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Improved hybrid displacement function (IHDF) element scheme for analysis of Mindlin-Reissner plate with edge effect

Yan Shang, Song Cen, Zhi Li, Chen-Feng Li, Chenfeng Li Orcid Logo

International Journal for Numerical Methods in Engineering

Swansea University Author: Chenfeng Li Orcid Logo

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DOI (Published version): 10.1002/nme.5496

Abstract

For a Mindlin–Reissner plate subjected to transverse loadings, the distributions of the rotations and some resultant forces may vary very sharply within a narrow district near certain boundaries. This edge effect is indeed a great challenge for conventional finite element analysis. Recently, an effe...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 00295981
Published: 2017
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa32717
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Abstract: For a Mindlin–Reissner plate subjected to transverse loadings, the distributions of the rotations and some resultant forces may vary very sharply within a narrow district near certain boundaries. This edge effect is indeed a great challenge for conventional finite element analysis. Recently, an effective hybrid displacement function (HDF) finite element method was successfully developed for solving such difficulty [1, 2]. Although good performances can be obtained in most cases, the distribution continuity of some resulting resultants is destroyed when coarse meshes are employed. Moreover, an additional local coordinate system must be used for avoiding a singular problem in matrix inversion, which makes the derivations more complicated. Based on a modified complementary energy functional containing Lagrangian multipliers, an improved HDF (IHDF) element scheme is proposed in this work. And two new special IHDF elements, named by IHDF-P4-Free and IHDF-P4-SS1, are constructed for modeling plate behaviors near free and soft simply supported boundaries, respectively. The present modeling scheme not only greatly improves the precision of the numerical results but also avoids usage of the additional local Coordinate system. The numerical tests demonstrate that the new IHDF element scheme is an effective way for solving the challenging edge effect problem in Mindlin–Reissner plates.
Keywords: finite element; improved hybrid displacement function (IHDF) element scheme; Mindlin–Reissner plate; edge effect; Lagrangian multiplier
College: College of Engineering