Integration of geometric modeling and numerical analysis based on Constructive Solid Geometry, Boundary Representation, and the Finite Cell Method Part 2: Extension to flawed geometry and volumetric spline-based models

• Applicant: Professor Dr. Ernst Rank
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: from 2013 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 232449854

• Final Report Year: 2020

Final Report Abstract

The two main objectives of the second phase of this project were the extension of the Finite Cell Method to (a) the direct simulation of flawed B-Rep models and (b) the utilization of volumetric models, i.e. V-models for the representation and simulation of functionally graded materials (FGM). Both objectives were successfully accomplished. Due to the vulnerability to all kinds of flaws, a large portion of all non-trivial B-Rep models used in industry are flawed. A classical numerical simulation of these models is impossible in general and typically requires an often tedious geometry healing involving manual work. With the point-inclusion test developed in this project for flawed B-Rep models an immediate simulation of those imprecise models is now possible using the FCM. The developed point-inclusion test is robust w.r.t. a large number of topological and geometrical flaws of industrial relevance and thereby ensures robustness of the CAD to analysis process up to a defined feature size ecrit of a flawed model. Moreover, the geometric errors translate to inaccuracies only in a small vicinity of the flaws, but in general do not inhibit computation. The extension of the FCM with V models could be based in a collaboration with the Technion (Haifa) on the existing functionality of a V-Rep framework. It was demonstrated that the FCM is able to fully exploit the capabilities of this framework w.r.t the modeling and representation of functionally graded materials. To this end, models with single-material, as well as multi-material functional graded materials were investigated and simulated. For discontinuous material distributions in particular, the developed adaptive local refinement within the FCM proved to be a very valuable asset.

Publications

• “Multi-level hp-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes”. In: Computational Mechanics 55.3 (Feb. 2015), pp. 499-517
  N. Zander, T. Bog, S. Kollmannsberger, D. Schillinger, and E. Rank
  
• Smart octrees: Accurately integrating discontinuous functions in 3D”. In: Computer Methods in Applied Mechanics and Engineering 306 (July 2016), pp. 406-426
  L. Kudela, N. Zander, S. Kollmannsberger, and E. Rank
  
• “A Design-Through-Analysis Approach Using the Finite Cell Method”. In: EC COM AS Congress SO 16. Crete Island, Greece, June 2016
  B. Wassermann, T. Bog, S. Kollmannsberger, and E. Rank
  
• “Multi-level hp-adaptivitv and explicit error estimation”. In: Advanced Modeling and Simulation in Engineering Sciences 3.1 (Dec. 2016), p. 33
  D. D’Angella, N. Zander, S. Kollmannsberger, F. Frischmann, E. Rank, A. Schroder, and A. Reali
  
• “The multi-level hp-method for three-dimensional problems: Dynamically changing high-order mesh refinement with arbitrary hanging nodes”. In: Computer Methods in Applied Mechanics and Engineering 310 (Oct. 2016), pp. 252-277
  N. Zander, T. Bog, M. Elhaddad, F. Frischmann, S. Kollmannsberger, and E. Rank
  
• “From geometric design to numerical analysis: A direct approach using the Finite Cell Method on Constructive Solid Geometry”. In: Computers & Mathematics with Applications (Mar. 2017)
  B. Wassermann, S. Kollmannsberger, T. Bog, and E. Rank
  
• “Multi-level hp-FEM: dynamically changing high-order mesh refinement with arbitrary hanging nodes”. PhD Thesis. München: Technische Universität München, 2017
  N. Zander
  
• “Multi-level Bezier extraction for hierarchical local refinement of Isogeometric Analysis”. In: Computer Methods in Applied Mechanics and Engineering 328 (Jan. 2018), pp. 147-174
  D. D’Angella, S. Kollmannsberger, E. Rank, and A. Reali
  
• “Weak imposition of frictionless contact constraints on automatically recovered high-order, embedded interfaces using the finite cell method”. In: Computational Mechanics 61.4 (Apr. 2018) , pp. 385-407
  T. Bog, N. Zander, S. Kollmannsberger, and E. Rank
  
• “Integrating CAD and numerical analysis: ‘Dirty geometry’ handling using the Finite Cell Method”. In: Computer Methods in Applied Mechanics and Engineering 351 (July 2019) , pp. 808-835
  B. Wassermann, S. Kollmannsberger, S. Yin, L. Kudela, and E. Rank