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A Locking-Free and Reduction-Free Conforming Finite Element Method for the Reissner-Mindlin Plate on Rectangular Meshes

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Abstract

A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation. The rotation is approximated by \(C^1-Q_{k+1}\) in one direction and \(C^0-Q_k\) in the other direction finite elements. The displacement is approximated by \(C^1-Q_{k+1,k+1}\). The method is locking-free without using any projection/reduction operator. Theoretical proof and numerical confirmation are presented.

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  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Shangyou Zhang

  2. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Zhimin Zhang

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  1. Shangyou Zhang
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Zhang, S., Zhang, Z. A Locking-Free and Reduction-Free Conforming Finite Element Method for the Reissner-Mindlin Plate on Rectangular Meshes. Commun. Appl. Math. Comput. (2024). https://doi.org/10.1007/s42967-023-00343-0

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  • DOI: https://doi.org/10.1007/s42967-023-00343-0

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