Linear Elasticity: General Considerations and Boundary-Value Problems

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


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.


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© Springer Nature B.V. 2020

Authors and Affiliations

  1. 1.School of Computing and EngineeringUniversity of HuddersfieldHuddersfieldUK

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