<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si27.gif" overflow="scroll"><mml:mrow><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> regularity properties of singular parameterizations in isogeometric analysis

Takacs, Thomas; Jüttler, Bert

doi:10.1016/j.gmod.2012.05.006

Cited by 33 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, if we look at 'Case I' from in Sec. 4. of [23], we get with Theorem 4.4. from latter article that the coupled SB-IGA test functions are in H 2 (Ω m ) for each patch. To see this, we observe that we use for the coupling method only such B-splines B r i,p • B r j,p with j > 2 or the additional scaling center test functions, which are obviously smooth in a whole neighborhood of the scaling center.…”

Section: Remarks On Stabilitymentioning

confidence: 83%

Scaled boundary isogeometric analysis with C¹ coupling for Kirchhoff‐Love theory

Jeremias

Reichle

Klinkel

et al. 2023

Proc Appl Math and Mech

View full text Add to dashboard Cite

Scaled boundary isogeometric analysis (SB-IGA) describes the computational domain by proper boundary NURBS together with a well-defined scaling center; see [5]. More precisely, we consider star convex domains whose domain boundaries correspond to a sequence of NURBS curves and the interior is determined by a scaling of the boundary segments with respect to a chosen scaling center. However, providing a decomposition into star shaped blocks one can utilize SB-IGA also for more general shapes. Even though several geometries can be described by a single patch, in applications frequently there appear multipatch structures. Whereas a C 0 continuous patch coupling can be achieved relatively easily, the situation becomes more complicated if higher regularity is required. Consequently, a suitable coupling method is inevitably needed for analyses that require global C 1 continuity.In this contribution we apply the concept of analysis-suitable G 1 parametrizations [2] to the framework of SB-IGA for the C 1 coupling of planar domains with a special consideration of the scaling center. We obtain globally C 1 regular basis functions and this enables us to handle problems such as the Kirchhoff-Love plate and shell, where smooth coupling is an issue. Furthermore, the boundary representation within SB-IGA makes the method suitable for the concept of trimming. In particular, we see the possibility to extend the coupling procedure to study trimmed plates and shells.The approach was implemented using the GeoPDEs package [1] and its performance was tested on several numerical examples. Finally, we discuss the advantages and disadvantages of the proposed method and outline future perspectives.

show abstract

Section: Remarks On Stabilitymentioning

confidence: 83%

Scaled boundary isogeometric analysis with C¹ coupling for Kirchhoff‐Love theory

Jeremias

Reichle

Klinkel

et al. 2023

Proc Appl Math and Mech

View full text Add to dashboard Cite

show abstract

“…Singularly-parameterized C 1 surface constructions include [2, 3, 4, 5, 6, 7, 10]; [9] even shows how to construct C 2 surfaces (but specifies no rules that generically yield good shape). Independently, in the context of iso-geometry, Takacs and Jüttler [11] discussed singular spline constructions for analysis and observed that specific linear combinations of singular splines can be sufficiently regular for iso-geometric analysis. The monograph [12] characterizes subdivision surfaces as smooth spline surfaces with singularities at the irregular points and establishes the differential-geometric properties of subdivision surfaces at the singularities.…”

Section: Introductionmentioning

confidence: 99%

Improved shape for refinable surfaces with singularly parameterized irregularities

Karčiauskas

Peters

2017

Computer-Aided Design

View full text Add to dashboard Cite

To date, singularly-parameterized surface constructions suffer from poor highlight line distributions, ruling them out as a surface representation of choice for primary design surfaces. This paper explores graded, many-piece, everywhere C1 singularly-parameterized surface caps that mimic the shape of a high-quality guide surface. The approach illustrates the trade-off between polynomial degree and surface quality. For bi-degree 5, minor flaws in the highlight line distribution are still visible when zooming in on the singularity, but the distribution is good at the macroscopic level. Constructions of degree bi-4 or bi-3 may require one or more steps of guided subdivision to reach the same macroscopic quality. Akin to subdivision surfaces, singularly-parameterized functions on the surfaces are straightforward to refine.

show abstract

“…A major contribution of Reif’s singular construction [Rei97] was a proof showing that the corner singularity is removable by a local change of variables; and that the resulting surface is tangent continuous at and near the central irregular point where more of fewer than four tensor-product patches come together. More recently, in the context of iso-geometry, Takacs and Jüttler [TJ12] analyzed singular spline constructions, but did not draw the connection to the earlier surface constructions. They observed that specific linear combinations of singular splines can be sufficiently regular for isogeometric analysis and closed with the prediction that “main targets for further analysis are approximation properties on singular domains”.…”

Section: Introductionmentioning

confidence: 99%

Refinable C1 spline elements for irregular quad layout

Nguyen

Peters

2016

Computer Aided Geometric Design

View full text Add to dashboard Cite

Building on a result of U. Reif on removable singularities, we construct C1 bi-3 splines that may include irregular points where less or more than four tensor-product patches meet. The resulting space complements PHT splines, is refinable and the refined spaces are nested, preserving for example surfaces constructed from the splines. As in the regular case, each quadrilateral has four degrees of freedom, each associated with one spline and the splines are linearly independent. Examples of use for surface construction and isogeometric analysis are provided.

show abstract

H2 regularity properties of singular parameterizations in isogeometric analysis

Cited by 33 publications

References 27 publications

Scaled boundary isogeometric analysis with C¹ coupling for Kirchhoff‐Love theory

Scaled boundary isogeometric analysis with C¹ coupling for Kirchhoff‐Love theory

Improved shape for refinable surfaces with singularly parameterized irregularities

Refinable C1 spline elements for irregular quad layout

Contact Info

Product

Resources

About

H2 regularity properties of singular parameterizations in isogeometric analysis

Cited by 33 publications

References 27 publications

Scaled boundary isogeometric analysis with C1 coupling for Kirchhoff‐Love theory

Scaled boundary isogeometric analysis with C1 coupling for Kirchhoff‐Love theory

Improved shape for refinable surfaces with singularly parameterized irregularities

Refinable C1 spline elements for irregular quad layout

Contact Info

Product

Resources

About

Scaled boundary isogeometric analysis with C¹ coupling for Kirchhoff‐Love theory

Scaled boundary isogeometric analysis with C¹ coupling for Kirchhoff‐Love theory