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Nonlinear bending of size-dependent circular microplates based on the modified couple stress theory

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Abstract

The present study proposes a nonclassical Kirchhoff plate model for the axisymmetrically nonlinear bending analysis of circular microplates under uniformly distributed transverse loads. The governing differential equations are derived from the principle of minimum total potential energy based on the modified couple stress theory and von Kármán geometrically nonlinear theory in terms of the deflection and radial membrane force, with only one material length scale parameter to capture the size-dependent behavior. The governing equations are firstly discretized to a set of nonlinear algebraic equations by the orthogonal collocation point method, and then solved numerically by the Newton–Raphson iteration method to obtain the size-dependent solutions for deflections and radial membrane forces. The influences of length scale parameter on the bending behaviors of microplates are discussed in detail for immovable clamped and simply supported edge conditions. The numerical results indicate that the microplates modeled by the modified couple stress theory causes more stiffness than modeled by the classical continuum plate theory, such that for plates with small thickness to material length scale ratio, the difference between the results of these two theories is significantly large, but it becomes decreasing or even diminishing with increasing thickness to length scale ratio.

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Authors and Affiliations

  1. Department of Applied Mechanics, China Agricultural University, Beijing, 100083, People’s Republic of China

    Yong-Gang Wang, Wen-Hui Lin & Chang-Ling Zhou

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  1. Yong-Gang Wang
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  2. Wen-Hui Lin
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  3. Chang-Ling Zhou
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Correspondence to Yong-Gang Wang.

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Wang, YG., Lin, WH. & Zhou, CL. Nonlinear bending of size-dependent circular microplates based on the modified couple stress theory. Arch Appl Mech 84, 391–400 (2014). https://doi.org/10.1007/s00419-013-0807-9

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  • DOI: https://doi.org/10.1007/s00419-013-0807-9

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