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→Stress formulation: Fix indices on Kronecker delta Tag: Reverted |
Undid revision 1203863563 by 81.158.156.80 (talk); not an improvement; inconsistent with tensors around there |
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The strains in this equation are then expressed in terms of the stresses using the constitutive equations, which yields the corresponding constraints on the stress tensor. These constraints on the stress tensor are known as the ''Beltrami-Michell'' equations of compatibility:
<math display="block">\sigma_{ij,kk} + \frac{1}{1+\nu}\sigma_{kk,ij} + F_{i,j} + F_{j,i} + \frac{\nu}{1-\nu}\delta_{
In the special situation where the body force is homogeneous, the above equations reduce to<ref name="tribonet">{{Cite news| url=http://www.tribonet.org/wiki/elastic-deformation/ |title=Elastic Deformation|last=tribonet|date=2017-02-16 | newspaper=Tribology |access-date=2017-02-16 | language=en-US}}</ref>
<math display="block"> (1+\nu)\sigma_{ij,kk}+\sigma_{kk,ij}=0.</math>
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