Objective Function

Overview

The OBJECTIVE FUNCTION is the function, which value can be maximized or minimized during the optimization. This function depends on the results of the FE analysis. Therefore, the values of interest must be derived from the FE results in order to define an objective function and functional constraints. The results of the FE analysis (total displacement, energy, etc.) for determining the objective function and functional constraints are called ’design responses.’ A single value from the design response must be specified for the definition of the objective function using the command DRESP (Design Response).


Static analysis	Description
CENTER_GRAVITY_X CENTER_GRAVITY_Y CENTER_GRAVITY_Z	Center of gravity design responses
DENSITY_MEASURE	Density measure design response
DISP_ABS DISP_X DISP_Y DISP_Z DISP_X_ABS DISP_Y_ABS DISP_Z_ABS	Displacement design responses
ENERGY_STIFF_MEASURE	Energy Stiffness Measure design response
INERTIA_XX INERTIA_XY INERTIA_XZ INERTIA_YY INERTIA_YZ INERTIA_ZZ	Moment of inertia design responses
INTERNAL_FORCE_ABS INTERNAL_FORCE_X INTERNAL_FORCE_Y INTERNAL_FORCE_Z INTERNAL_FORCE_X_ABS INTERNAL_FORCE_Y_ABS INTERNAL_FORCE_Z_ABS	Internal force design responses
INTERNAL_MOMENT_ABS INTERNAL_MOMENT_X INTERNAL_MOMENT_Y INTERNAL_MOMENT_Z INTERNAL_MOMENT_X_ABS INTERNAL_MOMENT_Y_ABS INTERNAL_MOMENT_Z_ABS	Internal moment design responses
REACTION_FORCE_ABS REACTION_FORCE_X REACTION_FORCE_Y REACTION_FORCE_Z REACTION_FORCE_X_ABS REACTION_FORCE_Y_ABS REACTION_FORCE_Z_ABS	Reaction force design responses
REACTION_MOMENT_ABS REACTION_MOMENT_X REACTION_MOMENT_Y REACTION_MOMENT_Z REACTION_MOMENT_X_ABS REACTION_MOMENT_Y_ABS REACTION_MOMENT_Z_ABS	Reaction moment design responses
ROT_ABS ROT_X ROT_Y ROT_Z ROT_X_ABS ROT_Y_ABS ROT_Z_ABS	Rotation design responses
SIG_1	Maximum principal stress.
SIG_3	Minimum principal stress.
SIG_SENS_MISES	Von Mises Stress design responses `SIG_SENS_MISES` is used for sensitivity calculation.
SIG_SIGNED_MISES	Signed von Mises stress failure criteria.
SIG_GLINKA_EEQ SIG_GLINKA_PEEQ SIG_GLINKA_SEQ SIG_NEUBER_EEQ SIG_NEUBER_PEEQ SIG_NEUBER_SEQ	Glinka and Neuber formulations for equivalent strain (_EEQ), stress (_SEQ) and plastic strain (_PEEQ) using the plastic correction factor, respectively**.
STRAIN_ENERGY	Strain energy design response*
WEIGHT	Weight design response
VOLUME	Volume design response
Modal analysis	Description
DYN_FREQ DYN_FREQ_KREISSEL	Dynamic frequency design response (Kreisselmeier-Steinhauser formulation)
Thermal analysis	Description
ENERGY_THERMAL_MEASURE	Energy thermal measure design response
INTERNAL_HFLUX	Internal heat flux design response
REACTION_HFLUX	Reaction heat flux design response
TEMPERATURE	Temperature design response

Important:

Only design responses marked with * are allowed in controller-based algorithm (TOPO_CONTROLLER).
The Gravity / Inertia design response types are only usable if at least one design response of the other types is used in the objective function or constraints.
Design responses marked with ** are only allowed using Abaqus sensitivities.

Differences in Objective Target Formulation

The objective formulation for the optimization varies depending on the objective target such as minimization/ maximization or a Min-Max/ Max-Min definition. For further details and formulas, see Minimization or Maximization of an Objective Function and Multidisciplinary Objectives (Minmax and Maxmin Formulations)