Explicit finite deformation analysis of isogeometric membranes

Lei Chen, Nhon Nguyen-Thanh, Hung Nguyen-Xuan, Timon Rabczuk, Stéphane Pierre Alain Bordas, Georges Limbert

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear kinematics employs the Kirchhoff-Love shell theory to describe the mechanical behaviour of thin to ultra-thin structures. The displacement fields are interpolated from the displacements of control points only, and no rotational degrees of freedom are used at control points. Due to the high order C k (k ≥ 1) continuity of NURBS shape functions the Kirchhoff-Love theory can be seamlessly implemented. An explicit time integration scheme is used to compute the transient response of membrane structures to time-domain excitations, and a dynamic relaxation method is employed to obtain steady-state solutions. The versatility and good performance of the present formulation are demonstrated with the aid of a number of test cases, including a square membrane strip under static pressure, the inflation of a spherical shell under internal pressure, the inflation of a square airbag and the inflation of a rubber balloon. The mechanical contribution of the bending stiffness is also evaluated.

Original languageEnglish
Pages (from-to)104-130
Number of pages27
JournalComputer Methods in Applied Mechanics and Engineering
Volume277
DOIs
Publication statusPublished - 2014 Aug 1

Fingerprint

membrane structures
Membrane structures
Shells (structures)
membranes
shell theory
Membranes
shape functions
internal pressure
static pressure
Balloons
spherical shells
transient response
balloons
versatility
rubber
continuity
Transient analysis
Stretching
deflection
strip

Keywords

  • Dynamic relaxation
  • Explicit
  • Isogeometric
  • Kirchhoff-Love shell
  • Membrane
  • NURBS

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

Cite this

Chen, L., Nguyen-Thanh, N., Nguyen-Xuan, H., Rabczuk, T., Bordas, S. P. A., & Limbert, G. (2014). Explicit finite deformation analysis of isogeometric membranes. Computer Methods in Applied Mechanics and Engineering, 277, 104-130. https://doi.org/10.1016/j.cma.2014.04.015

Explicit finite deformation analysis of isogeometric membranes. / Chen, Lei; Nguyen-Thanh, Nhon; Nguyen-Xuan, Hung; Rabczuk, Timon; Bordas, Stéphane Pierre Alain; Limbert, Georges.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 277, 01.08.2014, p. 104-130.

Research output: Contribution to journalArticle

Chen, L, Nguyen-Thanh, N, Nguyen-Xuan, H, Rabczuk, T, Bordas, SPA & Limbert, G 2014, 'Explicit finite deformation analysis of isogeometric membranes', Computer Methods in Applied Mechanics and Engineering, vol. 277, pp. 104-130. https://doi.org/10.1016/j.cma.2014.04.015
Chen, Lei ; Nguyen-Thanh, Nhon ; Nguyen-Xuan, Hung ; Rabczuk, Timon ; Bordas, Stéphane Pierre Alain ; Limbert, Georges. / Explicit finite deformation analysis of isogeometric membranes. In: Computer Methods in Applied Mechanics and Engineering. 2014 ; Vol. 277. pp. 104-130.
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