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Studies of refinement and continuity in isogeometric structural analysis. (English) Zbl 1173.74407
Summary: We investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework. We consider two simple one-dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate NURBS solids. We also develop a local refinement strategy that we utilize in one of the shell analyses. We find that increased smoothness, that is, the “\(k\)-method,” leads to a significant increase in accuracy for the problems of structural vibrations over the classical \(C^{0}\)-continuous “\(p\)-method,” whereas a judicious insertion of \(C^{0}\)-continuous surfaces about singularities in a mesh otherwise generated by the \(k\)-method, usually outperforms a mesh in which all basis functions attain their maximum level of smoothness. We conclude that the potential for the \(k\)-method is high, but smoothness is an issue that is not well understood due to the historical dominance of \(C^{0}\)-continuous finite elements and therefore further studies are warranted.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
Software:
Jnurbs
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