Modeling Deficiencies in the Eight-Node Mindlin Plate Finite Element Physically Explained
Publication: Journal of Engineering Mechanics
Volume 146, Issue 2
Abstract
Modeling errors that prevent the eight-node Mindlin plate finite element to behave correctly, namely shear locking and spurious zero-energy modes, can be explained using strain gradient notation. This notation is physically interpretable, and it allows for the sources of shear locking and spurious zero-energy modes to be clearly identified a priori. This means that spurious terms in shear strain polynomials are precisely identified as parasitic shear terms. Once this is done, such spurious terms are simply removed to correct the element model, resulting in a shear locking-free element. In order to avoid introducing spurious zero-energy modes, the analyst must recognize and retain the compatibility modes in the shear strain polynomials. As the study shows, compatibility modes can easily be confused with parasitic shear terms. Numerical displacement and stress solutions from models containing parasitic shear terms revisit important locking effects. Further, solutions obtained using corrected models are qualitatively correct and have higher rates of convergence.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request. The finite element Fortran code LAMFEM, developed by the authors, as well as the input data required to run the problems presented in the paper can be provided.
Acknowledgments
This work was partially prepared when the first author stayed at the University of Colorado Boulder as a Visiting Senior Research Scholar during the 2015–2016 academic year. He acknowledges Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES), a foundation affiliated with the Ministry of Education of Brazil, for its financial support.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 2 • February 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Oct 11, 2018
Accepted: Jun 24, 2019
Published online: Dec 9, 2019
Published in print: Feb 1, 2020
Discussion open until: May 9, 2020
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