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Explicit finite deformations of isogeometric membranes

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 ultrathin
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 Ck (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 is 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.

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