Volume Control

If the task specified by the user is iso or all_iterations, the result of the calculation is the isosurface generated by isocut and possibly modified by the smoothing and data reduction. After these operations are successively finished, the user gets the message that looks as follows:


Iso-surface successfully generated - iso-value: 0.300 - relative volume: 57.3%

For solid models, the volume displayed in this message is the ratio of the volume of solid(s) defined by the isosurface to the original volume, which is the sum of the volumes of all solid elements used in the topology optimization, except those excluded using the group commands. The original volume is also equal to the volume of the solid(s) defined by the surface produced from the same model file using the surface task, provided that the data reduction is turned off. For shell element models, the definition is the same except that "volume" should be replaced with "area". If the model contains both solid and shell elements, only the solid elements are considered.

In order to achieve a required relative volume, the user might change the isovalue and recalculate the isosurface, keeping in mind that larger isovalues usually lead to smaller volumes. The same result can be achieved using the automatic approach implemented in Tosca Structure.smooth.

In order to turn it on, the parameter TARGET_VOLUME should be set to a value between 0 and 1. Then, the isovalue specified by the ISO_VALUE parameter is ignored and an iterative equation solving method is used to determine the isovalue that leads to the specified target relative volume.

Important: If this volume is larger than the volume for isovalue equal to zero or smaller than the volume for isovalue equal to 1, an error message is produced; in this case, it is unlikely that the required relative volume can be achieved for any isovalue between 0 and 1.

Otherwise, the convergence to a solution is guaranteed unless the dependence of target volume on isovalue is noncontinuous, that sometimes occurs for small models.

The maximal number of iterations is fixed (currently 20).

Important: If the iterations fail to converge before this number is reached, an error message will be produced.

In this case, it is recommended to run Tosca Structure.smooth again using the isovalue obtained in the last iteration, although the resulting relative volume would probably differ from the value used initially. The iterations are treated as having converged if the difference between the calculated and the desired values is less than 10% of the desired value, and, in the same time, less than 1%.

If the model contains several design areas, different target relative volumes might be needed for one or more regions. For this reason, the possibility to define isovalues and target volumes differently for each group is implemented in Tosca Structure.smooth; however, it is not supported in Tosca Structure.gui.

The command


TARGET_VOLUME_GROUP = <group name>, <target relative volume>

with <group name> being a name of a group defined in an ONF group file defines the relative volume for this group. Then, for each such command, the isovalue for the group will be found first by using the iterative method applied to this group alone, after excluding the elements marked as deleted.

For other groups, the isovalue can be specified directly using the following command:

    ISO_VALUE_GROUP = <group name>, <isovalue>

For the rest of the material, the default isovalue given by ISO_VALUE command (or, equivalently, ISO_VALUE_GROUP command for the group all) is used.

Important:

The groups for which the target relative volumes or the isovalues are defined must be disjoint.

In particular, the command TARGET_VOLUME (or, equivalently, TARGET_VOLUME_GROUP for the group all) is not allowed if TARGET_VOLUME_GROUP or ISO_VALUE_GROUP commands with groups not equal to all are used.

After the isovalues for all groups with the specified target relative volumes are calculated, they are interpolated to get the nodal isovalues, which are then used for the isocut. Therefore, in an area between two regions with different isovalues the average values are used. This leads to smooth transition between the regions, but also might change the relative volumes of the regions; additional error might be introduced by the surface smoothing. Generally, the number of elements in the transition region is relatively small, therefore the error can be neglected.