A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach

Handle URI:
http://hdl.handle.net/10754/566067
Title:
A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach
Authors:
Espath, L. F R; Braun, Alexandre Luis; Awruch, Armando Miguel; Dalcin, Lisandro ( 0000-0001-8086-0155 )
Abstract:
A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Publisher:
Wiley-Blackwell
Journal:
International Journal for Numerical Methods in Engineering
Issue Date:
3-Feb-2015
DOI:
10.1002/nme.4870
Type:
Article
ISSN:
00295981
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorEspath, L. F Ren
dc.contributor.authorBraun, Alexandre Luisen
dc.contributor.authorAwruch, Armando Miguelen
dc.contributor.authorDalcin, Lisandroen
dc.date.accessioned2015-08-12T09:26:51Zen
dc.date.available2015-08-12T09:26:51Zen
dc.date.issued2015-02-03en
dc.identifier.issn00295981en
dc.identifier.doi10.1002/nme.4870en
dc.identifier.urihttp://hdl.handle.net/10754/566067en
dc.description.abstractA numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.en
dc.publisherWiley-Blackwellen
dc.subjectCorotational kinematicsen
dc.subjectGeneralized energy-momentum method+ξen
dc.subjectGeneralized-α methoden
dc.subjectIsogeometric analysisen
dc.subjectNURBSen
dc.titleA NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approachen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalInternational Journal for Numerical Methods in Engineeringen
dc.contributor.institutionGraduate Program in Civil Engineering (PPGEC) Federal University of Rio Grande do Sul (UFRGS) Porto Alegreen
dc.contributor.institutionNational Scientific and Technical Research Council (CONICET) Santa Fe Argentinaen
kaust.authorDalcin, Lisandroen
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