Isogeometric shell formulation based on a classical shell model

Handle URI:
http://hdl.handle.net/10754/564609
Title:
Isogeometric shell formulation based on a classical shell model
Authors:
Niemi, Antti; Collier, Nathaniel Oren; Dalcín, Lisandro D.; Ghommem, Mehdi; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
This paper constitutes the first steps in our work concerning isogeometric shell analysis. An isogeometric shell model of the Reissner-Mindlin type is introduced and a study of its accuracy in the classical pinched cylinder benchmark problem presented. In contrast to earlier works [1,2,3,4], the formulation is based on a shell model where the displacement, strain and stress fields are defined in terms of a curvilinear coordinate system arising from the NURBS description of the shell middle surface. The isogeometric shell formulation is implemented using the PetIGA and igakit software packages developed by the authors. The igakit package is a Python package used to generate NURBS representations of geometries that can be utilised by the PetIGA finite element framework. The latter utilises data structures and routines of the portable, extensible toolkit for scientific computation (PETSc), [5,6]. The current shell implementation is valid for static, linear problems only, but the software package is well suited for future extensions to geometrically and materially nonlinear regime as well as to dynamic problems. The accuracy of the approach in the pinched cylinder benchmark problem and present comparisons against the h-version of the finite element method with bilinear elements. Quadratic, cubic and quartic NURBS discretizations are compared against the isoparametric bilinear discretization introduced in [7]. The results show that the quadratic and cubic NURBS approximations exhibit notably slower convergence under uniform mesh refinement as the thickness decreases but the quartic approximation converges relatively quickly within the standard variational framework. The authors future work is concerned with building an isogeometric finite element method for modelling nonlinear structural response of thin-walled shells undergoing large rigid-body motions. The aim is to use the model in a aeroelastic framework for the simulation of flapping wings.
KAUST Department:
Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Numerical Porous Media SRI Center (NumPor)
Publisher:
Civil-Comp, Ltd.
Journal:
Proceedings of the Eleventh International Conference on Computational Structures Technology
Conference/Event name:
11th International Conference on Computational Structures Technology, CST 2012
Issue Date:
4-Sep-2012
DOI:
10.4203/ccp.99.221
Type:
Conference Paper
ISBN:
9781905088546
Appears in Collections:
Conference Papers; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorNiemi, Anttien
dc.contributor.authorCollier, Nathaniel Orenen
dc.contributor.authorDalcín, Lisandro D.en
dc.contributor.authorGhommem, Mehdien
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-08-04T07:05:03Zen
dc.date.available2015-08-04T07:05:03Zen
dc.date.issued2012-09-04en
dc.identifier.isbn9781905088546en
dc.identifier.doi10.4203/ccp.99.221en
dc.identifier.urihttp://hdl.handle.net/10754/564609en
dc.description.abstractThis paper constitutes the first steps in our work concerning isogeometric shell analysis. An isogeometric shell model of the Reissner-Mindlin type is introduced and a study of its accuracy in the classical pinched cylinder benchmark problem presented. In contrast to earlier works [1,2,3,4], the formulation is based on a shell model where the displacement, strain and stress fields are defined in terms of a curvilinear coordinate system arising from the NURBS description of the shell middle surface. The isogeometric shell formulation is implemented using the PetIGA and igakit software packages developed by the authors. The igakit package is a Python package used to generate NURBS representations of geometries that can be utilised by the PetIGA finite element framework. The latter utilises data structures and routines of the portable, extensible toolkit for scientific computation (PETSc), [5,6]. The current shell implementation is valid for static, linear problems only, but the software package is well suited for future extensions to geometrically and materially nonlinear regime as well as to dynamic problems. The accuracy of the approach in the pinched cylinder benchmark problem and present comparisons against the h-version of the finite element method with bilinear elements. Quadratic, cubic and quartic NURBS discretizations are compared against the isoparametric bilinear discretization introduced in [7]. The results show that the quadratic and cubic NURBS approximations exhibit notably slower convergence under uniform mesh refinement as the thickness decreases but the quartic approximation converges relatively quickly within the standard variational framework. The authors future work is concerned with building an isogeometric finite element method for modelling nonlinear structural response of thin-walled shells undergoing large rigid-body motions. The aim is to use the model in a aeroelastic framework for the simulation of flapping wings.en
dc.publisherCivil-Comp, Ltd.en
dc.titleIsogeometric shell formulation based on a classical shell modelen
dc.typeConference Paperen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalProceedings of the Eleventh International Conference on Computational Structures Technologyen
dc.conference.date4 September 2012 through 7 September 2012en
dc.conference.name11th International Conference on Computational Structures Technology, CST 2012en
dc.conference.locationDubrovniken
dc.contributor.institutionConsejo Nacional de Investigaciones Científicas y Técnicas, Santa Fe, Argentinaen
kaust.authorNiemi, Anttien
kaust.authorCollier, Nathaniel Orenen
kaust.authorCalo, Victor M.en
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