New MEMS Stochastic Model Order Reduction Method: Research and Application

Multiscale, Multiphysics Modeling of Electromechanical Coupling in Surface‐Dominated Nanostructures

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