Constraints for Controller-Based Shape Optimization

Volume Constraint

To select volume as the design response, the volume must be requested with TYPE=VOLUME. The individual element volumes of the element group (EL_GROUP parameter) are then added together by the summation parameter (GROUP_OPER=SUM parameter) to achieve the total volume. The volume is a variable independent of the load cases. The design response is labeled with a unique name (ID_NAME parameter) so it can be referenced as a constraint.

A typical definition of a design response appears as follows:


DRESP
 ID_NAME    = dresp_volume
 DEF_TYPE   = SYSTEM
 EL_GROUP   = all_elements
 TYPE       = VOLUME
 GROUP_OPER = SUM
 UPDATE     = EVER
END_

Once the volume of an element area has been defined as the design response, the design response must be defined as a constraint using the CONSTRAINT parameter. The value of the equality constraint (EQ_VALUE parameter) is also declared. In addition, the parameter EQ_VALUE is declared as absolute value (MAGNITUDE=ABS) or relative value (MAGNITUDE=REL) in relation to the initial volume. The constraint is labeled with a unique name (ID_NAME parameter) so it can be referenced in an optimization job (see OPTIMIZE command).

A typical definition of a constraint appears as follows:


CONSTRAINT
ID_NAME    = volume_constraint
 DRESP     = dresp_volume
 MAGNITUDE = REL
 EQ_VALUE  = 1
END_

Example:

The total volume of an element group in the start model is 2000. For the optimized model a total volume of 1800 is requested for the element group. Using absolute values, MAGNITUDE=ABS, EQ_VALUE=1800 must be declared. Using relative values, MAGNITUDE=REL, EQ_VALUE=0.9 must be declared.

Note:

The CONSTRAINT definition must be activated by a reference in the OPTIMIZE command.
It is highly recommended to choose a volume constraint near the original volume, say +/- 5% depending on the mesh quality and size of design area.

Important:

Tosca Structure.shape enforces the volume constraint in the first design cycle. This might destroy the mesh, especially if the volume constraint is far away from the initial volume. If you want to turn off this mechanism and let Tosca Structure.shape iterate for more iteration to achieve volume constraint use OPTIONS:
```
OPTIONS
 SHAPE_FORCE_VOLUME = OFF
END_
```
This setting is not recommended as it simply causes more design cycles before the mesh is corrupted.

Important:

Maintaining the volume constraint involves an iterative process; several steps are performed within each design cycle to approximate the volume constraint. Each step in the volume iteration involves executing a complete MESH_SMOOTH algorithm. To keep the computing time within limits, it is strongly recommended to select the MESH_SMOOTH area as small as possible and to keep the various levels of the MESH_SMOOTH definition (particularly LEVEL_CONV, LEVEL_DVCON and LEVEL_QUAL) as low as possible. A complex mesh smoothing can result in a significant increase in computing time.
It is also recommended to define a volume constraint when using the objective function ‘maximization of the lowest natural frequency’. The user can control the volume increase or decrease by activating this constraint. Consequently, it might be possible to achieve a further increase in the frequency

Weight constraint

Weight constraints are defined in the same way as volume constraints. Using this design response a physical target weight can be set explicitly. This is in particular useful when different materials are present in the model. The corresponding design response is defined as follows:


DRESP
 ID_NAME    = dresp_volume
 DEF_TYPE   = SYSTEM
 EL_GROUP   = all_elements
 TYPE       = WEIGHT
 GROUP_OPER = SUM
 UPDATE     = EVER
END_

Once the volume of an element area has been defined, the design response must be referenced in the CONSTRAINT definition.