Robert J. Twiss schrieb:
> Wojtek,
>
> The simple intuitive answer, if you are thinking of the stress or
> the strain ellipsoid, is that the eigenvalues are the magnitudes of the
> principal axes of the ellipsoid (i.e. the principal stresses or principal
> strains), and the eigenvectors define the orientations of those principal
> axes (the principal directions).
>
> Rob
Not quite.
a) Eigendirections and principal axes of ellipsoids coincide only if the
representative matrix is symmetric. This is not always the case. Strain is a
symmetric tensor by definition, so that's ok; however, whatever stress is, it
need not be symmetric.
b) The stress ellipsoid cannot have eigendirections or principal axes because
the stress tensor does not exist. The derivation of stress theory is at variance
with the divergence theorem in particular, and with potential theory in general.
For proof see http://home.t-online.de/home/peregrine/hp-tut01.htm
Falk
_______________________________________________________________
Falk H. Koenemann Aachen, Germany [log in to unmask]
http://home.t-online.de/home/peregrine/hp-fkoe.htm
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