Isogeometric Analysis: Representation of Geometry

Haberleitner, Michael; Jüttler, Bert; Scott, Michael A.; Thomas, Derek C.

doi:10.1002/9781119176817.ecm2106

Cited by 5 publications

(2 citation statements)

References 94 publications

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“…Their primary goal is to alleviate meshing related obstacles that often appear for geometrically complex domains. In this work, the flexibility of cut-cell methods with respect to complex geometries is important [57][58][59], since generating boundaryfitted spline discretizations of inhomogeneity problems outside of a CAD environment is not a trivial task. First, cut-cell methods need to be able to evaluate surface and volume integrals in cut elements [60][61][62][63][64], which we will describe in the following.…”

Section: Cut-cell Finite Element Methodsmentioning

confidence: 99%

Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods

Han

Stoter

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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Many interface formulations, e.g. based on asymptotic thin interphase models or material surface theories, involve higher-order differential operators and discontinuous solution fields. In this article, we are taking first steps towards a variationally consistent discretization framework that naturally accommodates these two challenges by synergistically combining recent developments in isogeometric analysis and cut-cell finite element methods. Its basis is the mixed variational formulation of the elastic interface problem that provides access to jumps in displacements and stresses for incorporating general interface conditions. Upon discretization with smooth splines, derivatives of arbitrary order can be consistently evaluated, while cut-cell meshes enable discontinuous solutions at potentially complex interfaces. We demonstrate via numerical tests for three specific nontrivial interfaces (two regimes of the Benveniste-Miloh classification of thin layers and the Gurtin-Murdoch material surface model) that our framework is geometrically flexible and provides optimal higher-order accuracy in the bulk and at the interface.

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Section: Cut-cell Finite Element Methodsmentioning

confidence: 99%

Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods

Han

Stoter

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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“…In this paper, we employ splines as basis functions, which are widely used today in the context of isogeometric analysis [57,58]. For further details, we refer to the recent reviews [59,60,61] and the references therein.…”

Section: Standard Isogeometric Finite Element Discretizationmentioning

confidence: 99%

Leveraging spectral analysis to elucidate membrane locking and unlocking in isogeometric finite element formulations of the curved Euler-Bernoulli beam

Nguyen,

Hiemstra,

Schillinger

2021

Preprint

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We initiate the use of spectral analysis for assessing locking phenomena in finite element formulations.• We illustrate this idea for a circular ring discretized with isogeometric curved Euler-Bernoulli beam elements.• We assess the displacement-based formulation with full and reduced integration, and the B-bar, discrete strain gap and Hellinger-Reissner methods.• Our study shows that spectral analysis can rigorously characterize membrane locking and unlocking for Euler-Bernoulli beam formulations.

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Template Mapping Using Adaptive Splines and Optimization of the Parameterization

Sajavičius

Jüttler

Ṡ́peh

2019

Advanced Methods for Geometric Modeling and Numerical Simulation

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Isogeometric Analysis: Representation of Geometry

Cited by 5 publications

References 94 publications

Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods

Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods

Leveraging spectral analysis to elucidate membrane locking and unlocking in isogeometric finite element formulations of the curved Euler-Bernoulli beam

Template Mapping Using Adaptive Splines and Optimization of the Parameterization

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