As discussed in Axisymmetric Elements with Nonaxisymmetric Loads of the Element Reference, results from load cases with different values of mode number (input as MODE on MODE command) but at the same angular location (input as ANGLE on the SET command) can be combined in POST1 (with the LCOPER command). The below assumes values of the mode number and angle and shows how the results are extracted.
Data processed in a harmonic fashion includes nodal temperatures, element data stored on a per node basis (thermal gradient and thermal flux) and nodal heat flow. Nodal temperature is calculated at harmonic angle θ for each node j.
 | (17–113) |
where:
| Tjθ = temperature at node j at angle q |
| F = scaling factor (input as FACT, SET command) |
|
| n = mode number (input as MODE on MODE command) |
| θ = angle at which harmonic calculation is being made (input as ANGLE, SET command) |
| Tj = temperature at node j from nodal solution |
Thermal gradient are calculated at harmonic angle θ for each node j of element i:
 | (17–114) |
 | (17–115) |
 | (17–116) |
where:
 = thermal gradient in x (radial)
direction at node j of element i at angle θ |
|
 = thermal gradient in x (radial) direction at node
j of element i |
Nodal heat flow is processed in the same way as temperature. Thermal flux is processed in the same way as thermal gradient.
Data processed in a harmonic fashion include nodal displacements, nodal forces, and element data stored on a per node basis (stress and elastic strain).
Nodal displacement is calculated at harmonic angle θ for each node j:
 | (17–117) |
 | (17–118) |
 | (17–119) |
where:
| uxjθ = x (radial) displacement at node j at angle θ |
| uxj = maximum x (radial) displacement at node j (from nodal solution) |
Stress is calculated at harmonic angle θ for each node j of element i:
 | (17–120) |
 | (17–121) |
 | (17–122) |
 | (17–123) |
 | (17–124) |
 | (17–125) |
where:
| σxijθ = x (radial) stress at node j of element i at angle θ |
| σxij = maximum x (radial) stress at node j of element i |
Nodal forces are processed in the same way as nodal displacements. Strains are processed in the same way as stresses.
17.8.3. Structural Shell Element (SHELL61)
Data processed in a harmonic fashion include displacements, nodal forces, member forces, member moments, in-plane element forces, out-of-plane element moments, stress, and elastic strain.
Nodal displacement is calculated at harmonic angle θ for each node j:
 | (17–126) |
 | (17–127) |
 | (17–128) |
 | (17–129) |
where:
| φzjθ = rotation about z (hoop) direction at node j at angle θ |
| φzj = maximum rotation about z (hoop) direction at node j (from nodal solution) |
Stress is calculated at harmonic angle θ for each node/interior point j of element i:
 | (17–130) |
 | (17–131) |
 | (17–132) |
 | (17–133) |
where:
| σmijθ = meridional stress at point j of element i at angle θ |
| σmij = meridional stress j of element i |
In-plane element forces at harmonic angle θ for each node/interior point j of element i:
 | (17–134) |
 | (17–135) |
 | (17–136) |
where:
 = in-plane element force in x (meridional) direction
at point j of element i at angle θ |
| Txij = maximum in-plane element force in x (meridional) direction at point j of element i |
Nodal forces, member forces, and member moments are processed in the same way as nodal displacements. Strains are processed in the same way as stresses. Finally, out-of-plane element moments are processed in the same way as in-plane element forces.