# Difference

The nodal difference is the difference between the maximum and minimum corner results at a node.

For tensor/vector components, the corresponding components from each element corner are extracted and the difference is calculated. For invariants, the corresponding invariants are computed from each element corner and then the difference is calculated.

The sign of a value is considered in the difference calculation. For example, the difference for the values, 200, 400, -100, and -500 is 900.

In the example shown in the Nodal Averaging of Elemental Results topic, the nodal difference of tensor component xx at node 400 is:
Where,
The difference calculation methods for solid elements and shell elements are different.
Element Type Reference System Projection Rule Description
Solid Global N/A All corresponding tensors and vectors are transformed to the global coordinate system and then the difference for a component or invariant is calculated as explained above.
Analysis N/A All corresponding tensors and vectors are left in their original coordinate system (no transformation occurs) and then the difference for a component or invariant is calculated as explained above.

In this case, each participating element result can be in a different system. Difference calculation for components ignores variations in systems. Since invariance does not depend on the coordinate system, all reference systems will produce the same results for invariants.

Elemental N/A All corresponding tensors and vectors are transformed to the elemental coordinate system and then the difference for a component or invariant is calculated as explained above.

In this case, each participating element result can also be in a different system. Difference calculation for components ignores variations in systems.

User-defined N/A All corresponding tensors and vectors are transformed to the user-defined coordinate system and then the difference for a component or invariant is calculated as explained above.
Shell Global ON All corresponding tensors and vectors are transformed to the projected system (following the projection rule) of the participating elements and then the difference for a component or invariant is calculated as explained above.

As a result, even if the reference system is the same, the projected systems in participating elements can be different. Difference calculation for components ignores variations in systems.

OFF All corresponding tensors and vectors are transformed to the global coordinate system and then the difference for a component or invariant is calculated as explained above.
Analysis N/A All corresponding tensors and vectors are left in their original coordinate system (no transformation occurs) and then the difference for a component or invariant is calculated as explained above.

In this case, each participating element result can be in a different system. Difference calculation for components ignores variations in systems.

Elemental N/A All corresponding tensors and vectors are transformed to the elemental coordinate system and then a component or invariant is averaged as explained above.

In this case, each participating element result can also be in a different system. Difference calculation for components ignores variations in systems.

User-defined ON All corresponding tensors and vectors are transformed to the projected system (following the projection rule) of the participating elements and then the difference for a component or invariant is calculated as explained above.

As a result, even if the reference system is the same, the projected systems in participating elements can be different. Difference calculation for components ignores variations in systems.

OFF All corresponding tensors and vectors are transformed to the user-defined coordinate system and then the difference for a component or invariant is calculated as explained above.

Valid reference coordinate system: All (Global, Analysis, Elemental, and User-defined)