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A size-dependent axisymmetric plate element: application to MEMS

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Abstract

This paper presents the formulation of a novel axisymmetric plate element capable of capturing size effects observed in micro-scaled structures. To establish the element formulation, a size-dependent beam element is considered, and by axisymmetric expansion of the model, the stiffness and mass matrices and force vector for an axisymmetric plate element are derived. Comparing the results of this model with those from literature and the outcomes of COMSOL confirms that the present FE formulation can accurately predict the static and dynamic behavior of microplates as well as macro-scale plates. Furthermore, a convergence analysis is performed which indicates that this model can accurately predict the static deflection and natural frequency of circular plates utilizing very low number of elements and consequently with low values of computation cost. As an example of real-world application, the model is applied to analysis of microelectromechanical devices and its accuracy is confirmed.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Ardakan University, P.O. Box 184, Ardakan, Iran

    Masoud Rahaeifard

  2. Department of Mechanical Engineering, Faculty of Engineering, Fasa University, Fasa, Iran

    Ali Karimzadeh

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  1. Masoud Rahaeifard
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  2. Ali Karimzadeh
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M. Rahaeifard and A.Karimzadeh wrote the main manuscript text and prepared all figures. All authors reviewed the manuscript.

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Correspondence to Ali Karimzadeh.

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Rahaeifard, M., Karimzadeh, A. A size-dependent axisymmetric plate element: application to MEMS. Arch Appl Mech 94, 667–681 (2024). https://doi.org/10.1007/s00419-024-02544-2

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