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The Equations of Linear Elasticity

  • B. M. Fraeijs de Veubeke
Part of the Applied Mathematical Sciences book series (AMS, volume 29)

Abstract

The geometric linearization
$$ \left| {{D_i}{u_j}} \right| < < 1 $$
(5.1)
allowed the displacement gradient tensor
$$ {D_i}{u_j} = {\varepsilon_{{ij}}} + {\omega_{{ji}}} $$
(5.2)
to be expressed as the sum of a symmetric tensor of infinitesimal strains
$$ {\varepsilon_{{ij}}} = \frac{1}{2}({D_i}{u_j} + {D_j}{u_i}) = {\varepsilon_{{ji}}} $$
(5.3)
and a skew tensor of infinitesimal rotations
$$ {\omega_{{ji}}} = \frac{1}{2}({D_i}{u_j} - {D_j}{u_i}) = - {\omega_{{ij}}} $$
(5.4)

Keywords

Strain Field Initial Stress Principal Direction Linear Elasticity Strain Energy Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • B. M. Fraeijs de Veubeke
    • 1
  1. 1.University of Liege and LouvainBelgium

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