A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects

Marussig, Benjamin; Hughes, Thomas J.R.

doi:10.1007/s11831-017-9220-9

Cited by 167 publications

(106 citation statements)

References 301 publications

(364 reference statements)

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“…Further literature on trimming and the achievable quality of the solutions by employing alternative approaches to the presented AGIP method by [1] in "Numerical integration of surfaces" section, can be found in [19][20][21][22][23][24][25][26] (Fig. 7).…”

Section: Surface Integration Proceduresmentioning

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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Section: Surface Integration Proceduresmentioning

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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“…Trimming involves the computation of the intersection between spline surfaces with other surfaces or curves. The respective nonlinear root-finding problems look deceptively simple but are extremely hard to robustly solve and lead to non-watertight geometries [1][2][3]. In the analysis context, the non-watertight geometries obtained from trimming pose unique challenges.…”

Section: Introductionmentioning

confidence: 99%

Manifold-based isogeometric analysis basis functions with prescribed sharp features

Zhang

Cirak

2020

Computer Methods in Applied Mechanics and Engineering

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We introduce manifold-based basis functions for isogeometric analysis of surfaces with arbitrary smoothness, prescribed C 0 continuous creases and boundaries. The utility of the manifold-based surface construction techniques in isogeometric analysis was demonstrated in Majeed and Cirak (CMAME, 2017). The respective basis functions are derived by combining differential-geometric manifold techniques with conformal parametrisations and the partition of unity method. The connectivity of a given unstructured quadrilateral control mesh in R 3 is used to define a set of overlapping charts. Each vertex with its attached elements is assigned a corresponding conformally parametrised planar chart domain in R 2 so that a quadrilateral element is present on four different charts. On the collection of unconnected chart domains, the partition of unity method is used for approximation. The transition functions required for navigating between the chart domains are composed out of conformal maps. The necessary smooth partition of unity, or blending, functions for the charts are assembled from tensor-product B-spline pieces and require in contrast to earlier constructions no normalisation. Creases are introduced across user tagged edges of the control mesh. Planar chart domains that include creased edges or are adjacent to the domain boundary require special local polynomial approximants in the partition of unity method. Three different types of chart domain geometries are necessary to consider boundaries and arbitrary number and arrangement of creases. The new chart domain geometries are chosen so that it becomes trivial to establish local polynomial approximants that are always C 0 continuous across the tagged edges. The derived non-rational manifold-based basis functions correspond to the vertices of the mesh and may have an arbitrary number of creases and prescribed smoothness. This makes them particularly well suited for isogeometric analysis of Kirchhoff-Love thin shells with kinks, which require C 1 continuous basis functions that are C 0 continuous across the kinks. We demonstrate the convergence and utility of the new basis functions with linear and nonlinear beam, plate and shell examples.

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“…Without dedicated treatments, the severe ill-conditioning of linear systems derived from immersed finite element methods generally forestalls convergence of iterative solution procedures. Multiple resolutions for these conditioning problems have been proposed, the most prominent of which are the ghost penalty, e.g., [4,5,37], constraining, extending, or aggregation of basis functions, e.g., [13,[38][39][40][41][42][43][44][45][46], and preconditioning, which is discussed in detail below.…”

Section: Introductionmentioning

confidence: 99%

Multigrid solvers for immersed finite element methods and immersed isogeometric analysis

et al. 2019

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Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system matrix, which generally degrades efficiency and robustness of iterative solvers. In this contribution we investigate the spectral properties of immersed finite element systems treated by Schwarz-type methods, to establish the suitability of these as smoothers in a multigrid method. Based on this investigation we develop a geometric multigrid preconditioner for immersed finite element methods, which provides mesh-independent and cut-element-independent convergence rates. This preconditioning technique is applicable to higher-order discretizations, and enables solving large-scale immersed systems in parallel, at a computational cost that scales linearly with the number of degrees of freedom. The performance of the preconditioner is demonstrated for conventional Lagrange basis functions and for isogeometric discretizations with both uniform B-splines and locally refined approximations based on truncated hierarchical B-splines.

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A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects

Cited by 167 publications

References 301 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

Manifold-based isogeometric analysis basis functions with prescribed sharp features

Multigrid solvers for immersed finite element methods and immersed isogeometric analysis

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