Advanced Averaging
Advanced averaging means that tensor (or vector) results are transformed into a consistent system and then each component is averaged separately to obtain an average tensor (or vector).
![](../../images/post_processing/advanced_avg_formula1.png)
Where, are
tensors transformed to the reference system for corners A2, B1, C3, and D4,
respectively.
The components are extracted and the invariants are computed from this
averaged tensor or vector .
Element Type | Reference System | Projection Rule | Description |
---|---|---|---|
Solid | Global | N/A | All corresponding tensors and vectors are transformed to the global coordinate system and an average tensor/vector is calculated. The components and invariants are obtained from this tensor/vector as explained above. |
User-defined | N/A | Variation ON All corresponding tensors and vectors are transformed to the user-defined coordinate system and an average tensor/vector is calculated. The components and invariants are obtained from this tensor/vector. Variation OFF All corresponding tensors and vectors are transformed to the global coordinate system and an average tensor/vector is calculated. Then, this average tensor/vector is transformed to the user-defined system for components extraction and invariants calculation. |
|
Shell | Global | ON | The global co-ordinate system is projected to the Nodal Projection plane
(described in the Projection rule) to obtain the Nodal Projection system. All
corresponding tensors/vectors are then transformed to the Nodal projection system
and an average tensor/vector is calculated. The components and invariants are
obtained from this tensor/vector. As a result, even if the reference system is the same, the projected systems in participating elements can be different. Simple averaging for components ignores variations in systems. |
OFF | All corresponding tensors and vectors are transformed to the global coordinate system and an average tensor/vector is calculated. The components and invariants are obtained from this tensor/vector. | ||
User-defined | ON | The user-defined co-ordinate system is projected to the Nodal Projection
plane (described in the Projection rule) to obtain the Nodal Projection system.
Variation ON All corresponding tensors/vectors are then transformed to the Nodal projection system and an average tensor/vector is calculated. The components and invariants are obtained from this tensor/vector. Variation OFF All corresponding tensors and vectors are transformed to the global coordinate system and an average tensor/vector is calculated. Then, this average tensor/vector is transformed to the Nodal projection system for components extraction and invariants calculation. |
|
OFF | Variation ON All corresponding tensors and vectors are transformed to the user-defined coordinate system and an average tensor/vector is calculated. The components and invariants are obtained from this tensor/vector. Variation OFF All corresponding tensors and vectors are transformed to the global coordinate system and an average tensor/vector is calculated. Then, this average tensor/vector is transformed to the user-defined system for components extraction and invariants calculation. |
Valid reference coordinate system: Global and User-defined.