Spatial fields and maps

When the independent domain of a field is spatial coordinates, the field is referred to as a spatial field. Spatial fields are typically used to define how boundary conditions vary spatially. You can define the coordinate basis of a spatial field to be one of the following:

• The global coordinate system

• A local coordinate system

• A parametric coordinate system

You can use spatial fields to do the following:

• Apply a 3D field representation of a boundary condition over a volume.For example, you can apply an enforced displacement field over a volume.

• Map a 3D field representation of a boundary condition to curves and surfaces.For example, you can apply a pressure field over a surface.

• Create a 3D field representation of a boundary condition from a 2D field defined in an axisymmetric plane.For example, if a thermal stress problem is thermally axisymmetric, but structurally non-axisymmetric, you can create a 3D temperature field from the axisymmetric thermal results to apply over the entire volume for the structural analysis.

• Define thickness variations for a 2D or 3D surface.For example, you can apply a thickness field to a shell mesh.

Inherent 3D behavior of spatial fields

By default, the software interprets any spatial field as 3D. For example, suppose you create a formula field to represent the following functional relationship:

T = 200xy

where T is temperature and x and y are Cartesian coordinates.

The software calculates the temperature at both (x,y,z) = (1,1,0) and (1,1,1) to be 200. Thus, the software treats the formula field as 3D, even though z does not show up explicitly in the formula.

Similarly, the software interprets table fields as 3D, even when the tabular data is defined in a single coordinate plane or along a single coordinate direction.

Using parametric plane spatial maps and surface spatial maps to minimize interpolation errors

Interpolation errors can arise when you use a table field to define a boundary condition on a surface, even if the tabular data all lies on the surface. The following example shows how interpolation errors can arise.

Table lookup is for point “A”

The figure shows the edge view of a surface that wraps back upon itself. Suppose you create a table field to define the temperature throughout the surface. The table field includes 11 tabular data points along the visible edge. Each tabular data point has a set of coordinates and the corresponding temperature. Suppose the temperature at point 1 is 0 °C, the temperature at point 2 is 10 °C, the temperature at point 3 is 20 °C, and so on. The temperature at point 11 is 100 °C.

If the only mode of heat transfer is conduction within the surface, the thickness and conductivity are uniform throughout, and the temperature distribution does not vary through the depth, the correct temperature at point A can be interpolated from the temperatures at points 1 and 2 to be about 6 °C. However, the interpolated value that the software returns depends on the following:

• The interpolation method that you select.You select the interpolation method in the Table Field dialog box, on the Table Options page, from the Interpolation list.

• Whether or not you create a parametric plane spatial map or surface spatial map.You select the mapping option in the Table Field dialog box, on the Independent Domain page.

Without a parametric plane spatial map or surface spatial map, the software looks up temperature values by interpolating the tabular data in 3D space. Thus, if you select a Delaunay interpolation method, the software creates a Delaunay tetrahedralization of the tabular data rather than a Delaunay triangularization over the surface. If you select the inverse distance or nearest neighbor method as the interpolation method, the software calculates the distances it uses in these methods from differences in Cartesian coordinates rather than geodetic distances. Because point 11 is closest in proximity to point A in 3D space, the temperature at point 11 has considerable influence on the lookup value at point A even though it should not.

To avoid interpolation errors of this type, create a parametric plane spatial map or a surface spatial map. When you create a parametric plane spatial map or a surface spatial map, the software performs the interpolation in 2D space.

• For parametric plane spatial maps, you relate the parametric plane to model geometry. You then define the tabular data for the table field in terms of the parametric (u,v) coordinates.For more information on parametric plane spatial maps, see Parametric spatial maps.

• For surface spatial maps, you can either map 3D tabular data to existing surfaces or you can create a surface directly from the 3D tabular data.For more information, see Surface spatial maps.

The software does not contain similar capabilities for mapping 2D or 3D tabular data to a curve.

How do I

Create a surface spatial map

Create a table field along a parametric line

Define a boundary condition along a parametric line using a table field

Create a table field over a parametric plane

Define a boundary condition over a parametric plane using a table field

Learn more

Parametric spatial maps

Surface spatial maps

Axisymmetric spatial maps

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Spatial fields and maps, Simcenter 3D 2021.1 Series

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