Adaptive isogeometric analysis by local h-refinement with T-splines

By M. R. Dörfel, Bert Jüttler, Bernd Simeon. 2010

433 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/99327b477572d5a31a8c09598827c35408f7964d

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces (2012, methodology): “This is an improvement in comparison to recent works on adaptive isogeometric analysis [89, 90], where automatic local refinement employing cubic T-splines was reported to result in globally refined T-meshes when applied to a very similar advection-diffusion problem.”
Isogeometric collocation for large deformation elasticity and frictional contact problems (2015, background): “In so-called open knot vectors, the first p+ 1 knots and the last p+ 1 terms are equal, so that the basis is interpolatory at the ends.”
T‐spline finite element method for the analysis of shell structures (2009, methodology): “[22] introduced a posteriori error estimation techniques for local h-refinement with T-splines.”
Divergence-conforming discretization for Stokes problem on locally refined meshes using LR B-splines (2015, background): “For T-splines consider [5, 16, 33, 37, 38], for Hierarchical B-splines consider [30, 39, 8, 34], and for LR-splines see [25, 27].”
Numerical method for shape optimization using T-spline based isogeometric method (2010, methodology): “Also, T-spline can be utilized in image processing and visualization combined with a level set approach (Yang and Jüttler 2007, 2008), and in analysis (Dörfel et al. 2008; Uhm et al. 2008).”
Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory (2015, positive): “basis functions typically used in the CAD environment (most notably NURBS, T-Splines [23], PHT-Splines [24]) to describe the geometry of the problem exactly as it is produced from CAD as well as to approximate the solution fields for the analysis.”
Isogeometric analysis using T-splines (2010, background): “We have experienced similar behavior, and this indicates to us the importance of developing new reﬁne-ment algorithms with better invariance and localization properties (see also [20]).”
Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials (2015, neutral): “Keywords: Isogeometric; Kirchhoff–Love; Thin shell; Hyperelastic; Finite strain; Nonlinear material; Incompressibility”