IDEAS home Printed from https://ideas.repec.org/h/spr/spochp/978-0-387-95857-6_14.html
   My bibliography  Save this book chapter

Lekhnitskii’s Formalism for Stress Concentrations Around Irregularities in Anisotropic Plates: Solutions for Arbitrary Boundary Conditions

In: Variational Analysis and Aerospace Engineering

Author

Listed:
  • Sotiris Koussios

    (Delft University of Technology)

  • Adriaan Beukers

    (Delft University of Technology)

Abstract

Considering analytical methods in anisotropic elasticity, the complex potentials method (as extensively formulated by Lekhnitskii) may be regarded as a powerful tool. Among the various solutions generated by this approach, the analysis of thin anisotropic plates containing a geometrically simple irregularity is the most classical one as it reflects on an extensive collection of structures: from pinloaded holes to cutouts in aircraft fuselages. In this chapter we outline the complete solution for this particular geometry where the boundary conditions on the edge of the irregularity (forces or displacements) are formulated in Fourier series. The analytical solutions provided here can directly be evaluated as a function of the external boundary loads and the coefficients in the Fourier series, which represent the boundary conditions at the edge of the irregularity. Therefore, the analytical solutions provided here are able to cover a large variety of structural problems. Although Lekhnitskii’s formalism may be regarded as a well-established solution procedure, the availability of engineering-oriented, directly implementable solutions is rather limited. In this chapter we attempt to fill this gap.

Suggested Citation

  • Sotiris Koussios & Adriaan Beukers, 2009. "Lekhnitskii’s Formalism for Stress Concentrations Around Irregularities in Anisotropic Plates: Solutions for Arbitrary Boundary Conditions," Springer Optimization and Its Applications, in: Variational Analysis and Aerospace Engineering, chapter 0, pages 243-265, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-95857-6_14
    DOI: 10.1007/978-0-387-95857-6_14
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:spochp:978-0-387-95857-6_14. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.