Skip to main content

Brittle and Quasi-Brittle Materials

  • Chapter
  • First Online:
Structural Optimization with Uncertainties

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 162))

  • 1294 Accesses


The optimization problems considered in this section consist in finding the shape and the thickness distribution of axisymmetric shells in the framework of membrane theory, loaded by fixed statical forces in such a way that the cost functional reaches a maximum, while satisfying some strength mechanics constraints. In this section the mass effectiveness of the shell is considered as a cost functional, and as constraints we use bounds on the maximum normal stresses; this is typical for shells made from brittle or quasi-brittle materials. Analytical investigations and corresponding optimal solutions are presented [BRS08].

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

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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


  1. N. V. Banichuk, F. Ragnedda, and M. Serra. Optimization of mass effectiveness of axisymmetric pressure vessels. Structural and Multidisciplinary Optimization, 35(5): 453–459, 2008. DOI 10.1007/s00158-007-0149-8

    Article  MathSciNet  Google Scholar 

  2. W. Flugge. Stresses in Shells. 2nd ed., Springer-Verlag, Berlin, 1973

    Google Scholar 

  3. S. Timoshenko. Strength of Materials. Part II, Advanced Theory and Problems, Van Nostrag Co., New York, 1956

    Google Scholar 

  4. S. Timoshenko and S. Woinowsky-Krieger. Theory of Plates and Shells, McGraw-Hill, New York, 1959

    Google Scholar 

  5. F. L. Chernousko and N. V. Banichuk. Variational Problems of Mechanics and Control. Numerical Methods. Nauka, Moscow, 1973, in Russian

    Google Scholar 

  6. N. V. Banichuk. Problems and Methods of Optimal Structural Design. Number 26 in Mathematical Concepts and Methods in Science and Engineering. Plenum Press, New York, 1983

    Google Scholar 

  7. N. V. Banichuk. Introduction to Optimization of Structures. Springer-Verlag, New York, 1990

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to N. V. Banichuk .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Banichuk, N.V., Neittaanmäki, P. (2010). Brittle and Quasi-Brittle Materials. In: Structural Optimization with Uncertainties. Solid Mechanics and Its Applications, vol 162. Springer, Dordrecht.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-2517-3

  • Online ISBN: 978-90-481-2518-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics