Blended isogeometric shells

Benson, David J.; Hartmann, Stefan; Bazilevs, Yuri; Hsu, Ming‐Chen; Hughes, Thomas J.R.

doi:10.1016/j.cma.2012.11.020

Cited by 145 publications

(85 citation statements)

References 25 publications

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“…In particular, the average operator for vector quantities is defined in (18), t denotes the shell thickness, and the terms in brackets correspond to definitions (53) to (57). We note that the stabilization terms of equation (76) refer to the global Cartesian basis.…”

Section: Robustness and Additional Stabilizationmentioning

confidence: 99%

“…From a technology viewpoint, the latter three components of the above list profit from significant progress in both isogeometric analysis and embedded domain methods in recent years. On the isogeometric side, a variety of advanced formulations for isogeometric shell analysis on spline surfaces have been developed, e.g., based on solid shell theories [14,15], Kirchhoff-Love [16] and ReissnerMindlin theories [17][18][19], and hierarchic combinations thereof [20]. Isogeometric shells have been successfully applied for large-deformation analysis [21], in conjunction with various nonlinear material models [22,23], and in contact and fluid-structure interaction problems [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A parameter-free variational coupling approach for trimmed isogeometric thin shells

2016

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The non-symmetric variant of Nitsche's method was recently applied successfully for variationally enforcing boundary and interface conditions in non-boundary-fitted discretizations. In contrast to its symmetric variant, it does not require stabilization terms and therefore does not depend on the appropriate estimation of stabilization parameters. In this paper, we further consolidate the non-symmetric Nitsche approach by establishing its application in isogeometric thin shell analysis, where variational coupling techniques are of particular interest for enforcing interface conditions along trimming curves. To this end, we extend its variational formulation within Kirchhoff-Love shell theory, combine it with the finite cell method, and apply the resulting framework to a range of representative shell problems based on trimmed NURBS surfaces. We demonstrate that the non-symmetric variant applied in this context is stable and can lead to the same accuracy in terms of displacements and stresses as its symmetric counterpart. Based on our numerical evidence, the non-symmetric Nitsche method is a viable parameter-free alternative to the symmetric variant in elastostatic shell analysis.

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Section: Robustness and Additional Stabilizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A parameter-free variational coupling approach for trimmed isogeometric thin shells

2016

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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 isogeometric Kirchhoff-Love shell is proposed by Kiendl et al [8]. Benson et al [9] use a rotation-free shell [10] in regular regions and a Reissner-Mindlin shell [11] in regions with geometric discontinuities. The rotation-based Reissner-Mindlin shell formulation proposed by the authors [6] uses a new concept for the interpolation of the director vector adapted to the characteristics of NURBS surfaces.…”

Section: Introductionmentioning

confidence: 99%

Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework

Dornisch

Klinkel

2014

Computer Methods in Applied Mechanics and Engineering

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This work presents a framework for the computation of complex geometries containing intersections of multiple patches with Reissner-Mindlin shell elements. The main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization, nor user interaction to quantify the number of rotational degrees of freedom for every node. For this purpose, the following set of methods is presented. Control points with corresponding physical location are assigned to one common node for the finite element solution. A nodal basis system in every control point is defined, which ensures an exact interpolation of the director vector throughout the whole domain. A distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented. An isogeometric Reissner-Mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches. The parametrization of adjacent patches along the interface has to be conforming. The shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector. The nonlinear kinematic allows the computation of large deformations and large rotations. Two concepts for the description of rotations are presented. The first one uses an interpolation which is commonly used in standard Lagrange-based shell element formulations. The second scheme uses a more elaborate concept proposed by the authors in prior work, which increases the accuracy for arbitrary curved geometries. Numerical examples show the high accuracy and robustness of both concepts. The applicability of the proposed framework is demonstrated.

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Blended isogeometric shells

Cited by 145 publications

References 25 publications

A parameter-free variational coupling approach for trimmed isogeometric thin shells

A parameter-free variational coupling approach for trimmed isogeometric thin shells

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

Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework

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