Duality and unified analysis of discrete approximations in structural dynamics and wave propagation : Comparison of p-method finite elements with k-method NURBS

By Thomas J. R. Hughes, Alessandro Reali, Giancarlo Sangalli. 2008

442 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3c31778f3b8d8ca4a29940599d7a8242b906563f

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In Computational Mechanics

In Statistical and Nonlinear Physics

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Citations in the corpus

Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review (2015, methodology): “A recently published approach employs non-uniform rational B-splines (NURBS) as shape functions [37,54,106,107,270,270].”
Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems (2014, methodology): “As has been mentioned in previous works [7,13], there are a collection of so-called ‘‘outlier’’ modes in the NURBS spectrum that appear to offer no approximability when a uniform mesh is utilized.”
Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids (2011, background): “the results in [7–12]), it was found that NURBS-based isogeometric FEs give more accurate results than their traditional FE-counterparts.”
Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique (2013, methodology): “Numerical tests shown in literature and the studies (Hughes et al., 2008; Evans et al., 2009; Beirão da Veiga et al., 2011) proved that higher smoothness is advantageous.”
Rotation free isogeometric thin shell analysis using PHT-splines (2011, background): “Therefore, most studies in the context of isogeometric analysis focus on NURBS-based isogeometric finite element formulations [20–25].”
Locking-free isogeometric collocation methods for spatial Timoshenko rods (2013, unknown): “, [14,21,31,40,43]).”
A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM (2010, background): “Additional benefits may include higher order accuracy [2, 8, 9, 10, 11, 12, 13, 14], C(1) or higher continuity, and increased robustness [15].”
Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (2013, background): “Of particular importance in this respect is the observation that, unlike standard FEM, the higher modes of IGA basis functions do not diverge with increasing degree, but achieve almost spectral accuracy that improves with degree [8,9].”
Isogeometric analysis using T-splines (2010, background): “Not only do smooth bases lead to superior accuracy per degree-of-freedom compared with C 0 -continuous bases [2,19,32], but the continuity can be reduced to better resolve steep gradients [18].”
A NURBS-based immersed methodology for fluid–structure interaction (2015, methodology): “IGA has been successfully applied to a large number of fields including body-fitted FSI problems [14, 38], fluid mechanics [39, 40], phase-filed models [26, 41, 42, 43, 44, 45], structural vibrations [46, 47], quasi-incompressible elasticity [48], shell modeling [49, 50], contact problems [51, 52, 5”