Isogeometric Analysis

Historically, the fields of Computer Aided Design (CAD) and Computer Aided Engineering (CAE) have developed independently from each other and different mathematical descriptions are used in the two fields. This has led to a gap between design and analysis models that has to be bridged by model conversion. This model conversion (meshing) often is the most time-consuming step in the design-through-analysis process. Additionally, this introduces the so-called discretization error, which describes the difference between the design model and the analysis model.  Isogeometric analysis is a new development in computational analysis which aims to close this gap by using the same mathematical description for the design and the analysis model. NURBS (Non-Uniform Rational B-Splines) are the most widespread functions in CAD and hence they are used as basis functions for the Isogeometric analysis.

workflow with classic finite-element analysis
workflow with isogeometric B-Rep analysis

Isogeometric analysis is a new development in computational analysis which aims to close this gap by using the same mathematical description for the design and the analysis model. NURBS (Non-Uniform Rational B-Splines) are the most widespread functions in CAD and hence they are used as basis functions for the Isogeometric analysis.

recursive formula to determine the basis functions
cubic basis functions

Motivation

(a) geometry of a sphere (b) geometric representation by control polygon, (c) degree elevation, (d) knot refinement

Isogeometric Analysis (IGA) merges the models for design and analysis into one. Therefore, no model conversion is needed and refinement can be performed on the analysis model while the exact geometry is preserved in each refinement level. Furthermore, the smoothness of the NURBS ensures higher accuracy compared to standard polynomials which are commonly used in the “traditional” Finite Element Analysis (FEA). Another important idea behind IGA is the "isoparametric concept" i.e. the same basis is used to model the geometry and to approximate the unknown solution fields.

Displacement of a spring under a point load (modeled by a nonlinear isogeometric spatial Bernoulli beam [Bauer 2016]


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Publications

  • 1/19
    Apostolatos, Andreas; Nayer, Guillaume De; Bletzinger, Kai-Uwe; Breuer, Michael; Wüchner, Roland: Systematic evaluation of the interface description for fluid–structure interaction simulations using the isogeometric mortar-based mapping. Journal of Fluids and Structures 86, 2019, 368 - 399 more… BibTeX Full text ( DOI )
  • 2/19
    Apostolatos, Andreas; Bletzinger, Kai-Uwe; Wüchner, Roland: Weak imposition of constraints for structural membranes in transient geometrically nonlinear isogeometric analysis on multipatch surfaces. Computer Methods in Applied Mechanics and Engineering, 2019 more… BibTeX Full text ( DOI )
  • 3/19
    Teschemacher, T.; Bauer, A. M.; Oberbichler, T.; Breitenberger, M.; Rossi, R.; Wüchner, R.; Bletzinger, K.-U.: Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis. Advanced Modeling and Simulation in Engineering Sciences 5 (1), 2018 more… BibTeX Full text ( DOI )
  • 4/19
    Bauer, A.M.; Wüchner, R.; Bletzinger, K.-U.: Innovative CAD-integrated Isogeometric Simulation of Sliding Edge Cables in Lightweight Structures. Journal of the International Association for Shell and Spatial Structures 59 (4), 2018, 251-258 more… BibTeX Full text ( DOI )
  • 5/19
    Apostolatos, Andreas; Bletzinger, Kai-Uwe; Wüchner, Roland: Nitsche's method for form-finding of multipatch isogeometric membrane analysis. PAMM 18 (1), 2018, e201800106 more… BibTeX Full text ( DOI )
  • 6/19
    Wüchner, Roland; Apostolatos, Andreas; de Nayer, Guillaume; Breuer, Michael; Bletzinger, Kai-Uwe: Coupled simulations involving light-weight structures within turbulent flows: FSI strategy and non-matching interface treatment for isogeometric b-rep analysis. PAMM 18 (1), 2018, e201800107 more… BibTeX Full text ( DOI )
  • 7/19
    Bauer, A.M.; Breitenberger, M.; Philipp, B.; Wüchner, R.; Bletzinger, K.-U.: Embedded structural entities in NURBS-based isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 325, 2017, 198-218 more… BibTeX Full text ( DOI )
  • 8/19
    Philipp, Benedikt; Wüchner, Roland; Bletzinger, Kai-Uwe: Advances in the Form-finding of Structural Membranes. Procedia Engineering 155, 2016, 332-341 more… BibTeX Full text ( DOI )
  • 9/19
    Bauer, A.M.; Breitenberger, M.; Philipp, B.; Wüchner, R.; Bletzinger, K.-U.: Nonlinear isogeometric spatial Bernoulli Beam. Computer Methods in Applied Mechanics and Engineering 303, 2016, 101-127 more… BibTeX Full text ( DOI )
  • 10/19
    Philipp, B.; Breitenberger, M.; D’Auria, I.; Wüchner, R.; Bletzinger, K.-U.: Integrated design and analysis of structural membranes using the Isogeometric B-Rep Analysis. Computer Methods in Applied Mechanics and Engineering 303, 2016, 312-340 more… BibTeX Full text ( DOI )
  • 11/19
    Ann-Kathrin Goldbach, Michael Breitenberger, Armin Widhammer, Kai-Uwe Bletzinger: Computational Cutting Pattern Generation using Isogeometric B-Rep Analysis. Procedia Engineering 155, 2016, 249-255 more… BibTeX Full text ( DOI )
  • 12/19
    Breitenberger, M.; Apostolatos, A.; Philipp, B.; Wüchner, R.; Bletzinger, K.-U.: Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures. Computer Methods in Applied Mechanics and Engineering 284, 2015, 401--457 more… BibTeX Full text ( DOI )
  • 13/19
    Kiendl, J.; Schmidt, R.; Wüchner, R.; Bletzinger, K.-U.: Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting. Computer Methods in Applied Mechanics and Engineering 274, 2014, 148-167 more… BibTeX
  • 14/19
    Apostolatos, A.; Schmidt, R.; Wüchner, R.; Bletzinger, K.-U.: A Nitsche-type formulation and comparison of the most common domain decomposition methods in isogeometric analysis. International Journal for Numerical Methods in Engineering 97 (7), 2014, 473-504 more… BibTeX Full text ( DOI )
  • 15/19
    R. Schmidt, R. Wüchner, K.-U. Bletzinger: Isogeometric analysis of trimmed NURBS geometries. Computer Methods in Applied Mechanics and Engineering (241-244), 2012, 93-111 more… BibTeX Full text ( DOI )
  • 16/19
    N. Nguyen-Thanh; J. Kiendl; H. Nguyen-Xuan; R. Wüchner; K.-U. Bletzinger; Y. Bazilevs; T. Rabczuk: Rotation free isogeometric thin shell analysis using PHT-splines. Computer Methods in Applied Mechanics and Engineering 200, 2011, 3410--3424 more… BibTeX Full text ( DOI )
  • 17/19
    R. Schmidt; J. Kiendl; R. Wüchner; K.-U. Bletzinger: Realization of an integrated structural design process: analysis-suitable geometric modelling and isogeometric analysis. Computing and Visualization in Science (13), 2010, 315--330 more… BibTeX Full text ( DOI )
  • 18/19
    J. Kiendl; Y. Bazilevs; M.-C. Hsu; R. Wüchner; K.-U. Bletzinger: The Bending Strip Method for Isogeometric Analysis of Kirchhoff-Love Shell Structures Comprised of Multiple Patches. Computer Methods in Applied Mechanics and Engineering 199, 2010, 2403--2416 more… BibTeX Full text ( DOI )
  • 19/19
    Kiendl, J.; Bletzinger, K.-U.; Linhard, J.; Wüchner, R.: Isogeometric shell analysis with Kirchhoff-Love elements. Computer Methods in Applied Mechanics and Engineering 198 (49-52), 2009, 3902-3914 more… BibTeX