Embedded structural entities in NURBS-based isogeometric analysis

Bauer, Anna; Breitenberger, M.; Philipp, Benedikt; Wüchner, Roland; Bletzinger, Kai‐Uwe

doi:10.1016/j.cma.2017.07.010

Cited by 34 publications

(13 citation statements)

References 19 publications

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“…Nevertheless, the construction of geometric representations suitable to IGA, from CAD geometries, remains the major unsolved issue and IGA is indeed a very efficient strategy on "simple" geometries (i.e., on 2D or 2.5D geometries [10,4,27]) but not for general three dimensional problems. For 3D objects the conversion of a CAD geometry into a geometry on which isogeometric methods are defined (IGA-ready) is challenging and has many similarities with the conversion to a FE domain: its automation is far from being at the state of the art.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric Analysis on V-reps: First results

Antolín

Buffa

Martinelli

2019

Computer Methods in Applied Mechanics and Engineering

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Inspired by the introduction of Volumetric Modeling via volumetric representations (V-reps) by Massarwi and Elber in 2016, in this paper we present a novel approach for the construction of isogeometric numerical methods for elliptic PDEs on trimmed geometries, seen as a special class of more general V-reps. We develop tools for approximation and local re-parameterization of trimmed elements for three dimensional problems, and we provide a theoretical framework that fully justifies our algorithmic choices. We validate our approach both on two and three dimensional problems, for diffusion and linear elasticity.

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Section: Introductionmentioning

confidence: 99%

Isogeometric Analysis on V-reps: First results

Antolín

Buffa

Martinelli

2019

Computer Methods in Applied Mechanics and Engineering

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“…We introduce the concept of embedded surface in order to overcome the geometric challenges highlighted in the previous section. The idea comes from Bauer et al [54] who considered univariate embedded entities. More precisely, they embed a curve into a surface.…”

Section: Main Ideamentioning

confidence: 99%

The embedded isogeometric Kirchhoff–Love shell: From design to shape optimization of non-conforming stiffened multipatch structures

Hirschler

Bouclier

Duval

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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Isogeometric shape optimization uses a unique model for the geometric description and for the analysis. The benefits are multiple: in particular, it avoids tedious procedures related to mesh updates. However, although the analysis of complex multipatch structures now becomes tractable with advanced numerical tools, isogeometric shape optimization has not yet been proven to be applicable for designing such structures. Based on the initial concept of integrating design and analysis, we develop a new approach that deals with the shape optimization of non-conforming multipatch structures. The model is built by employing the Free-Form Deformation principle. Introducing NURBS composition drastically simplifies the imposition of the shape updates in case of a non-conforming multipatch configuration. In the case of stiffened structures, the use of embedded surfaces enables to tackle the geometric constraint of connecting interfaces between the panel and the stiffeners during shape modifications. For the analysis, we introduce the embedded Kirchhoff-Love shell formulation. The NURBS composition defines the geometry of the shell while the displacement field is approximated using the same spline functions as for the embedded surface. We also formulate a new mortar method to couple non-conforming Kirchhoff-Love shells which intersect with any angle. We apply the developed method on different examples to demonstrate its efficiency and its potential to optimize complex industrial structures in a smooth manner.

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“…Die Idee des Trimmens und der Kopplungen kann zum Konzept der eingebetteten Elemente erweitert werden . Ein Punkt auf einer Kurve kann z.…”

Section: Voraussetzungen Für Eine Cad‐integrierte Analyseunclassified

CAD‐integrierte Analyse im Entwurfsprozess

et al. 2019

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Leichtbau ist geprägt von seiner filigranen Tragstruktur, die sich durch eine Vielfalt von grazilen Formen und organisch wirkenden Freiformflächen auszeichnet. Moderne CAD‐Systeme nutzen NURBS (Non‐uniform rational B‐Splines), um die Formsprache des Leichtbaus dem Computer zugänglich zu machen. Die isogeometrische B‐Rep‐Analyse (IBRA) verwendet NURBS für das Lösen strukturmechanischer Probleme. Durch die Nutzung der gleichen geometrischen und topologischen Beschreibungen wird der kontinuierliche Datenaustausch zwischen CAD‐ und Analyse‐Software vereinfacht. Die einheitliche Modellbeschreibung begünstigt parametrische Entwurfsprozesse. Vorteile ergeben sich auch dort, wo die Ergebnisse einer Analyse wieder in das CAD übertragen werden sollen; beispielsweise bei einer Baufortschrittsmodellierung oder einer Formfindung, wenn es darum geht, die berechneten Geometrien erneut in den Entwurfsprozess einzubinden und mit ihnen weiterzuarbeiten. Im Hinblick auf biegeaktive Strukturen spielen die Glattheit der Modellgeometrie und die Abbildung ihrer Verformung eine bedeutende Rolle. Durch die Verwendung von NURBS ist dies gegeben.

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Embedded structural entities in NURBS-based isogeometric analysis

Cited by 34 publications

References 19 publications

Isogeometric Analysis on V-reps: First results

Isogeometric Analysis on V-reps: First results

The embedded isogeometric Kirchhoff–Love shell: From design to shape optimization of non-conforming stiffened multipatch structures

CAD‐integrierte Analyse im Entwurfsprozess

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