An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces

By Dominik Schillinger, Luca Dede', Michael A. Scott, John A. Evans, Michael J. Borden, Ernst Rank, Thomas J. R. Hughes. 2012

498 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c6777687a1a1356deb4b422925a8f643b7e12ada

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

In Mechanics of Materials

Citations in the corpus

Mathematical analysis of variational isogeometric methods* (2014, background): “…paradigm in the papers by Vuong, Giannelli, Jüttler and Simeon (2011), Giannelli, Jüttler and Speleers (2012), Giannelli and Jüttler (2013), Schillinger et al. (2012) and others; LR splines were defined in Dokken, Lyche and Pettersen (2013) and further investigated in Johannessen,…”
A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework (2014, unknown): “[36] for a discussion of hierarchical B-splines).”
Multiscale isogeometric topology optimization for lattice materials (2017, background): “In recent years, isogeometric analysis (IGA) [34, 35], where the basis functions of the geometric model are directly used for finite element computations, has much attracted the attention of researchers in a variety of domains, as an efficient alternative to other conventional methods [36-42].”
Integration by interpolation and look-up for Galerkin-based isogeometric analysis (2015, methodology): “First, we will explore the extension of the IIL approach to the case of non-uniform knot vectors and to hierarchical splines [18,25,28,34].”
Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review (2015, methodology): “The p-version of the FEM and the IGA have been used mainly for static or modal analyses [68, 102, 219, 221].”
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.”
Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone (2015, methodology): “For all results reported in this section second-order B-splines have been used, ϱmax = 3 and rtol = 2−6.”
Three-dimensional isogeometrically enriched finite elements for frictional contact and mixed-mode debonding (2015, background): “Note that the generation of volumetric NURBS and T-spline meshes is challenging for general geometries and is a topic of current research, e.g. see Escobar et al. (2011), Wang et al. (2013), Liu et al. (2014), and Schillinger et al. (2012).”