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Mathematical justification of an obstacle problem in the case of a plate

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Abstract

In this paper the modeling of a thin plate in unilateral contact with a rigid plane is properly justified. Starting from the three-dimensional nonlinear Signorini problem, by an asymptotic approach the convergence of the displacement field as the thickness of the plate goes to zero is studied. It is shown that the transverse mechanical displacement field decouples from the in-plane components and solves an obstacle problem.

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Acknowledgments

The author is greatly indebted to Professor Li Tatsien and Professor Zhou Yi for their instructive questions, corrections, encouragement, and help.

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Authors and Affiliations

  1. Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, China

    Yan Guan

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  1. Yan Guan
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Correspondence to Yan Guan.

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Project supported by the Innovation Program of Shanghai Municipal Education Commission (No. 11YZ80) and the Program of Shanghai Normal University (No. SK201301).

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Guan, Y. Mathematical justification of an obstacle problem in the case of a plate. Chin. Ann. Math. Ser. B 38, 1047–1058 (2017). https://doi.org/10.1007/s11401-017-1021-9

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  • DOI: https://doi.org/10.1007/s11401-017-1021-9

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