Pattern Grouping Options for Topography Optimization

There are over 70 pattern grouping options and variations available for topography optimization. A summary of the major categories is shown below:

Variable grouping pattern	Pattern Option	Type #	Required Vector Definitions	Description
None	-	0	-	Variables grouped as points.
One plane symmetry	-	10	One	Reflection of variables across one plane normal to first vector.
Two plane symmetry	-	20	Two	Reflection of variables across two planes, one normal to the first vector and one normal to second vector.
Three plane symmetry	-	30	Two	Reflection of variables across three planes, one normal to first vector, one normal to the second vector and one perpendicular to both vectors.
Linear	-	1	One	Variables grouped as lines extending in direction of first vector.
	+1 plane	21	Two	Reflection of variables across one plane normal to second vector.
	+2 planes	31	Two	Reflection of variables across two planes, one normal to second vector and one perpendicular to both vectors.
Circular	-	2	One	Variables grouped as circles around anchor node lying in a plane normal to first vector.
Circular	+1 plane	12	One	Reflection of variables across one plane normal to first vector.
Planar	-	3	One	Variables grouped as planes extending normal to first vector.
Planar	+1 plane	13	One	Reflection of planes across plane normal to first vector.
Radial 2D	-	4	One	Variables grouped as rays extending radially and normal to first vector.
	+1 plane	14	One	Reflection of rays across plane normal to first vector.
	+2 planes	24	Two	Reflection of rays across two planes, one normal to the first vector and one normal to second vector.
	+3 planes	34	Two	Reflection of rays across three planes, one normal to first vector, one normal to the second vector and one perpendicular to both vectors.
Cylindrical	-	5	One	Variables grouped as endless cylinders extending along and centered around first vector.
Radial 2D & Linear	-	6	One	Variables grouped as a combination of radial and linear patterns.
	+1 plane	26	Two	Reflection of radial planes across plane normal to second vector.
	+2 planes	36	Two	Reflection of radial planes across plane normal to both first and second vectors.
Radial 3D	-	7	-	Variables grouped as rays extending radially outward from anchor node.
	+1 plane	17	One	Reflection of rays across plane normal to first vector.
	+2 planes	27	Two	Reflection of rays across two planes, one normal to the first vector and one normal to second vector.
	+3 planes	37	Two	Reflection of rays across three planes, one normal to first vector, one normal to the second vector and one perpendicular to both vectors.
Vector defined	-	8	-	Variables grouped along vectors defined by the draw vectors of the individual nodes.
	+1 plane	18	One	Reflection of variables across plane normal to first vector.
	+2 planes	28	Two	Reflection of variables across two planes, one normal to the first vector and one normal to second vector.
	+3 planes	38	Two	Reflection of variables across three planes, one normal to first vector, one normal to the second vector and one perpendicular to both vectors.
Cyclical*	-	40,41	Two	Cyclical repetition of variables about axis defined by first vector.
	+1 plane	50,51	Two	Reflection of variables across one plane normal to first vector.
	+ linear	60,61	Two	Cyclically repeated variables grouped as lines extending in direction of first vector.
	+ radial	70,71	Two	Cyclically repeated variables grouped as rays extending radially and normal to first vector.
	+ radial & linear	80,81	Two	Cyclically repeated variables grouped as a combination of radial and linear patterns.

* For cyclical symmetry, the UCYC parameter (field 30) controls the number of repetitions (and thus the repetition angle) for the cycles. If the TYP option selected for cyclical symmetry is 40, 50, 60, 70, or 80, the cyclical repetition pattern will be non-reflective. If the TYP option selected for cyclical symmetry is 41, 51, 61, 71, or 81, the cyclical repetition pattern will be reflective.

These options can be used with shell and solid models to create reinforcement patterns that obey manufacturing constraints and which conform to the shapes of the parts. Examples of pattern grouping options are given in the following sections:

Cross-section Optimization of a Spot Welded Tube

Optimization of the Modal Frequencies of a Disc Using Constrained Beading Patterns

Multi-plane Symmetric Reinforcement Optimization for a Pressure Vessel

Shape Optimization of a Stamped Hat Section

Shape Optimization of a Solid Control Arm

Using Topography Optimization to Forge a Design Concept Out of a Solid Block