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Wrinkled and slack membranes: nonlinear 3D elasticity solutions via smooth DMS‐FEM and experiment
Author(s) -
Sunilkumar N.,
Lalmoni G.,
Roy D.,
Reid S. R.,
Vasu R. M.
Publication year - 2012
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.3359
Subject(s) - finite element method , discretization , nonlinear system , membrane , mathematical analysis , mathematics , tangent , boundary value problem , elasticity (physics) , geometry , materials science , physics , composite material , chemistry , thermodynamics , quantum mechanics , biochemistry
SUMMARY The smooth DMS‐FEM, recently proposed by the authors, is extended and applied to the geometrically nonlinear and ill‐posed problem of a deformed and wrinkled/slack membrane. A key feature of this work is that three‐dimensional nonlinear elasticity equations corresponding to linear momentum balance, without any dimensional reduction and the associated approximations, directly serve as the membrane governing equations. Domain discretization is performed with triangular prism elements and the higher order ( C 1 or more) interelement continuity of the shape functions ensures that the errors arising from possible jumps in the first derivatives of the conventional C 0 shape functions do not propagate because the ill‐conditioned tangent stiffness matrices are iteratively inverted. The present scheme employs no regularization and exhibits little sensitivity to h ‐refinement. Although the numerically computed deformed membrane profiles do show some sensitivity to initial imperfections (nonplanarity) in the membrane profile needed to initiate transverse deformations, the overall patterns of the wrinkles and the deformed shapes appear to be less so. Finally, the deformed profiles, computed through the DMS FEM‐based weak formulation, are compared with those obtained through an experiment on an ultrathin Kapton membrane, wherein wrinkles form because of the applied boundary displacement conditions. Comparisons with a reported experiment on a rectangular membrane are also provided. These exercises lend credence to the feasibility of the DMS FEM‐based numerical route to computing post‐wrinkled membrane shapes. Copyright © 2012 John Wiley & Sons, Ltd.