The University of Southampton
University of Southampton Institutional Repository

Explicit finite deformation analysis of isogeometric membranes

Explicit finite deformation analysis of isogeometric membranes
Explicit finite deformation analysis 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 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 CkCk (k?1k?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.
Membrane, Kirchhoff–Love shell, isogeometric, NURBS, explicit, dynamic relaxation
0045-7825
104-130
Chen, Lei
7540f09c-36b5-443c-ae07-137886a3ce48
Nguyen-Thanh, Nhon
80fa9e08-b74d-405e-bab7-677ffe614313
Nguyen-Xuan, Hung
3096a5d5-a8ad-440e-9a94-6a8eb335bb32
Rabczuk, Timon
74e28aae-9830-47f5-a317-babf2100388c
Bordas, Stéphane Pierre Alain
a65669d8-a254-498f-82c2-c99056842235
Limbert, Georges
a1b88cb4-c5d9-4c6e-b6c9-7f4c4aa1c2ec
Chen, Lei
7540f09c-36b5-443c-ae07-137886a3ce48
Nguyen-Thanh, Nhon
80fa9e08-b74d-405e-bab7-677ffe614313
Nguyen-Xuan, Hung
3096a5d5-a8ad-440e-9a94-6a8eb335bb32
Rabczuk, Timon
74e28aae-9830-47f5-a317-babf2100388c
Bordas, Stéphane Pierre Alain
a65669d8-a254-498f-82c2-c99056842235
Limbert, Georges
a1b88cb4-c5d9-4c6e-b6c9-7f4c4aa1c2ec

Chen, Lei, Nguyen-Thanh, Nhon, Nguyen-Xuan, Hung, Rabczuk, Timon, Bordas, Stéphane Pierre Alain and Limbert, Georges (2014) Explicit finite deformation analysis of isogeometric membranes. Computer Methods in Applied Mechanics and Engineering, 277, 104-130. (doi:10.1016/j.cma.2014.04.015).

Record type: Article

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 CkCk (k?1k?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.

Text
J - CMAME 2014 (Chen et al.).pdf - Version of Record
Restricted to Repository staff only
Request a copy

More information

e-pub ahead of print date: 1 May 2014
Published date: 1 August 2014
Keywords: Membrane, Kirchhoff–Love shell, isogeometric, NURBS, explicit, dynamic relaxation
Organisations: nCATS Group

Identifiers

Local EPrints ID: 371847
URI: http://eprints.soton.ac.uk/id/eprint/371847
ISSN: 0045-7825
PURE UUID: bad0eef4-6efa-4858-b70e-324475408ded

Catalogue record

Date deposited: 19 Nov 2014 11:53
Last modified: 14 Mar 2024 18:27

Export record

Altmetrics

Contributors

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

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×