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

Anisotropy Assure Dition Librium Verse 

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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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