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 journalArticlepeer-review

50 Citations (Scopus)


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
Publication statusPublished - 2014 Aug 1


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

ASJC Scopus subject areas

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


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