Robustness of isogeometric structural discretizations under severe mesh distortion

By Scott Lipton, John A. Evans, Yuri Bazilevs, Thomas Elguedj, Thomas J. R. Hughes. 2010

295 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/075221f5b5dd0b87a4e3e3eb9aac2325db8405df

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Isogeometric boundary element analysis using unstructured T-splines (2013, methodology): “A small sampling includes fluids and turbulence [5, 6, 7, 8], fluid-structure interaction [9, 10, 11, 12], incompressibility [13, 14, 15], structural and vibration analysis [16, 3], plates and shells [17, 18, 19, 20, 21], phase-field analysis [22, 23, 24], large deformation structural analysis with ”
The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches (2010, methodology): “[25] S.”
X‐FEM in isogeometric analysis for linear fracture mechanics (2011, background): “They also possess the higher order continuity required for a rotation-free shell formulation [12], permit explicit time integration with higher order elements without the usual FEM stable time step size penalty [13], and generally add robustness to the computations [14].”
Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity (2019, background): “In particular, several investigations have demonstrated superior robustness and accuracy per degree of freedom [9, 30, 36], and excellent spectral behavior has been shown in a number of studies [19, 23, 31, 32] explaining the excellent results ob20 tained in applications such as structural dynamics ”
Bounding the influence of domain parameterization and knot spacing on numerical stability in Isogeometric Analysis (2014, background): “Lipton et al. [27] discovered the effect of severe distortion of the control and physical mesh.”
Isogeometric analysis and domain decomposition methods (2012, methodology): “Isogeometric analysis has been applied to the field of fluid mechanics [2], structural analysis [9,10,28], shell formulations [3], phase field models [13] and contact problems [33,29].”
Mathematical analysis of variational isogeometric methods* (2014, methodology): “…use of Kirchhoff models is made possible by the higher regularity of splines; for nonlinear solid mechanics (Elguedj, Bazilevs, Calo and Hughes 2008, Lipton et al. 2010, Echter and Bischoff 2010, Auricchio, Beirão da Veiga, Lovadina and Reali 2010a), shape optimization (Wall, Frenzel and Cyron…”
A NURBS-based immersed methodology for fluid–structure interaction (2015, methodology): “The same fact was shown for isogeometric structural analysis in [35].”
Isogeometric shell analysis: The Reissner-Mindlin shell (2010, background): “[33], it is noted that robustness of isogeometric NURBS elements increases with order.”
Local refinement of analysis-suitable T-splines (2012, methodology): “Areas of application of NURBS-based isogeometric analysis include turbulence [5–8], fluid–structure interaction [9–12], incompressibility [13–15], structural analysis [16,3], plates and shells [17–21], phase-field analysis [22,23], large deformation with mesh distortion [24], shape optimization [25–”
The variational collocation method (2016, methodology): “The higher-order continuity of the basis functions used in IGA (among other advantages [7, 8, 9, 10]) allows for a straightforward application of the collocation method, while retaining the geometric flexibility of finite elements [11, 12, 13].”
An unconditionally energy-stable method for the phase field crystal equation (2012, background): “been successfully applied to a number of problems in solid [13,19,37,38] and fluid mechanics [5,6] showing significant efficiency and robustness.”
Isogeometric analysis: An overview and computer implementation aspects (2012, background): “(ii) The effect of mesh distortion on the performance of IGA for solid mechanics was discussed in [74] in which it was found that higher-order NURBS functions are able to somewhat alleviate the impact of the distortions.”
Optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis (2017, background): “It appears that isogeometric analysis offers several important advantages over classical finite element analysis, such as increased robustness and accuracy on a per degree-of-freedom basis [17, 26, 35], and improved spectral properties [18, 19, 28], important in hyperbolic problems.”
Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique (2013, background): “…a growing impact on several fields, from fluid dynamics (Bazilevs et al., 2007, 2008, 2010; Zhang et al., 2007; Gomez et al., 2010; Buffa et al., 2011) to structural mechanics (Cottrell et al., 2006; Auricchio et al., 2007; Lipton et al., 2010) and electromagnetics (Buffa et al., 2010, 2011).”