Isogeometric boundary element analysis using unstructured T-splines

By Michael A. Scott, R. Simpson, John A. Evans, Scott Lipton, Stéphane P.A. Bordas, Thomas J. R. Hughes, Thomas W. Sederberg. 2013

434 citations recorded by the source corpus.

We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to encompass unstructured control grids (unstructured meshes) and develop basis functions which are smooth (rational) polynomials defined in terms of the Bezier extraction framework and which pass standard patch tests. We then develop a collocation procedure which correctly accounts for sharp edges and corners, extraordinary points, and T-junctions. This approach is applied to several three-dimensional problems, including a real-world T-spline model of a propeller. We believe this work clearly illustrates the power of combining new analysis-suitable computer aided design technologies with established analysis methodologies, in this case, the boundary element method.

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

View Paper: https://www.semanticscholar.org/paper/1504acfad430e653ee8a2c7907e0b014510d1a86

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Implementation of regularized isogeometric boundary element methods for gradient‐based shape optimization in two‐dimensional linear elasticity (2016, methodology): “3) More importantly, we use regularized boundary integral equations [64, 65, 66, 56] for sensitivity analysis, which is in opposition to existing work in the literature [55, 59].”
Isogeometric boundary-element analysis for the wave-resistance problem using T-splines (2014, background): “However, when T-splines have no T-junctions or extraordinary points, the 1-ring collocation points described in [18] are equivalent to the two-dimensional Greville abscissae.”
Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth (2017, methodology): “The conjoint use of IGA and BEM (IGABEM) permits the direct use of the CAD model, without any mesh generation and was developed for stress analysis [63,62,64], shape optimization [65–67].”
Isogeometric analysis: An overview and computer implementation aspects (2012, methodology): “Isogeometric boundary element methods for elastostatic analysis were presented in [118, 126], demonstrating that mesh generation can be completely circumvented by using CAD discretizations for analysis.”
Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems (2013, neutral): “[10] employed T-splines for elastostatic problems.”
Efficient finite element methodology based on cartesian grids: application to structural shape optimization (2013, methodology): “[32] where the Isogeometric Analysis IGA [33] with NURBS and TSplines, respectively, have been adapted to the BEM.”
A parameter-free variational coupling approach for trimmed isogeometric thin shells (2017, methodology): “, based on embedded domain methods [10,11] or boundary element methods [12,13].”
Isogeometric collocation using analysis-suitable T-splines of arbitrary degree (2016, background): “Note that we exclude ab initio the presence of extraordinary nodes [74, 64, 75] in the T-mesh.”
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.”
Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods (2015, methodology): “– unsymmetric formulations [11, 12] – hybrid Trefftz FEM [13, 14] – polygonal FEM (PFEM) [15] Coupling geometry and analysis, for example, isogeometric analysis [16, 17], isogeometric boundary element method [18, 19].”
Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity (2019, background): “[46] contains an analytical solution to the displacement and stress, the former which is correct and the latter which is not.”
Isogeometric analysis with geometrically continuous functions on planar multi-patch geometries (2017, background): “Related results include the recent publications [17, 21, 22], which are based on different G(1)-smooth multi-patch spline surfaces, and the use of EVs in T-spline-based representations [25].”