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A locking‐free nine‐DOF triangular plate element with incompatible approximation
Author(s) -
Cai Yongchang,
Zhu Hehua
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5307
Subject(s) - degrees of freedom (physics and chemistry) , element (criminal law) , simple (philosophy) , robustness (evolution) , finite element method , mathematics , convergence (economics) , mathematical analysis , geometry , physics , engineering , structural engineering , philosophy , biochemistry , chemistry , epistemology , quantum mechanics , economic growth , political science , law , economics , gene
Summary In this paper, a simple locking‐free triangular plate element, labeled here as Mindlin‐type triangular plate element with nine degrees of freedom (MTP9), is presented. The element employs an incompatible approximation with nine degrees of freedom (DOFs) independent of the nodes and the shape of the triangle to define the displacements u / v / w (which is similar to a general solid element) along the x / y / z axes. It is free of shear locking, has a proper rank, and provides stable solutions for thick and thin plates. Moreover, the paper provides a new way to develop simple and efficient locking‐free thick–thin‐plate/shell elements. A variety of numerical examples demonstrate the convergence, accuracy, and robustness of the present element MTP9. Copyright © 2016 John Wiley & Sons, Ltd.