Pattern Repetition

To achieve this, a main DTPL card needs to be defined, followed by any number of secondary DTPL cards which reference the main. The main and secondary components are related to each other through local coordinate systems, which are required, and through scaling factors, which are optional.

Other manufacturing constraints, such as minimum or maximum member size, draw direction constraints or extrusion constraints, can be applied to the main DTPL card. These constraints will then automatically be applied to the secondary DTPL card(s).

The following procedure should be followed to set up pattern repetition:

Create a main DTPL card.
Apply other manufacturing constraints as needed.
Define the local coordinate system associated to the main DTPL card.
Create a secondary DTPL card.
Define the local coordinate systems associated to the secondary DTPL card.
Apply scaling factors as needed.
Repeat steps 4-6 for any number of secondary DTPL cards.

Local Coordinates Systems

Local coordinates systems are generated by providing four points. These points can be defined either by entering explicit coordinates or by referencing existing grids, as follows:

CAID: Defines the anchor point for the local coordinates system.
CFID: Defines the direction of the X-axis.
CSID: Defines the XY plane and indicates the positive sense of the Y-axis.
CTID: Indicates the positive sense of the Z-axis.

The definition of the fourth point allows for both right-handed and left-handed coordinate systems, which facilitates the creation of reflection patterns.

Figure 1. Right-handed Coordinates System and Left-handed Coordinates System

Alternatively, local coordinate systems can be defined by referencing an existing rectangular coordinate system in the CID field, and by defining an anchor point in the CAID field.

Note: If the fields defining CFID, CSID, CTID, and CID are left blank, the global coordinates system is used by default. The anchor point CAID; however, is always required.

Scaling Factors

Scaling factors in the X, Y, and Z directions can be defined for each secondary DTPL card. These factors are always related to the local coordinate system. By playing with the local coordinate systems and the scaling factors, a wide range of effects can be obtained as illustrated in Figure 2.

Pattern Repetition with Draw Direction Constraints

Draw direction constraints can be applied simultaneously with pattern repetition. To achieve this, simply define the draw direction for the main DTPL card, and the draw direction for the secondary(ies) will automatically be generated based on the local coordinate system.

Even if some components are not naturally identical, the optimized design for each component will still satisfy the draw direction constraints. In particular, if different components contain different obstacles, the combination of all obstacles will always be considered.

Pattern Repetition with Extrusion Constraints

Extrusion constraints can also be used in conjunction with pattern repetition. This allows for creating parts which have identical cross-sections. The components do not need to be identical in a three-dimensional sense; each part can have its own extrusion path.

If the components have different extrusion paths, these paths have to be defined explicitly on each DTPL card. However, if the components have identical extrusion paths, the paths for the secondary(ies) will automatically be computed based on the main's extrusion path.

Example: Block Models

This example shows how pattern repetition may be used to generate the same topology in different parts. The first figure shows two similar blocks loaded in two different ways. The optimization problem is to minimize the compliance with 30 percent volume fraction.

patrep3 — Figure 3. Similar Blocks Loaded in Two Different Ways

If pattern repetition is not used, the optimized topologies are different, as shown in Figure 4 and Figure 5.

patrep4 — Figure 4. Same View as in the First Figure

patrep5 — Figure 5. Back View Showing that the Turquoise Block is Hollowed Out

Using pattern repetition, both of the loads on the main (the left hand block in first figure) and the loads on the secondary are taken into account, and the optimized topology is repeated for both blocks (Figure 6).

Example: Simplified Wing Model

patrep7 — Figure 7. Simplified Wing Model

The internal wing structure consists of 2 spars and 11 ribs. In this example, each rib is subdivided into three sections; the nose section, the center section and the tail section, and each of these sections is chosen as a topology design region.

The optimization problem is to minimize compliance for 30 percent of the design volume fraction. Here you see the optimized topology when each region is independent.

patrep9 — Figure 9. Optimized Topology of Independent Region

Pattern repetition is used to group all of the noses together, all of the centers together and all of the tails together, resulting in 3 main pattern definitions, each with 10 secondary definitions. Notice how different meshes are used for each rib; pattern repetition is mesh independent. Also the wing tapers, so the outboard ribs are shorter and thinner than the inboard ribs, scaling is defined for the secondary so that the pattern fits in the design space.

The optimized topology achieved using pattern repetition (Figure 11), and you can see how the same topological layout is repeated for each rib.