Skip to main content
SpringerLink
Log in

Model Reduction of Contact Problems in Elasticity: Proper Orthogonal Decomposition for Variational Inequalities

  • Conference paper
  • First Online:
Progress in Industrial Mathematics at ECMI 2012

Part of the book series: Mathematics in Industry ((TECMI,volume 19))

Abstract

In this contribution a model order reduction method is applied to a Signorini contact problem. Due to the contact constraints classical linear reduction methods such as Craig–Bampton are not applicable. The Signorini contact problem is formulated as a variational inequality and Proper Orthogonal Decomposition (POD) is used to calculate an optimal projection subspace. Numerical results of the reduced model’s quality and efficiency for an Encastre beam with contact are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Cao-Rial, M.T., Quintela, P., Moreno, C.: Numerical solution of a time-dependent signorini contact problem. Discrete Continuous Dyn. Syst., 201–211 (2007)

    Google Scholar 

  2. Geiger, C., Kanzow, C.: Theorie und Numerik restringierter Optimierungsaufgaben. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  3. Haasdonk, B., Salomon, J., Wohlmuth, B.: A reduced basis method for parametrized variational inequalities. SIAM J. Numer. Anal. 50, 2656–2676 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hinze, M., Volkwein, S.: Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: error estimates and suboptimal control. In: Benner, P., Sorensen, D.C., Mehrmann, V. (eds.) Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering, vol. 45, pp. 261–306. Springer, Berlin (2005)

    Chapter  Google Scholar 

  5. Kikuchi, N., Oden, J.: Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia (1988)

    Book  MATH  Google Scholar 

  6. Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications. Academic, New York (1980)

    MATH  Google Scholar 

  7. Kunisch, K., Volkwein, S.: Galerkin proper orthogonal decomposition methods for parabolic problems. Numerische Mathematik 148, 117–148 (2001)

    Article  MathSciNet  Google Scholar 

  8. Kunisch, K., Volkwein, S.: Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM J. Numer. Anal. 40(2), 492–515 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Kaiserslautern, 3049, 67653, Kaiserslautern, Germany

    Joachim Krenciszek & René Pinnau

Authors
  1. Joachim Krenciszek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. René Pinnau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joachim Krenciszek .

Editor information

Editors and Affiliations

  1. Lunds Universitet, Centre for Mathematical Sciences, Lund, Sweden

    Magnus Fontes

  2. Bergische Universität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany

    Michael Günther

  3. Lehrstuhl für Angew.Math. 1, Friedrich-Alexander-Universität Erlangen, Department of Mathematics, Erlangen, Germany

    Nicole Marheineke

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Krenciszek, J., Pinnau, R. (2014). Model Reduction of Contact Problems in Elasticity: Proper Orthogonal Decomposition for Variational Inequalities. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_38

Download citation

Publish with us

Policies and ethics

Search

Navigation