Isogeometric analysis and the finite cell method

Dominik Schillinger, Michael A. Scott, John A. Evans, Michael J. Borden, Luca Dedè, Thomas J.R. Hughes, Ernst Rank

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions. Its main idea consists of the extension of the physical domain of interest beyond its potentially complex boundaries into a larger embedding domain of simple geometry, which can be meshed easily by a structured grid. We present an isogeometric design-through-analysis methodology based on the B-spline version of the finite cell method, which allows for the seamless integration of fully three-dimensional parameterizations of complex engineering parts described by T-spline surfaces into finite element analysis. The approach is demonstrated to achieve optimal rates of convergence and to yield accurate stress results not only within the domain of interest, but also directly on the immersed boundary. We also show that hierarchical refinement of B-splines considerably increases the flexibility of the immersed boundary approach in terms of adaptive resolution of local features in the geometry and the solution fields. At the same time, hierarchical refinement maintains the key advantage of fully automated mesh generation for complex geometries due to its simplicity and straightforward implementation. We illustrate the versatility of our methodology by two complex industrial examples of a ship propeller and an automobile wheel.

Original languageEnglish (US)
Title of host publicationECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
Pages6781-6791
Number of pages11
StatePublished - Dec 1 2012
Event6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 - Vienna, Austria
Duration: Sep 10 2012Sep 14 2012

Publication series

NameECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

Other

Other6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
CountryAustria
CityVienna
Period9/10/129/14/12

Keywords

  • Finite cell method
  • Hierarchical refinement
  • Immersed boundary analysis
  • Isogeometric analysis
  • T-spline surfaces

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