Principal Stresses next up previous contents
Next: Tresca Stresses Up: Pre-defined Calculations Previous: Von Mises Equivalent Stress   Contents

Principal Stresses

Entity names: P1, P2, P3, worstPS

The principal stresses $\sigma$ are named P1, P2, P3. From the three principal stresses $\sigma$ the absolute maximum value will be calculated and named worstPS. For example if a node has the three values 100, 0 and -110 MPa then -110 MPa would be shown. The three principal stresses $\sigma_{1}$ $\sigma_{2}$ $\sigma_{3}$ are derived from the following equation:

\left [
\sigma_{xx}-\lambda & \sigma_{xy}...
... ]
\left [
\end{array}\right ]

They are given by the three roots of the equation (stress tensor is symmetric: $\sigma_{xy}$ = $\sigma_{yx}$ etc.):

\begin{displaymath}\sigma^3 - (\sigma_{xx}+\sigma_{yy}+\sigma_{zz})\sigma^2 + (\...

\begin{displaymath}\sigma_{zx}^2)\sigma - (\sigma_{xx}\sigma_{yy}\sigma_{zz}+2\s...
..._{yz}^2-\sigma_{yy}\sigma_{zx}^2-\sigma_{zz}\sigma_{xy}^2) = 0 \end{displaymath}

root 2012-10-04