Using unit normal vector components as variables in expressions

You can use the components of unit normal vectors as system variables in expressions that define boundary conditions where Cartesian coordinates (x,y,z) are also supported as system variables.

The software calculates the components of the unit normal vectors for:

• Plate and shell elements.

• Solid element free faces.

• Axisymmetric element free edges.

Plate elements, shell elements, and solid element faces

For plate elements, shell elements, and solid element free faces, the software calculates the normal from three corner nodes of the plate element, shell element, or solid element free face. The software uses the same normal across the entire plate element, shell element, or solid element free face, except along shared edges. Along shared edges, the software averages the normals of the elements or element faces that share the edge. The software calculates the average of the two unit normal vectors as follows:

{\hat n_{ave}} = \frac{{{{\hat n}_1} + {{\hat n}_2}}}{{\left| {{{\hat n}_1} + {{\hat n}_2}} \right|}}

The positive direction of the normal to a plate element or shell element is consistent with the underlying element definitions.

The positive direction of the normal to a solid element free face is always outward.

Axisymmetric elements

For axisymmetric elements, the software calculates the normal to be perpendicular to the line formed by the two corner nodes on the free edge of the axisymmetric element.

The positive direction of the normal to an axisymmetric element edge is always outward.

Example of unit normal vector components as variables in an expression

The cylinder shown in the figure is subjected to a uniform radiant heat flux of q0 = 5 W/mm2 that is directed in the -x direction. You can use the Heat Flux command to model the heat flux that is incident on the cylinder.

The heat flux that is incident on each element face depends on the orientation of the element face relative to the x-direction.

• If the x-component of the unit normal vector to the element face is positive, that is nx > 0, then the heat flux on the element face is:q = \frac{{{q_0}{A_x}}}{A} = \frac{{{q_0}A{n_x}}}{A} = {q_0}{n_x}where A is the surface area of the element face and Ax is the projection of A in the x-direction.

• If the x-component of the unit normal vector to the element face is negative, that is nx < 0, then there is no heat flux on the element face.

Thus, an expression for the heat flux incident on the cylinder is as follows:

if ug_var("nx")>0 then 5[W/mm^2]*ug_var("nx") else 0[W/mm^2]

When you use this expression to define the Heat Flux command, the resulting heat flux distribution is as follows:

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