Trivariate spline representations for computer aided design and additive manufacturing

Dokken, Tor; Skytt, Vibeke; Barrowclough, Oliver J. D.

doi:10.1016/j.camwa.2018.08.017

Cited by 35 publications

(15 citation statements)

References 19 publications

(31 reference statements)

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“…One popular method for local refinement is the Locally Refined Bsplines (LR B-Splines), see [85] and [86]. In [87] and [88] LR B-Splines have been proposed for achieving more compact representation of the object geometry. In fact LR B-Splines approach appears to be very efficient in achieving high data compression ratios, which is very advantageous in a digital twin context.…”

Section: A Physics-based Modelingmentioning

confidence: 99%

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

2020

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A digital twin can be defined as an adaptive model of a complex physical system. Recent advances in computational pipelines, multiphysics solvers, artificial intelligence, big data cybernetics, data processing and management tools bring the promise of digital twins and their impact on society closer to reality. Digital twinning is now an important and emerging trend in many applications. Also referred to as a computational megamodel, device shadow, mirrored system, avatar or a synchronized virtual prototype, there can be no doubt that a digital twin plays a transformative role not only in how we design and operate cyber-physical intelligent systems, but also in how we advance the modularity of multi-disciplinary systems to tackle fundamental barriers not addressed by the current, evolutionary modeling practices. In this work, we review the recent status of methodologies and techniques related to the construction of digital twins. Our aim is to provide a detailed coverage of the current challenges and enabling technologies along with recommendations and reflections for various stakeholders.

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Section: A Physics-based Modelingmentioning

confidence: 99%

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

2020

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“…If bilinear SR is considered, C 0,0 continuity is satisfied along the four half axes. Since in each quadrant there are four Bézier ordinates, applying all the relations above, only b 1 1,1 , b 1 1,0 , b 4 1,0 and b 3 0,0 are remained to be assigned. With simple sign assignment, we get the bilinear SR. For biquadratic and bicubic SR, there are relations as in the Boolean intersection case, where there exist ordinates that have signs that do not align with each other.…”

Section: Sr In Bézier Form For Boolean Union Operationmentioning

confidence: 99%

“…Recent years have witnessed a rapid development of 3D printing together with the related studies derived in topics such as modeling and analysis [1][2][3][4][5][6][7]. Due to the several modeling requirements of 3D printing, implicit representation forms an ideal choice for such technology.…”

Section: Introductionmentioning

confidence: 99%

Spline R-Function and Applications in FEM

sci¹

2020

NMTMA

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R-function is a widely used tool when considering objects obtained through the Boolean operations start from simple base primitives. However, there is square root operation in the representation. Considering that the use of splines will facilitate the calculations within the CAD system, in this paper, we propose a system of R-functions represented in spline form called Spline R-function (SR). After transforming the function ranges of two base primitives to a new coordinate system, a series of sign constraints following a specific Boolean operation are derived and the spline R-function can be formulated as a piecewise function. Representation of SR in both Bézier form and B-spline form have been given. Among which the Bézier ordinates are determined with the help of the B-net method through setting up a series of relations according to the sign constraints and properties of R-functions. The construction processes for both Boolean intersection and union operations with different smoothness are discussed in detail. Numerical experiments are conducted to show the potential of the proposed spline R-function.

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“…Here we mention only two such aspects, which both concern the interplay between geometry representation and PDE solutions. First, it is important to point out that most industrial CAD software represent 3D objects by their boundaries only, so that a preliminar non-trivial conversion to a 3D B-Spline/NURBS model is needed [42,43]; moreover, such software often complex geometries are represented by boolean operation between elementary shapes by so-called "trimming operations", which partially destroy the tensor structure and require ad-hoc treatment [44,45].…”

Section: Isogeometric Solversmentioning

confidence: 99%

IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains

Beck

Tamellini

Tempone

2019

Computer Methods in Applied Mechanics and Engineering

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This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC algorithm is very natural since they are tensor-based PDE solvers, which are precisely what is required by the MISC machinery. Moreover, the combination-technique formulation of MISC allows the straight-forward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach. Highlights• Isogeometric solvers used in a MISC framework for forward UQ problems.• The combination-technique formulation of the method allows straight-forward reuse of legacy IGA solvers.

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Trivariate spline representations for computer aided design and additive manufacturing

Cited by 35 publications

References 19 publications

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

Spline R-Function and Applications in FEM

IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains

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