Re-use of this resource is governed by a Creative Commons
Attribution-
NonCommercial-ShareAlike 4.0 International
https://creativecommons.org/licenses/by-nc-sa/4.0/
NonCommercial-ShareAlike 4.0 International
https://creativecommons.org/licenses/by-nc-sa/4.0/
Symmetric tensor principal value generator
If one of the principal values is already known, the other
two are readily calculated, as shown below (assuming T33
= 1)
input tensor
(
)
Mohr's Circle
From the previous page we note that the secular equation
is of the form
|
|
T11−z
T12
0
T12
T22−z
0
0
0
1
(T11−z)(T22−z)
− T12² = 0
z² −(T11
+ T22)z + T11T22 − T12²
= 0
z =
Tm + T22
±
T11 − T22;
+ T12²
We see that this is in fact
an equation of a circle that can be plotted to give us a simple geometrical
method for finding the roots (principal values) as well as the orientation
relationships between different bases.
Symmetric tensor principal value generator
This page calculates the secular equation and the principal
values for an arbitrary second rank tensor.
input tensor
(
)
| Term | z3 | z2 | z | const |
| Coefficient | 1 |
With roots z1 = z2 = z3 =