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Axisymmetric bending of strain gradient elastic circular thin plates

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Abstract

Axisymmetric bending of strain gradient elastic circular thin plates is studied, adopting Kirchhoff’s theory of plates. Based on the principle of minimum potential energy, the governing equation with its boundary conditions is derived through a variational method. It turns out that new terms depending upon the thickness are introduced. Those terms are missing from the existing strain gradient elastic circular thin plate theories; however, they strongly increase the stiffness of the thin plate. In addition, the static deformations and the natural frequencies of two circular gradient elastic microplates, clamped and simply supported at edges, are analyzed. This article may contribute to the design of the microstructures.

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Authors and Affiliations

  1. Mechanics Department, School of Mathematical Sciences (SEMFE), National Technical University of Athens, 5 Heroes of Polytechnion Ave., Zografou Campus, 157 73, Athens, Greece

    N. Gousias

  2. Department of Mathematics and Mechanics, Hellenic Army Academy, 166 73, Vari, Greece

    A. K. Lazopoulos

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  1. N. Gousias
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  2. A. K. Lazopoulos
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Correspondence to A. K. Lazopoulos.

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Gousias, N., Lazopoulos, A.K. Axisymmetric bending of strain gradient elastic circular thin plates. Arch Appl Mech 85, 1719–1731 (2015). https://doi.org/10.1007/s00419-015-1014-7

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  • DOI: https://doi.org/10.1007/s00419-015-1014-7

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