Hierarchic isogeometric large rotation shell elements including linearized transverse shear parametrization

Oesterle, Bastian; Sachse, Renate; Ramm, Ekkehard; Bischoff, Manfred

doi:10.1016/j.cma.2017.03.031

Cited by 58 publications

(47 citation statements)

References 49 publications

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“…The other Euler-Lagrange equations are the equilibrium equations. Solving (20) for ,x and replacing the corresponding expression in Equation (18) exactly reproduces the hierarchic displacement formulation from the work of Oesterle et al, 29 where v s (here denoted asv s ) is introduced as an extra primary variable in addition to v. The bending part resulting from u = ,x is identical to a standard primal formulation, since no treatment by a specific u parameter is performed. This fact can also be deduced in a more general way by inserting the condition Eū = E u into Equation (9), reproducing the internal energy expression of a standard displacement formulation.…”

Section: Timoshenko Beamsmentioning

confidence: 78%

“…The other Euler‐Lagrange equations are the equilibrium equations. Solving for φ , x and replacing the corresponding expression in Equation exactly reproduces the hierarchic displacement formulation from the work of Oesterle et al, where v s (here denoted as

{\overset{v}{true}}_{s}

) is introduced as an extra primary variable in addition to v .…”

Section: A Variational Methods To Avoid Lockingmentioning

confidence: 95%

“…A α are the in‐plane covariant base vectors of the reference configuration of the shell's mid surface. For further details concerning the underlying shell model and the notation used herein, the reader is referred to the works of Kiendl et al, Cirak et al, or Oesterle et al, where the Green‐Lagrange strains E u for a primal formulation are derived in more detail. Since only the membrane part of the strains

{boldE}_{normalu}^{normalm}

must be treated to remove membrane locking, the bending terms are not shown in the subsequent equations.…”

Section: A Variational Methods To Avoid Lockingmentioning

confidence: 99%

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A variational method to avoid locking—independent of the discretization scheme

Bieber

Oesterle

Ramm

et al. 2018

Numerical Meth Engineering

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Summary We present a variational method for problems in solid and structural mechanics that is designed to be intrinsically free from locking when using equal‐order interpolation for all involved fields. The specific feature of the formulation is that it avoids all geometrical locking effects (as opposed to material locking effects, for instance Poisson locking) for any type of structural or solid model, independent of the underlying discretization scheme. The possibility of employing equal‐order interpolation for all involved fields circumvents the task of finding particular function spaces to remove locking and avoid artificial stress oscillations. This is particularly attractive, for instance, for isogeometric analysis using unstructured meshes or T‐splines. Comprehensive numerical tests underline the promising behavior of the proposed method for geometrically linear and nonlinear problems in terms of displacements and stress resultants using standard finite elements, isogeometric finite elements, and a meshless method.

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Section: Timoshenko Beamsmentioning

confidence: 78%

{\overset{v}{true}}_{s}

) is introduced as an extra primary variable in addition to v .…”

Section: A Variational Methods To Avoid Lockingmentioning

confidence: 95%

{boldE}_{normalu}^{normalm}

must be treated to remove membrane locking, the bending terms are not shown in the subsequent equations.…”

Section: A Variational Methods To Avoid Lockingmentioning

confidence: 99%

See 1 more Smart Citation

A variational method to avoid locking—independent of the discretization scheme

Bieber

Oesterle

Ramm

et al. 2018

Numerical Meth Engineering

Self Cite

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“…Examples for element formulations of isogeometric surface elements for membranes can be found in [28,29] and for shells in [30][31][32][33][34][35][36][37][38].…”

Section: Analysis-related Enhancement Of Geometrical Datamentioning

confidence: 99%

Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis

Teschemacher

Bauer

Oberbichler

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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An entire design-through-analysis workflow solution for isogeometric B-Rep analysis (IBRA), including both the interface to existing CADs and the analysis procedure, is presented. Possible approaches are elaborated for the full scope of structural analysis solvers ranging from low to high isogeometric simulation fidelity. This is based on a systematic investigation of solver designs suitable for IBRA. A theoretically ideal IBRA solver has all CAD capabilities and information accessible at any point, however, realistic scenarios typically do not allow this level of information. Even a classical FE solver can be included in the CAD-integrated workflow, which is achieved by a newly proposed meshless approach. This simple solution eases the implementation of the solver backend. The interface to the CAD is modularized by defining a database, which provides IO capabilities on the base of a standardized data exchange format. Such database is designed to store not only geometrical quantities but also all the numerical information needed to realize the computations. This feature allows its use also in codes which do not provide full isogeometric geometrical handling capabilities. The rough geometry information for computation is enhanced with the boundary topology information which implies trimming and coupling of NURBS-based entities. This direct use of multi-patch trimmed CAD geometries follows the principle of embedding objects into a background parametrization. Consequently, redefinition and meshing of geometry is avoided. Several examples from illustrative cases to industrial problems are provided to demonstrate the application of the proposed approach and to explain in detail the proposed exchange formats.

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“…An application of a Kirchhoff-Love shell model to elasto-plastic materials was discussed by Ambati et al (2018). A hierarchic family of isogeometric shell elements was proposed by Echter et al (2013), and further developed by Oesterle et al (2016Oesterle et al ( , 2017, Recently, the focus in the shell finite element technology has shifted towards more advanced formulations such as thickness stretchable shell elements and solid-shells.…”

mentioning

confidence: 99%

Isogeometric shell analysis of incremental sheet forming

Hokkanen¹

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This thesis investigates the applicability and beneficiality of isogeometric analysis to the incremental sheet forming simulations. Incremental sheet forming (ISF) is a manufacturing process for sheet metals where the final shape is obtained incrementally using a blunt moving tool. ISF is a relatively slow process but does not need precise and expensive dies (which require a long lead time) in contrast to many other sheet forming processes. This makes it ideal for rapid prototyping, customized parts, and

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Hierarchic isogeometric large rotation shell elements including linearized transverse shear parametrization

Cited by 58 publications

References 49 publications

A variational method to avoid locking—independent of the discretization scheme

A variational method to avoid locking—independent of the discretization scheme

Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis

Isogeometric shell analysis of incremental sheet forming

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