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: A unified, macroscopic, one-dimensional

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SUMMARYThis paper describes the development of an efficient and accurate algebraic multigrid finite element solver for analysis of linear elasticity problems in two-dimensional thin body elasticity. Such problems are commonly encountered during the analysis of thin film devices in micro-electro-mechanical systems. An algebraic multigrid based on element interpolation is adopted and streamlined for the development of the proposed solver. A new node-based agglomeration scheme is proposed for computationally efficient, aggressive and yet effective generation of coarse grids. It is demonstrated that the use of appropriate finite element discretization along with the proposed algebraic multigrid process preserves the rigid body modes that are essential for good convergence of the multigrid solution. Several case studies are taken up to validate the approach. The proposed node-based agglomeration scheme is shown to lead to development of sparse and efficient intergrid transfer operators making the overall multigrid solution process very efficient. The proposed solver is found to work very well even for Poisson's ratio >0.4. Finally, an application of the proposed solver is demonstrated through a simulation of a micro-electro-mechanical switch.

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SUMMARYIn this paper, a methodology is proposed for expediting the coupled electro-mechanical two-dimensional finite element modeling of electrostatically actuated MEMS. The proposed methodology eliminates the need for repeated finite element meshing and subsequent electrostatic modeling of the device during mechanical deformation. We achieve this by mapping the deformed electrostatic domain to the reference undeformed domain 'conformally'. A 'conformal' map preserves the form of the Laplace equation and the boundary conditions; thus the electrostatic problem is solved only once in the undeformed electrostatic domain. The conformal map itself is generated through the solution of the same Laplace equation on the undeformed geometry and with displacement boundary conditions dictated by the movement of the mechanical domain. The proposed methodology is demonstrated through its application to the modeling of three MEMS devices with varying length-to-gap ratios, multiple dielectrics and complicated geometries. The accuracy of the proposed methodology is confirmed through comparisons of its results with results obtained using the conventional finite element solution.

SUMMARYIn this paper, a methodology is proposed for expediting the coupled electro-mechanical finite element modeling of electrostatically actuated MEMS. The proposed methodology eliminates the need for repeated finite element meshing and subsequent electrostatic modeling of the device during mechanical deformation. We achieve this by using an approximation of the charge density on the movable electrode in the deformed geometry in terms of the charge density in the non-deformed geometry and displacements of the movable electrode. The electrostatic problem has to be solved only once and thus this method speeds up the coupled electro-mechanical simulation process. The proposed methodology is demonstrated through its application to the modeling of four MEMS devices with varying length-to-gap ratios, multiple dielectrics and complicated geometries. Its accuracy is assessed through comparisons of its results with results obtained using both analytical solutions and finite element solutions obtained using ANSYS.