TY - JOUR
T1 - Explicit finite deformation analysis of isogeometric membranes
AU - Chen, Lei
AU - Nguyen-Thanh, Nhon
AU - Nguyen-Xuan, Hung
AU - Rabczuk, Timon
AU - Bordas, Stéphane Pierre Alain
AU - Limbert, Georges
N1 - Funding Information:
Georges Limbert and Lei Chen would like to acknowledge the financial support from the European Office of Aerospace Research and Development (Air Force Office of Scientific Research) [Grant FA8655-12-1-2103 ] and the Engineering and Physical Sciences Research Council (EPSRC) [Grant EP/F034296/1 ]. Stéphane Bordas and Timon Rabczuk would like to acknowledge the partial financial support of the Framework Programme 7 Initial Training Network Funding under grant number 289361 “Integrating Numerical Simulation and Geometric Design Technology”.
Funding Information:
Stéphane Bordas would like to thank partial funding for his time from: (1) the European Research Council Starting Independent Research Grant (ERC Stg Grant Agreement No. 279578 ) entitled “Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery; (2) the EPSRC under grant EP/G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method.
PY - 2014/8/1
Y1 - 2014/8/1
N2 - 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.
AB - 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.
KW - Dynamic relaxation
KW - Explicit
KW - Isogeometric
KW - Kirchhoff-Love shell
KW - Membrane
KW - NURBS
UR - http://www.scopus.com/inward/record.url?scp=84900494411&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2014.04.015
DO - 10.1016/j.cma.2014.04.015
M3 - Article
AN - SCOPUS:84900494411
SN - 0045-7825
VL - 277
SP - 104
EP - 130
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -