CMES-Vol. 33, No. 3, 2008

Open Access

ARTICLE

Innovative Numerical Methods for Nonlinear MEMS: the Non-Incremental FEM vs. the Discrete Geometric Approach
P. Bettini, E. Brusa, M. Munteanu, R. Specogna, F. Trevisan¹
CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 215-242, 2008, DOI:10.3970/cmes.2008.033.215
Abstract Electrostatic microactuator is a paradigm of MEMS. Cantilever and double clamped microbeams are often used in microswitches, microresonators and varactors. An efficient numerical prediction of their mechanical behaviour is affected by the nonlinearity of the electromechanical coupling. Sometimes an additional nonlinearity is due to the large displacement or to the axial-flexural coupling exhibited in bending. To overcome the computational limits of the available numerical methods two new formulations are here proposed and compared. Modifying the classical beam element in the Finite Element Method to allow the implementation of a \emph {Non incremental sequential approach} is firstly proposed. The so-called \emph… More >

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Node based Method of Moments Solution to Combined Layer Formulation of Acoustic Scattering
B. Chandrasekhar¹
CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 243-268, 2008, DOI:10.3970/cmes.2008.033.243
Abstract In this work, a novel numerical technique, based on method of moments solution, is presented to solve the Combined layer formulation (CLF) to insure unique solution to the exterior acoustic scattering problem at all frequencies. A new set of basis functions, namely, Node based basis functions are used to represent the source distribution on the surface of rigid body and the same functions are used as testing functions as well. Combined layer formulation (CLF) is defined by linearly combining the Single layer formulation (SLF) and Double layer formulation (DLF) with complex coupling parameter. The matrix equations for the SLF and… More >

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Numerical Simulations of Dynamic Fracture in Thin Shell Structures
C. Gato and Y. Shie¹
CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 269-292, 2008, DOI:10.3970/cmes.2008.033.269
Abstract Numerical simulations of large deformation dynamic fracture in thin shell structures using 3-D meshfree method is presented. Due to the smoothness of the meshfree shape functions, they are well suited to simulate large deformation of thin shell structures while avoiding ill-conditioning as well as stiffening in numerical computations. Dynamic fracture is modeled by simple criterion, i.e. removing connectivity between adjacent nodes once a fracture criterion is met. The main advantage of such 3-D meshfree continuum approach is its simplicity in both formulation and implementation as compared to shell theory approach, or degenerated continuum approach. Moreover, it is believed that the… More >

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Exact Large Deflection Solutions for Timoshenko Beams with Nonlinear Boundary Conditions
Sen Yung Lee¹, Shin Yi Lu², Yen Tse Liu², Hui Chen Huang²
CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 293-312, 2008, DOI:10.3970/cmes.2008.033.293
Abstract A new analytic solution method is developed to find the exact static deflection of a Timoshenko beam with nonlinear elastic boundary conditions for the first time. The associated mathematic system is shifted and decomposed into six linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Examples, limiting studies and numerical analysis are given to illustrate the analysis. The exact solutions are compared with the perturbation solutions.… More >

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