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A geometric nonlinear rotation‐free triangle and its application to drape simulation
Author(s) -
Zhou Y.X.,
Sze K.Y.
Publication year - 2011
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.3250
Subject(s) - rotation (mathematics) , displacement (psychology) , shell (structure) , geometry , mathematics , nonlinear system , matrix (chemical analysis) , bending , stiffness matrix , rotation matrix , finite element method , constant (computer programming) , stiffness , mathematical analysis , structural engineering , physics , engineering , computer science , materials science , mechanical engineering , psychology , quantum mechanics , composite material , psychotherapist , programming language
SUMMARY In this paper, a rotation‐free triangle is formulated. Unlike the thin and degenerated shell finite element models, rotation‐free triangles employ translational displacements as the only nodal DOFs. Compared with the existing rotation‐free triangles, the present triangle is simple and physical yet its accuracy remains competitive. Using a corotational approach and the small strain assumption, the tangential bending stiffness matrix of the present triangle can be approximated by a constant matrix that does not have to be updated regardless of the displacement magnitude. This unique feature suggests that the triangle is a good candidate for fabric drape simulation in which fabric sheets are often flat initially and the displacement is much larger than those in conventional shell problems. Nonlinear shell and fabric drape examples are examined to demonstrate the efficacy of the formulation. Copyright © 2011 John Wiley & Sons, Ltd.