The dot product of two vectors and is provided (with the VDOT command) as:

(17–4)

The cross product of two vectors {A} and {B} is also provided (with the VCROSS command) as:

(17–5)

In both operations, the components of vectors {A} and {B} are transformed to global Cartesian coordinates before the calculations. The results of the cross product are also in global Cartesian coordinates.

Nodal values across a free surface can be integrated (using the INTSRF command). The free surface is determined by a selected set of nodes which must lie on an external surface of the selected set of elements.

Only pressure values can be integrated (for purposes of lift and drag calculations in fluid flow analyses). As a result of the integration, force and moment components in the global Cartesian coordinate system are:

(17–6)

(17–7)

where:

{Ft} = force components

{Fr} = moment components

{r} = position vector =

{p} = distributed pressure vector

area = surface area

In the finite element implementation, the position vector {r} is taken with respect to the origin.