At 10:17 PM 2000/02/21 +0100, Falk Koenemann wrote:
>...
>a) ... 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
>...
This proof may be good math, but it cannot be good physics, Falk! Most
derivations of the stress field at a "point" start with an infinitesimal
unit cube with faces parallel to orthogonal coordinate axes and with the
forces acting on each face of the cube being resolved into three components.
But these forces and their components do not have independent values,
because the unit cube is constrained to be stationary; it cannot be
accelerating in any direction or accelerating around any axis of rotation.
This physical constraint is what makes it necessary that homogeneous stress
be a tensor no less symmetric than a triaxial ellipsoid.
Dugald
Dugald M Carmichael Phone/V-mail: 613-533-6182
Dept of Geological Sciences and Geological Engineering
Queen's University FAX: 613-533-6592
Kingston ON K7L3N6 E-mail: [log in to unmask]
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