Skip to main content
SpringerLink
Log in

Optimization Problems for Thin Elastic Structures

  • Conference paper
  • First Online:
Optimal Control of Coupled Systems of Partial Differential Equations

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 158))

  • 1252 Accesses

Abstract

We discuss shape optimization problems and variational methods for fundamental mechanical structures like beams, plates, arches, curved rods, and shells.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V. Arnâutu, H. Langmach, J. Sprekels, D. Tiba, On the approximation and the optimization of plates. Numer. Funct. Anal. Optim. 21:3–4 (2000), 337–354.

    Article  MathSciNet  MATH  Google Scholar 

  2. V. Arnâutu, J. Sprekels, D. Tiba, Optimization of curved mechanical structures. SIAM J. Control Optim. 44:2 (2005), 743–775.

    Article  MathSciNet  MATH  Google Scholar 

  3. Ph. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978.

    MATH  Google Scholar 

  4. Ph. Ciarlet, Mathematical Elasticity. Vol. III. Theory of Shells. North-Holland, Amsterdam, 2000.

    MATH  Google Scholar 

  5. Ph. Ciarlet, P. Ciarlet, Another approach to linearized elasticity and Korn’s inequality. C. R. Acad. Sci. Paris, Ser. I 339 (2004), 307–312.

    Article  MathSciNet  MATH  Google Scholar 

  6. Ph. Ciarlet, P. Ciarlet, Another approach to linearized elasticity and a new proof of Korn’s inequality. Math. Models Methods Appl. Sci. 15:2 (2005), 259–271.

    Article  MathSciNet  MATH  Google Scholar 

  7. Ph. Ciarlet, L. Gratie, A new approach to linear shell theory. C. R. Acad. Sci. Paris, Ser. I 340 (2005), 471–478.

    Article  MATH  Google Scholar 

  8. L. Gratie, New unknowns on the midsurface of a Naghdi’s shell model. An. St. Univ. Ovidius 12:2 (2004), 115–126.

    MathSciNet  MATH  Google Scholar 

  9. A. Ignat, J. Sprekels, D. Tiba, Analysis and optimization of nonsmooth arches. SIAM J. Control Optim. 40 (2001), 1107–1135.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Ignat, J. Sprekels, D. Tiba, A model of a general elastic curved rod. Math. Methods Appl. Sci. 25:10 (2002), 835–854.

    Article  MathSciNet  MATH  Google Scholar 

  11. P. Neittaanmäki, J. Sprekels, D. Tiba, Optimization of Elliptic Systems. Theory and Applications. Springer, New York, 2006.

    MATH  Google Scholar 

  12. J. Sprekels, D. Tiba, Propriétés de bang-bang généralisées dans l’optimisation des plaques. C. R. Acad. Sci. Paris, Ser. I 327 (1998), 705–710.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Sprekels, D. Tiba, A duality approach in the optimization of beams and plates. SIAM J. Control Optim. 37:2 (1998/1999), 486–501.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Sprekels, D. Tiba, A duality-type method for the design of beams. Adv. Math. Sci. Appl. 9:1 (1999), 84–102.

    MathSciNet  MATH  Google Scholar 

  15. J. Sprekels, D. Tiba, Sur les arches lipschitziennes. C. R. Acad. Sci. Paris, Sér. I 331:2 (2000), 179–184.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Sprekels, D. Tiba, An analytic approach to a generalized Naghdi shell model. Adv. Math. Sci. Appl. 12:1 (2002), 175–190.

    MathSciNet  MATH  Google Scholar 

  17. J. Sprekels, D. Tiba, Optimal design of mechanical structures. In: Control Theory of Partial Differential Equations, LN Pure Appl. Math. 242, Chapmann & Hall/CRC, Boca Raton, Florida, 2005, pp. 259–271.

    Chapter  MATH  Google Scholar 

  18. J. Sprekels, D. Tiba, The control variational method for differential systems, submitted to SIAM J. Control Optim, 2007.

    Google Scholar 

  19. D. Tiba, R. Vodák, A general asymptotic model for Lipschitzian curved rods. Adv. Math. Sci. Appl. 15:1 (2005), 137–198.

    MathSciNet  MATH  Google Scholar 

  20. L. Trabucho, J.M. Viaño, Mathematical modelling of rods. in: Handbook of Numerical Analysis, vol. IV (Ph. Ciarlet, J.L. Lions, eds.), Elsevier, Amsterdam, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117, Berlin, Germany

    Jürgen Sprekels

  2. Institute of Mathematics, Romanian Academy, P. O. Box 1-764, 014700, Bucharest, Romania

    Dan Tiba

Authors
  1. Jürgen Sprekels
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dan Tiba
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Karl Kunisch

  2. Abt. Partielle Differentialgleichung Weierstraß-Institut für Angewandte Analysis und Stochastik, Humboldt-Universität zu Berlin, Mohrenstrasse 39, 10117, Berlin, Germany

    Jürgen Sprekels

  3. LS Angewandte Mathematik II Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Martensstrasse 3, 91058, Erlangen, Germany

    Günter Leugering

  4. Institut für Mathematik Fak. II Mathematik & Naturwissenschaften, TU Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Fredi Tröltzsch

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Sprekels, J., Tiba, D. (2009). Optimization Problems for Thin Elastic Structures. In: Kunisch, K., Sprekels, J., Leugering, G., Tröltzsch, F. (eds) Optimal Control of Coupled Systems of Partial Differential Equations. International Series of Numerical Mathematics, vol 158. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8923-9_15

Download citation

Publish with us

Policies and ethics

Search

Navigation