Abstract
As declared in the title, this chapter deals with some aspects of linear elasticity. The list of topics includes (1) the theorem of minimum of total energy, (2) the analogous theorem in terms of complementary energy, (3) the Hellinger–Prange–Reissner principle, (4) the Fraeijs de Veubekele–Hu–Washizu variational principle, (5) the Betti reciprocal theorem, (6) the Kirchhoff uniqueness theorem, (7) the Navier and the Beltrami–Donati–Michell equations, (8) some aspects of the analysis of planar problems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
As we stated in the previous section, we exploit systematically the natural identification of \(\mathbb{R}^{3}\) with its dual \(\mathbb{R}^{3{\ast}}\), confusing in this way covariant and contravariant components, so ∇ with D, and adopt a flat metric. However, the result holds also in a more general setting (nonflat metric), provided some care is taken in writing appropriately the intermediate steps and writing ∇ or D depending on the initial choice of the contravariant, covariant, or mixed nature of the components of the strain \(\varepsilon\).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media New York
About this chapter
Cite this chapter
Mariano, P.M., Galano, L. (2015). Topics in Linear Elasticity. In: Fundamentals of the Mechanics of Solids. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-3133-0_5
Download citation
DOI: https://doi.org/10.1007/978-1-4939-3133-0_5
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-1-4939-3132-3
Online ISBN: 978-1-4939-3133-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)