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

doi:10.1007/s42967-023-00343-0

摘要/Abstract

摘要： A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation. The rotation is approximated by C¹ - Q_k+1 in one direction and C⁰ - Q_k in the other direction finite elements. The displacement is approximated by C¹ - Q_k+1,k+1. The method is locking-free without using any projection/reduction operator. Theoretical proof and numerical confirmation are presented.

关键词: Locking-free, Reissner-Mindlin equation, Finite element, Rectangular mesh

Abstract: A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation. The rotation is approximated by C¹ - Q_k+1 in one direction and C⁰ - Q_k in the other direction finite elements. The displacement is approximated by C¹ - Q_k+1,k+1. The method is locking-free without using any projection/reduction operator. Theoretical proof and numerical confirmation are presented.

Key words: Locking-free, Reissner-Mindlin equation, Finite element, Rectangular mesh

中图分类号:

Shangyou Zhang, Zhimin Zhang. A Locking-Free and Reduction-Free Conforming Finite Element Method for the Reissner-Mindlin Plate on Rectangular Meshes[J]. Communications on Applied Mathematics and Computation, 2025, 7(2): 470-484.

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