# Free-size Optimization Manufacturability

A concern in free-size optimization is that the design concepts developed are very often not manufacturable. Another problem is that the solution of a free-size optimization problem can be mesh dependent, if the appropriate measure is not taken.

OptiStruct offers a number of different methods to account for manufacturability when performing free-size optimization.

## Member Size Control

Member size control allows you some control over the member size in the final free-size design and the resulting degree of simplicity therein.

This feature may be added one of the two ways.

### DOPTPRM Card

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|

DOPTPRM | MINDIM |
VALUE |

### DSIZE Card

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|

MEMBSIZ |
MINDIM |

Here, only the preferred minimum diameter (width in 2D) of
members may be defined as the `VALUE` field, following the
`MINDIM` keyword. A global minimum member size is defined
in this way.Here, the preferred minimum,
`MINDIM` member may be defined on the
`MEMBSIZ` continuation line. Member size dimensions can be
defined differently for each DSIZE entry in this
way.

### Minimum Member Size Control

Although minimum member size control penalizes the formation of small members, results that contain members significantly under the specified minimum member size can still be obtained. This is because a small member in the structure can be very important to the load transmission and may not be removed by penalization. Minimum member size control functions more as a quality control than a quantity control.

A discrete solution is achieved in two iterative steps. The first step converges to a solution
with a large number of semi-dense elements. The second step tries to refine this
solution to a solution with fully dense members. Each step consists of a number of
iterations. The first step consists of two entire convergence phases - the first run
with the initial discreteness values (defined by `DISCRETE` and
`DISCRT1D` parameters on the DOPTPRM Bulk
Data Entry), followed by a run with the discreteness values increased by 1.0. This
procedure is implemented in order to achieve a solution with clearly defined
members. If this step does not create a solution with clearly defined members, the
preferred minimum member size will not be preserved in the second step. In which
case, you will need to increase the discreteness parameters and/or reduce the
convergence tolerance (defined by the `OBJTOL` parameter on the
DOPTPRM Bulk Data Entry) to improve the solution of the first
phase. The default discreteness is set to 1.0 for 1D elements, plates and shells,
and 2.0 for 3D solids.

In general, once `MINDIM` is activated, checkerboarding is controlled by the
methods applied for this feature, eliminating the need for the
`CHECKER` parameter. In rare circumstances, checkerboards may
still be introduced in the second phase described above for 3D solids. If this
happens, an additional checkerboard control algorithm can be activated with the
`MMCHECK` parameter. (The `CHECKER` and
`MMCHECK` parameters are defined using the
DOPTPRM Bulk Data Entry).

The use of this card will assure a checkerboard-free solution, although with the undesired side
effect of achieving a solution that involves a large number of semi-dense elements,
similar to the result of setting `CHECKER` equal to 1. Therefore,
use this card only when it is necessary.

It is recommended that `MINDIM` be at least 3 times the average element size for
all elements referenced by that DSIZE (or all designable elements
when defined on DOPTPRM). The average element size for 2D
elements is calculated as the average of the square root of the area of the
elements, and for 3D elements, as the average of the cubic root of the volume of the
elements.

This recommendation is enforced when combined with other manufacturing constraints, and if the
defined `MINDIM` is less than this value, it will be reset to a
default value equal to 3 times the average element size.

`MINDIM` can be smaller than the mesh size. When a value smaller
than the mesh size is applied, the effect is similar to checkerboard control but
with the 3-phase convergence phases process and possibly a more discrete result.
Minimum member size control has a 3-phase iterative process where the final phase
targets the removal of the semi-dense element layer. If manufacturing constraints
are applied, minimum member size control is always activated. However, the final
iterative phase will not target the removal of semi-dense elements as this may have
an adverse effect on manufacturing constraint preservation.

## Pattern Repetition

A technique where different structural components can be linked together so as to produce similar topological layouts.

To achieve this goal, a main DSIZE card needs to be defined, followed by any number of secondary DSIZE 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, can be applied to the main DSIZE card. These constraints will then automatically be applied to the secondary DSIZE card(s) as described in the sections below.

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

### Local Coordinates Systems

`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.

`CID`field, and by defining an anchor point in the

`CAID`field.

`CFID`,

`CSID`,

`CTID`, and

`CID`are left blank, then the global coordinates system is used by default. The anchor point

`CAID`, however, is always required.

### Scaling Factors

## Pattern Grouping

Pattern grouping is a feature where you can define a single part of the domain that should be designed in a certain pattern.pattern grouping - free-size optimization.

### Planar Symmetry

It is often desirable to produce a design that has symmetry. Unfortunately, even if the design space and boundary conditions are symmetric, conventional free-size optimization methods do not guarantee a perfectly symmetric design.

By using symmetry constraints in free-size optimization, symmetric designs can be attained regardless of the initial mesh, boundary conditions, or loads. Symmetry can be enforced across one plane, two orthogonal planes, or three orthogonal planes. A symmetric mesh is not necessary, as OptiStruct will create variables that are very close to identical across the plane(s) of symmetry.

### Uniform Element Thickness

Pattern grouping also provides the possibility to request a uniform element thickness throughout selected components.

This pattern group ensures that all elements of selected components maintain the same element thickness with respect to one another.

### Cyclical Symmetry

Cyclical symmetry can also be defined through the use of pattern grouping.

With cyclical pattern grouping, the design is repeated about a central axis a number of times determined by you. Furthermore, the cyclical repetitions can be symmetric within themselves. If that option is selected, OptiStruct will force each wedge to be symmetric about its centerline.

### Linear and Planar Pattern Grouping (TYP=20 and TYP=21)

`TYP`=21) is recommended.