Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures

Breitenberger, M.; Apostolatos, Andreas; Philipp, Benedikt; Wüchner, Roland; Bletzinger, K.‐U.

doi:10.1016/j.cma.2014.09.033

Cited by 196 publications

(139 citation statements)

References 51 publications

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“…Isogeometric B-Rep analysis [4] can be seen as an extension of the isogeometric analysis (IGA). IBRA uses in addition to the basis functions from CAD, the Boundary Representation (B-Rep, see also "Boundary representation (B-Rep)" section) description for approximating solution fields.…”

Section: Isogeometric B-rep Analysis (Ibra)mentioning

confidence: 99%

“…The method is then completed by reconstructing the desired continuity by constraining the solution to match the continuity requirements along the trimming boundary. The imposition of such constraint is typical to embedded/unfitted techniques and can be performed in different ways, for example by a penalty approach [4] but also by employing Lagrange multipliers [5,6] or Nitsche-type methods [5]. In a broad sense, CutFEM [7] and finite cell [8,9] approaches can be considered as variations of such idea.…”

Section: Introductionmentioning

confidence: 99%

“…More recently, the introduction of the isogeometric B-Rep analysis (IBRA) technology [1,4] provided a novel approach to address the challenge. The idea leveraged by IBRA is to keep using all control points included in the model, considering however that only a portion of the domain, the one enclosed by trimming lines, is actually considered in the computational structural analysis, more specifically in the integration process.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: Isogeometric B-rep Analysis (Ibra)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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.

Self Cite

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“…Integrated design-through-analysis workflows for thin shell structures described by trimmed NURBS surfaces can be based on the combination of concepts from isogeometric analysis and embedded domain methods. In this context, we identify four key components [5][6][7][8][9] 1. ability to query geometric information related to trimmed surfaces from CAD data structures, 2. efficient and accurate isogeometric shell technology, 3. quadrature methods for the integration of stiffness and residual forms in trimmed elements, 4. methods to enforce boundary and coupling conditions at non-matching trimming curves.…”

Section: Introductionmentioning

confidence: 99%

“…This leads to small gaps and overlaps between the space curves of two neighboring trimmed surfaces, so that NURBS-based B-Rep models are classified as not water-tight. For more details, we refer to the excellent summary and further references given in [5]. Integrated design-through-analysis workflows for thin shell structures described by trimmed NURBS surfaces can be based on the combination of concepts from isogeometric analysis and embedded domain methods.…”

Section: Introductionmentioning

confidence: 99%

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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References

2022

IGA: Non‐conforming Coupling and Shape Optimization of Complex Multipatch Structures

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Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures

Cited by 196 publications

References 51 publications

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

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

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

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