Locking free isogeometric formulations of curved thick beams

Bouclier, Robin; Elguedj, Thomas; Combescure, Alain

doi:10.1016/j.cma.2012.06.008

Cited by 117 publications

(99 citation statements)

References 34 publications

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“…Over the last decade, IGA has become a well-established method used in a wide range of problems including structural mechanics [3][4][5][6][7][8][9][10][11][12] with recent developments for spatial Bernoulli beams [13,14], turbulent flow and fluid-structure interaction [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Marino

2016

Computer Methods in Applied Mechanics and Engineering

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Highlights• Isogeometric collocation is extended to geometrically exact beams.• Consistent linearization of the strong form of the governing equations is derived.• Incremental rotations are parametrized through Eulerian rotation vectors.• Numerical tests show efficiency and high accuracy. AbstractWe extend the isogeometric collocation method to the geometrically nonlinear beams. An exact kinematic formulation, able to represent three-dimensional displacements and rotations without any restriction in magnitude, is presented without the introduction of the moving frame concept. A displacement-based formulation is adopted. Full linearization of the strong form of the governing equations is derived consistently with the underlying geometric structure of the configuration manifold. Incremental rotations are parametrized through Eulerian rotation vectors and configuration updates are performed by means of the exponential map. Numerical tests demonstrate that the proposed combination of isogeometric collocation method with the chosen rotations parametrization results in an efficient computational scheme able to model complex problems with high accuracy.

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Section: Introductionmentioning

confidence: 99%

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Marino

2016

Computer Methods in Applied Mechanics and Engineering

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“…The following lemmas, which have been proved in [23, Lemmas 2.1 and 2.2] show that the ellipticity in the kernel and inf-sup classical conditions of mixed problems holds true for (8)- (9).…”

Section: Introductionmentioning

confidence: 91%

“…The Timoshenko theory to date is one of the most used models to approximate the deformation of a thin or moderately thick elastic beam [5,9,12,18,20,26,30]. It is well understood that standard finite elements applied to this model lead to wrong results when the thickness of the beam is small due to the so called locking phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Analysis of a Bending Moment Formulation for the Vibration Problem of a Non-homogeneous Timoshenko Beam

2015

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In this paper we analyze a low-order finite element method for approximating the vibration frequencies and modes of a non-homogeneous Timoshenko beam. We consider a formulation in which the bending moment is introduced as an additional unknown. Optimal order error estimates are proved for displacements, rotations, shear stress and bending moment of the vibration modes, as well as a double order of convergence for the vibration frequencies.These estimates are independent of the beam thickness, which leads to the conclusion that the method is locking free. For its implementation, displacements and rotations can be eliminated leading to a well posed generalized matrix eigenvalue problem for which the computer cost of its solution is similar to that of other classical formulations. We report numerical experiments which allow us to assess the performance of the method.

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“…Also the field inconsistency within the term for shear strain causes that zero shear strain cannot be satisfied along entire patch when the same order interpolation of unknowns is used. Several locking removal techniques have been proposed to unlock isogeometric beam element including reduced integration,B-method, DSG method, see [2,3] for the references. In this study, the DSG-based formulation is used.…”

Section: Locking Treatmentmentioning

confidence: 99%

“…Our focus is placed on its application for the analysis of curved beams as the curved geometries can especially benefit from the isogeometric approach. We use the formulation of curved beam element presented by Bouclier et al [2] with the locking treatment based on Discrete Shear Gap (DSG) method [3,4]. The element has been implemented into OOFEM finite element solver [5] and our main goal is to develop a connection between CAD system and the solver to provide a tool encapsulating the analysis within the architectural design environment.…”

Section: Introductionmentioning

confidence: 99%

On Development of the Interactive Design Tool Based on Isogeometric Analysis

Dvořáková

Patzák

2017

APP

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Abstract. Isogeometric analysis is a new concept of Finite element method which has been proposed to bridge the gap between the CAD systems and the FEM solvers. In Isogeometric analysis, the same basis functions, typically splines or NURBS, are used for geometry description as well as for approximation of unknowns and thus the same model can be shared between CAD and IGA systems. This results in a higher accuracy and overall efficiency of the analysis.Many isogeometric elements have been already proposed and implemented into the existing finite element solvers, but the automatic connection with a CAD system is usually missing. Our goal is to develop such a connection and to provide a tool which would interactively run the analysis when the model changes. This approach can enormously enhance the design process as it can provide the basic knowledge about the structural behavior already in conceptual design phase.

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Locking free isogeometric formulations of curved thick beams

Cited by 117 publications

References 34 publications

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Finite Element Analysis of a Bending Moment Formulation for the Vibration Problem of a Non-homogeneous Timoshenko Beam

On Development of the Interactive Design Tool Based on Isogeometric Analysis

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