IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-4106-5_7.html
   My bibliography  Save this book chapter

Elastostatics

In: Fundamental Solutions for Differential Operators and Applications

Author

Listed:
  • Prem K. Kythe

    (University of New Orleans, Department of Mathematics)

Abstract

We shall discuss some basic concepts and results from the theory of linear elasticity, derive the fundamental solutions for the elastostatic operator in R 2 and R3, and present some applications. The theory of linear elastic continua is developed under the assumption that they undergo small strains. The linear theory of elasticity is based on the following two basic assumptions: (i) The material is subject to an infinitesimal strain and the stress is expressed as a linear function of strain, and (ii) any variation in the orientation of this material due to displacements is negligible. These assumptions lead to small strain and equilibrium equations under an undeformed geometry. The linearity assumption is an attempt to simplify the mathematical aspect of the behavior of solids. Although we assume that the material properties are linear, the deformations in a body may not be completely linear. For example, under certain loads, various materials exhibit plastic deformation while others creep with time, or they may crack in which case the stresses are redistributed.

Suggested Citation

  • Prem K. Kythe, 1996. "Elastostatics," Springer Books, in: Fundamental Solutions for Differential Operators and Applications, chapter 6, pages 138-161, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-4106-5_7
    DOI: 10.1007/978-1-4612-4106-5_7
    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
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    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:sprchp:978-1-4612-4106-5_7. 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.