Subdivision surfaces: a new paradigm for thin‐shell finite‐element analysis

By Fehmi Cirak, Magdalena Ortiz, Peter Schröder. 2000

701 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a8d351957b900ad9ef432166a8ba39e2b7d212e7

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Subdivision-stabilised immersed b-spline finite elements for moving boundary flows (2012, background): “Refinability is crucial to a number of b-spline techniques, such as subdivision curves and surfaces [16, 23, 24], hierarchical refinement [25, 26], t-splines [27] and wavelets [23].”
Smooth, second order, non‐negative meshfree approximants selected by maximum entropy (2009, methodology): “in Bézier, B-Spline techniques [13], natural neighbor approximations [14], and subdivision approximations [15].”
Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results (2011, background): “, 2002) and the subdivision surfaces paradigm (Cirak et al., 2000) – in fact, also the meshless methods mentioned above fall in this category.”
Fully C1‐conforming subdivision elements for finite deformation thin‐shell analysis (2001, methodology): “For regular elements, all of whose nodes are vertices of valence six, Loop’s scheme returns Box-splines in the limit and the surface can be interpolated directly by means of Box-spline shape functions, as discussed in [20].”
Phase-field modeling of fracture in linear thin shells (2014, neutral): “3 Thin shell model In this section, we review the mechanics of thin shells [42, 43], based on a geometrically exact formulation presented in [30, 44].”
A bridging domain and strain computation method for coupled atomistic–continuum modelling of solids (2007, methodology): “For the continuum domain in the coupled nanotube model, the subdivision finite elements based on Loop’s scheme [28] are used.”
Advances in the formulation of the rotation-free basic shell triangle (2005, neutral): “) based on Kirchhoff s theory [10–26].”