Explicit finite deformation analysis of isogeometric membranes

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

doi:10.1016/j.cma.2014.04.015

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 journal › Article › peer-review

61 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 language	English
Pages (from-to)	104-130
Number of pages	27
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	277
DOIs	https://doi.org/10.1016/j.cma.2014.04.015
Publication status	Published - 2014 Aug 1

Bibliographical note

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.

Keywords

Dynamic relaxation
Explicit
Isogeometric
Kirchhoff-Love shell
Membrane
NURBS

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2014.04.015

Cite this

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title = "Explicit finite deformation analysis of isogeometric membranes",

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.",

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note = "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 ]. St{\'e}phane 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: St{\'e}phane 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.",

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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.

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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.

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Explicit finite deformation analysis of isogeometric membranes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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