- #1
lanew
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Homework Statement
The components of stress in the [itex]x_i[/itex] reference Cartesian system at a point of interested have been determined to be:
[itex]
\left[\begin{array}{ccc}
500 & 0 & 300 \\
0 & 700 & 0 \\
300 & 0 & -100
\end{array}\right] \mathrm{MPa}
[/itex]
Determine the principal values and directions of stress. Determine the rotation tensor transforming the components of stress from the principal components into components along the [itex]x_i[/itex] reference Cartesian system.
Homework Equations
[itex]\mathbf{A} = \mathbf{R}^T \mathbf{V} \mathbf{R}[/itex]
where [itex]\mathbf{A}[/itex] is the original stress tensor, [itex]\mathbf{R}[/itex] is the rotation tensor, and [itex]\mathbf{V}[/itex] is a matrix of eigenvectors.
The Attempt at a Solution
I've solved for the principal values and directions, but don't know how to solve for the rotation tensor. It seems there's too many unknowns or I'm not making a necessary assumption. Does anyone have any suggestions?
Thank You.