i'm doing a module in fluid dynamics this year and i'm trying to work through some examples. i've got this question and i'm not sure how to go about tackling it, any help would b appricated. thanks
position vector x the stress tensor takes the form
and n is an unknown constant.
(question a) determine the value of n which ensures the existance of a plane passing through x on which the stress tensor s(t,x) is equal to 0.
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Last edited by the living legend; 13-11-2008 at 18:27.
- 13-11-2008 18:24
- 14-11-2008 10:15
- 14-11-2008 13:03
^what he said, set the determinant to zero
This would mean that at least one of the eigenvalues is zero*, i.e. there is a direction in which the stress tensor vanishes which I think is what the question is asking (the plane bit is confusing me though)
EDIT/ Actually I guess a plane would require that 2 of the directions had eigenvalue 0, so that would put a condition on the characteristic equation
*detA = product of eigenvaluesLast edited by MC REN; 14-11-2008 at 13:28.