Advertisement

Linear Elasticity: General Considerations and Boundary-Value Problems

  • Ciprian D. ComanEmail author
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 238)

Abstract

In this chapter, we introduce the mathematical model for a linearly elastic solid and its associated boundary-value problems. This is achieved by a judicious particularisation of the general theory developed in the previous chapters; broadly speaking, the reference and current configurations will be assumed to be very close to each other (in a sense that will be made clear shortly). The upshot of this simplification is the linearity of the aforementioned boundary-value problems, which can then be solved by a number of indirect strategies involving: superposition, semi-inverse approaches, and the Saint-Venant’s Principle. The last section touches upon some well-established approximations whereby a three-dimensional situation is reduced to a two-dimensional problem. These specific approximations are taken up in much greater detail in some of the subsequent chapters.

Bibliography

  1. 1.
    Barber JR (2002) Elasticity. Kluwer Academic Publishers, Dordrecht, The NetherlandsGoogle Scholar
  2. 2.
    Biezeno CB, Grammel R (1955) Engineering dynamics, vol 1 (Theory of Elasticity). Blackie & Son Ltd., London and GlasgowGoogle Scholar
  3. 3.
    Biezeno CB, Grammel R (1956) Engineering dynamics, vol 2 (Elastic Problems of Single Machine Elements). Blackie & Lon Ltd., London and GlasgowGoogle Scholar
  4. 4.
    Chou PC, Pagano NJ (1967) Elasticity: tensor, dyadic, and engineering approaches. D. Van Nostrand Company Inc, Princeton, New JerseyGoogle Scholar
  5. 5.
    Filonenko-Borodich M (1963) Theory of elasticity. Mir Publishers, MoscowGoogle Scholar
  6. 6.
    Leipholz H (1974) Theory of elasticity. Noordhoff International Publishing, LeydenGoogle Scholar
  7. 7.
    Lekhnitskii SG (1981) Theory of elasticity of an anisotropic body. Mir Publishers, MoscowGoogle Scholar
  8. 8.
    Little RW (1973) Elasticity. Prentice-Hall Inc, Englewood Cliffs, New JerseyGoogle Scholar
  9. 9.
    Love AEH (2011) A treatise of the mathematical theory of elasticity. Dover Publications, Mineola, New YorkGoogle Scholar
  10. 10.
    Malvern LE (1969) Introduction to the mechanics of a continuum medium. Prentice-Hall Inc, Englewood Cliffs, New JerseyGoogle Scholar
  11. 11.
    Nadeau G (1964) Introduction to elasticity. Holt, Rinehart and Winston Inc, New YorkGoogle Scholar
  12. 12.
    Teodorescu PP (2013) Treatise on classical elasticity. Springer, Dordrecht, The NetherlandsCrossRefGoogle Scholar
  13. 13.
    Timoshenko SP, Goodier JN (1970) Theory of elasticity, International edn. McGraw-Hill Book Company, AucklandGoogle Scholar

Copyright information

© Springer Nature B.V. 2020

Authors and Affiliations

  1. 1.School of Computing and EngineeringUniversity of HuddersfieldHuddersfieldUK

Personalised recommendations