*OBJECTIVE

Keyword type: step

With *OBJECTIVE one can define the objective functions in a sensitivity analysis. Right now the following objectives are allowed for TYPE=COORDINATE design variables:

• DISPLACEMENT: the square root of the sum of the square of the displacements in all nodes of the structure or of a subset if a node set is defined
• EIGENFREQUENCY: all eigenfrequencies calculated in a previous *FREQUENCY step (actually the eigenvalues, which are the square of the eigenfrequencies)
• MASS: mass of the total structure or of a subset if an element set is defined
• STRAIN ENERGY: internal energy of the total structure or of a subset if an element set is defined
• STRESS: the maximum von Mises stress of the total structure or of a subset if a node set is defined. The maximum is approximated by the Kreisselmeier-Steinhauser function

  f=\frac{1}{\rho} \ln \sum_i e^{\rho \frac{\sigma_{i}}{\bar{\sigma}}}, (813)

  where \sigma_i is the von Mises stress in node i, \rho and \bar{\sigma} are user-defined parameters. The higher \rho the closer f is to the actual maximum (a value of 10 is recommended; the higher this value, the sharper the turns in the function). \bar{\sigma} is the target stress, it should not be too far away from the actual maximum.

and for TYPE=ORIENTATION design variables:

• DISPLACEMENT: the displacements in all nodes.
• EIGENFREQUENCY: all eigenfrequencies (actually the eigenvalues, which are the square of the eigenfrequencies) and eigenmodes calculated in a previous *FREQUENCY step.
• GREEN: the Green functions calculated in a previous *GREEN step.
• MASS: mass of the total structure or of a subset if an element set is defined
• STRAIN ENERGY: internal energy of the total structure or of a subset if an element set is defined
• STRESS: the stresses in all nodes.

There is one optional parameter TARGET. If TARGET=MIN (= default) the sensivity is calculated for a minization of the objective, if TARGET=MAX for a maximization. The difference comes into play when determining which constraints are active. Exactly one *OBJECTIVE keyword is required in a *SENSITIVITY step. This keyword has to be followed by at least one objective function. If a *CONSTRAINT card is used within the step exactly one objective function must be defined within the step.

First line:

• *OBJECTIVE.

Second line:

• an objective function
• an element or node set, if appropriate
• \rho for the Kreisselmeier-Steinhauser function (only for the coordinates as design variables and the stress as target)
• \bar{\sigma} for the Kreisselmeier-Steinhauser function (only for the coordinates as design variables and the stress as target)

Repeat this line if needed.

The objective functions STRAIN ENERGY, MASS, DISPLACEMENT and STRESS require a *STATIC step before the *SENSITIVITY step, the objective function EIGENFREQUENCY requires a *FREQUENCY step immediately preceding the *SENSITIVITY step and the objective function GREEN requires a *GREEN step before the *SENSITIVITY step. Therefore, the {STRAIN ENERGY, MASS, DISPLACEMENT, STRESS} objective functions, the {EIGENFREQUENCY} objective function and the {GREEN} objective function are mutually exclusive within one and the same *SENSITIVITY step.

Example:

*OBJECTIVE
DISPLACEMENT,N1

defines the square root of the sum of the square of the displacements in set N1 to be the objective function.

Example files: sensitivity_I.