# Size (Parameter) Optimization

The properties of structural elements such as shell thickness, beam cross-sectional properties, spring stiffness, and mass are modified to solve the optimization problem.

OptiStruct has the capability of performing size optimization simultaneously with the other types of optimization.

Defining size variables in OptiStruct is similar to other size optimization codes. Each size variable is defined using a DESVAR Bulk Data Entry. If a discrete design variable is desired, a DDVAL Bulk Data Entry needs to be referenced for the design variable values. The DESVAR cards are related to size properties in the model using a DVPREL1 or DVPREL2 Bulk Data Entry. Each DVPREL Bulk Data Entry must reference at least one DESVAR Bulk Data Entry to be active during the optimization. Altair HyperWorks includes a pre-processor called HyperMesh that can be used to set up any number of size variables for the properties.

Mass | Volume | Center of Gravity |

Moment of Inertia | Static Compliance | Static Displacement |

Natural Frequency | Buckling Factor | Static Stress, Strain, Forces |

Static Composite Stress, Strain, Failure Index | Frequency Response Displacement, Velocity, Acceleration | Frequency Response Stress, Strain, Forces |

Weighted Compliance | Weighted Frequency | Combined Compliance Index |

Function | Temperature |

## Design Variables

In finite elements, the behavior of structural elements (as opposed to continuum elements), such as shells, beams, rods, springs, and concentrated masses are defined by input parameters, such as shell thickness, cross-sectional properties, and stiffness.

Those parameters are modified in a size (parameter) optimization. Some structural elements have several parameters depending on each other; like beams in which the area, moments of inertia, and torsional constants depend on the geometry of the cross-section.

The property itself is not the design variable in size (parameter) optimization, but the property is defined as a function of design variables. The simplest definition, as defined by the design-variable-to-property relationship DVPREL1, is a linear combination of design variables defined on a DESVAR statement such that:

- $p$
- Property to be optimized
- ${C}_{i}$
- Linear factors associated to the design variable ${d}_{i}$

Using the equation utility DEQATN, more complicated functional dependencies using even trigonometric functions can be established. Such design-variable-to-property relations are then defined using the DVPREL2 statement.

For a simple gage optimization of a shell structure, the design-variable-to-property relationship turns into:

Where, the gage thickness, $T$ is identical to the design variable.

If a discrete design variable is desired, a DDVAL Bulk Data Entry needs to be referenced on the DESVAR Bulk Data Entry for the design variable values.