New computational approaches for wrinkled and slack membranes

N A Pimprikar, B Banerjee, D Roy, R M Vasu, S R Reid

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The static response of thin, wrinkledmembranes is studied using both a tension field approximation based on plane stress conditions and a 3D nonlinear elasticity formulation, discretized through 8-noded Cosserat point elements. While the tension field approach only obtains the wrinkled/slack regions and at best a measure of the extent of wrinkliness, the 3D elasticity solution provides, in principle, the deformed shape of a wrinkled/slackmembrane. However, since membranes barely resist compression, the discretized and linearized system equations via both the approaches are ill-conditioned and solutions could thus be sensitive to discretizations errors as well as other sources of noises/imperfections. We propose a regularized, pseudo-dynamical recursion scheme that provides a sequence of updates, which are almost insensitive to the regularizing term as well as the time step size used for integrating the pseudo-dynamical form. This is borne out through several numerical examples wherein the relative performance of the proposed recursion scheme vis-à-vis a regularized Newton strategy is compared. The pseudo-time marching strategy, when implemented using 3D Cosserat point elements, also provides a computationally cheaper, numerically accurate and simpler alternative to that using geometrically exact shell theories for computing large deformations of membranes in the presence of wrinkles.
Original languageEnglish
Pages (from-to)2476-2486
Number of pages11
JournalInternational Journal of Solids and Structures
Volume47
Issue number18-19
DOIs
Publication statusPublished - Sep 2010

Fingerprint

Recursion
Elasticity
Membrane
elastic properties
membranes
time marching
shell theory
Membranes
Shell Theory
plane stress
Nonlinear Elasticity
Plane Stress
Discretization Error
Imperfections
Large Deformation
Resist
newton
Compaction
Compression
Update

Keywords

  • membrane wrinkling
  • tension field approximation
  • 3D nonlinear elasticity
  • cosserat points
  • pseudo-dynamical recursion

Cite this

New computational approaches for wrinkled and slack membranes. / Pimprikar, N A ; Banerjee, B; Roy, D; Vasu, R M; Reid, S R.

In: International Journal of Solids and Structures, Vol. 47, No. 18-19, 09.2010, p. 2476-2486.

Research output: Contribution to journalArticle

Pimprikar, N A ; Banerjee, B ; Roy, D ; Vasu, R M ; Reid, S R. / New computational approaches for wrinkled and slack membranes. In: International Journal of Solids and Structures. 2010 ; Vol. 47, No. 18-19. pp. 2476-2486.
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