A Nitsche embedded mesh method

Sanders, Jessica; Laursen, Tod A.; Puso, Michael A.

doi:10.1007/s00466-011-0641-2

Cited by 75 publications

(79 citation statements)

References 24 publications

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“…The use of Nitsche's technique in the imposition of interpatch-continuity also represents a common and well explored alternative [5,44,[47][48][49][50][51][52]. While such option is clearly superior to the use of simpler approaches, it is less efficient in implementation and computational costs, in the sense that it requires modifying the variational form as well as evaluating boundary integrals at the boundaries of interest.…”

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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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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“…In these techniques the finite element spaces can be freely chosen at the price of adding new stabilizing terms to the formulation. Modifications of the Nitsche method have been applied to standard FEM [26,57,29,13], X-FEM [21,4,3] and interface problems [23,12,45,2,1]. Other techniques use different stabilized formulations.…”

Section: Introductionmentioning

confidence: 99%

A modified perturbed Lagrangian formulation for contact problems

et al. 2015

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The aim of this work is to propose a formulation to solve both small and large deformation contact problems using the finite element method. We consider both standard finite elements and the so-called immersed boundary elements. The method is derived from a stabilized Nitsche formulation. After introduction of a suitable Lagrange multiplier discretization the method can be simplified to obtain a modified perturbed Lagrangian formulation. The stabilizing term is iteratively computed using a smooth stress field. The method is simple to implement and the numerical results show that it is robust. The optimal convergence rate of the finite element solution can be achieved for linear elements.

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“…For the interface conditions, the tractions are taken any convex average of the stresses from the intersecting regions The weight γ can be any value between zero and unity [53,1]. We make the trivial choice of γ = 0.5.…”

Section: Nitsche's Methodsmentioning

confidence: 99%

“…[53] uses the three approaches presented in this section for immersed boundaries ( ctitious domain) in 2D elasticity problems. The domains can also be attached by coupling nite elements [34] with large aspect ratios that model the interaction between the domains.…”

Section: Meshless Approximationmentioning

confidence: 99%

“…It has been applied with eXtended Finite Elements (XFEM) for EBCs and ICs in single-eld problems [15,25,28], to enforce weak discontinuities between elastic materials [51,52,2,1]; and applied to non conforming embedded FE meshes for elastostatics [53,54]. B-splines and NURBs-base FEs share similar features with meshless approximations and can also take advantage of Nitsche's Method, as in [16] for 2nd and 4th order problems, [46,33,49,50] for elasticity, [27,26] for thin plates and [22,23] for thin shells.…”

Section: Introductionmentioning

confidence: 99%

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Essential boundary and interface conditions in the meshless analysis of shells.

Costa¹

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AcknowledgmentsFirstly, I would like to thank Prof. Paulo Pimenta for taking me as a student and guiding me through my research and more importantly through a real academic formation.Thank you for the many fruitfull and happy get-togethers and conversations, about my research and a whole variaty of other subjects. It has been an honor to be your student.Other masters were also kind enough to advise and help me, especially Prof. Carlos Tiago who welcomed me for a stay in Lisbon during my masters and became my referrence for all matters of meshless methods, and Prof. Eduardo Campello for great insights and helpful discussions.My sincere gratitute to Prof. Peter Wriggers for receiving me at the Institut für Kontinuumsmechanik in Hannover for a proli c and very pleasant year. Thank you for helping my research and formation.To my co-workers and o ce mates, thank you for providing a nice working environment, for attentive ears to obstacles and smily faces for the happy-hours. We use the EFG discretization technique for thick Reissner-Mindlin shells and adapt the weak form as to separate displacement and rotational degrees of freedom and obtain suitable and separate stabilization parameters. This approach enables the modeling of discontinuous shells and local re nement on multi-region problems.

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A Nitsche embedded mesh method

Cited by 75 publications

References 24 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 modified perturbed Lagrangian formulation for contact problems

Essential boundary and interface conditions in the meshless analysis of shells.

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