Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

作者: Robin Bouclier , Jean-Charles Passieux , Michel Salaün

DOI: 10.1016/J.CMA.2016.05.037

关键词: Domain decomposition methodsLinear elasticityDevelopment (differential geometry)Lagrange multiplierGeometryIsogeometric analysisTopologyEngineeringDisplacement (vector)CouplingRange (mathematics)

摘要: In this work, we develop a mortar method for the coupling of NURBS sub-domains within patch that keeps benefit using more regular functions. The idea is to use two Lagrange multipliers match, across interface, tractions coming from discrete displacements in addition displacements. It results strategy suitable with continuity physical solution: when solution sufficiently smooth, enables represent C 1 behavior; but, only 0 displacement expected, no additional errors are introduced since traction force continuous and not whole derivative fields. Lower stress jumps at interface can then be observed which allows better transition information. As an application, non-intrusive algorithm also built proposed method, simple flexible local enrichments patches without loosing interest A range numerical examples two-dimensional linear elasticity carried out along comparisons other published techniques demonstrate performance its combined strategy.

参考文章(53)
J.A. Cottrell, A. Reali, Y. Bazilevs, T.J.R. Hughes, Isogeometric analysis of structural vibrations Computer Methods in Applied Mechanics and Engineering. ,vol. 195, pp. 5257- 5296 ,(2006) , 10.1016/J.CMA.2005.09.027
Vinh Phu Nguyen, Pierre Kerfriden, Marco Brino, Stéphane PA Bordas, Elvio Bonisoli, None, Nitsche's method for two and three dimensional NURBS patch coupling Computational Mechanics. ,vol. 53, pp. 1163- 1182 ,(2014) , 10.1007/S00466-013-0955-3
Christian Hesch, Peter Betsch, Isogeometric analysis and domain decomposition methods Computer Methods in Applied Mechanics and Engineering. ,vol. 213, pp. 104- 112 ,(2012) , 10.1016/J.CMA.2011.12.003
A.-V. Vuong, C. Giannelli, B. Jüttler, B. Simeon, A hierarchical approach to adaptive local refinement in isogeometric analysis Computer Methods in Applied Mechanics and Engineering. ,vol. 200, pp. 3554- 3567 ,(2011) , 10.1016/J.CMA.2011.09.004
Mickaël Duval, Jean-Charles Passieux, Michel Salaün, Stéphane Guinard, Non-intrusive Coupling: Recent Advances and Scalable Nonlinear Domain Decomposition Archives of Computational Methods in Engineering. ,vol. 23, pp. 17- 38 ,(2016) , 10.1007/S11831-014-9132-X
Dominik Schillinger, John A. Evans, Alessandro Reali, Michael A. Scott, Thomas J.R. Hughes, Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations Computer Methods in Applied Mechanics and Engineering. ,vol. 267, pp. 170- 232 ,(2013) , 10.1016/J.CMA.2013.07.017
Robin Bouclier, Jean-Charles Passieux, Michel Salaün, Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture Computer Methods in Applied Mechanics and Engineering. ,vol. 300, pp. 1- 26 ,(2016) , 10.1016/J.CMA.2015.11.007
Stéphane Bordas, VP Nguyen, Pierre Kerfriden, Spa Claus, Nitsche's method method for mixed dimensional analysis: conforming and non-conforming continuum-beam and continuum-plate coupling Computer Methods in Applied Mechanics and Engineering. ,(2013)
Wolfgang Dornisch, Ralf Müller, S34734551425 Klinkel, None, An efficient and robust rotational formulation for isogeometric Reissner–Mindlin shell elements Computer Methods in Applied Mechanics and Engineering. ,vol. 303, pp. 1- 34 ,(2016) , 10.1016/J.CMA.2016.01.018
Pierre Gosselet, Christian Rey, Non-overlapping Domain Decomposition Methods in Structural Mechanics Archives of Computational Methods in Engineering. ,vol. 13, pp. 515- 572 ,(2006) , 10.1007/BF02905857