Advertisement

Betti Extended

  • Friedel Hartmann
  • Peter Jahn
Chapter
  • 29 Downloads
Part of the Springer Series in Solid and Structural Mechanics book series (SSSSM, volume 13)

Abstract

In the previous chapter we repeatedly made use of the fact that the FE-solution \(u_h(x)\) is the superposition of the approximate influence function \(G_h(y,x)\) and the load p(y)
$$\begin{aligned} u_h(x) = \int _0^{\,l} G_h(y,x)\,p(y)\,dy\,. \end{aligned}$$
This result is based on a theorem which we call Betti extended.

References

  1. 1.
    Höllig K (2003) Finite element methods with B-splines. SIAMGoogle Scholar
  2. 2.
    Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. WileyGoogle Scholar
  3. 3.
    Babuška I, Strouboulis T (2001) The finite element method and its reliability. Oxford University PressGoogle Scholar
  4. 4.
    Hartmann F, Katz C (2010) Structural analysis with finite elements, 2nd edn. Springer, HeidelbergGoogle Scholar
  5. 5.
    Hartmann F (2013) Green’s functions and finite elements. Springer, HeidelbergGoogle Scholar
  6. 6.
    Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Num Methods Eng 24:337–357Google Scholar
  7. 7.
    Babuška I, Whiteman JR, Strouboulis T (2011) Finite elements. Oxford University Press, An Introduction to the Method and Error EstimationGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  • Friedel Hartmann
    • 1
  • Peter Jahn
    • 1
  1. 1.Institute of Structural MechanicsUniversity of KasselKasselGermany

Personalised recommendations