Combined Responses in Sensitivity-Based Optimization

Displacements


TYPE The allowable types for displacements and rotations	GROUP_OPER The allowable definition types for displacements and rotations	VAR_OPER The allowable operators for displacements and rotations
DISP_X DISP_Y DISP_Z ROT_X ROT_Y ROT_Z	MAX MIN SUM	SUB SUB_ABS COMBINE ADD_ABS
DISP_ABS	MAX	SUB SUB_ABS*
ROT_ABS	MAX	SUB_ABS*
DISP_X_ABS DISP_Y_ABS DISP_Z_ABS ROT_X_ABS ROT_Y_ABS ROT_Z_ABS	MAX MIN	---
* For these, `VAR_A` and `VAR_B` must have the same `DRESP` type. For example, the `DRESP` type for `VAR_A` and `VAR_B` is `TYPE = DISP_ABS` yielding: $\| ▵ u \| = \sqrt{{(u_{x 1} - u_{x 2})}^{2} + {(u_{y 1} - u_{y 2})}^{2} + {(u_{z 1} - u_{z 2})}^{2}}$

Remarks

For TYPE=DISP_ABS with VAR_OPER=SUB both VAR_A and VAR_B are TYPE=DISP_ABS. For this case the displacement of DRESP is calculated as following:


$DRESP= Δ u = l_{def} - l_{ini}$ with $l_{def} = \sqrt{{(Δ x_{pos} + Δ u_{x})}^{2} + {(Δ y_{pos} + Δ u_{y})}^{2} + {(Δ z_{pos} + Δ u_{z})}^{2}}$ as deformed length and $l_{ini} = \sqrt{{(Δ x_{pos})}^{2} + {(Δ y_{pos})}^{2} + {(Δ z_{pos})}^{2}}$ as initial length. Thereby $Δ n_{pos} = Δ n_{pos 1} - Δ n_{pos 2}$ , for n = x,y,z and $Δ u_{n} = Δ u_{n 1} - Δ u_{n 2}$ , for n = x,y,z, where pos1 and pos2 are the coordinates of the nodes and u the displacements. The DRESP can also be negative and gives the stretch between two nodes (that is, the difference between the two notes in deformed and undeformed configuration).

GROUP_OPER is default GROUP_OPER = MAX.
A node group (ND_GROUP) must be applied in the DRESP when more than one node is required.
Maximal 5000 DRESPs can be defined. Therefore, the maximal number of nodes for GROUP_OPER = MAX is 5000 or less as in this case one design response is created for each group member.
If possible, define design responses for displacements for single nodes (allows better control). Often 1 representative node is sufficient for the task.
The maximal number of nodes for GROUP_OPER = SUM us unlimited.
Design responses combined using VAR_OPER should refer to the same group.

Reaction Forces


TYPE The allowable types for reaction forces	GROUP_OPER The allowable definition types for reaction forces	VAR_OPER The allowable operators for reaction forces
REACTION_FORCE_X REACTION_FORCE_Y REACTION_FORCE_Z REACTION_MOMENT_X REACTION_MOMENT_Y REACTION_MOMENT_Z	MAX MIN SUM	SUB SUB_ABS COMBINE ADD_ABS
REACTION_FORCE_ABS REACTION_MOMENT_ABS	MAX	SUB_ABS*
REACTION_FORCE_X_ABS REACTION_FORCE_Y_ABS REACTION_FORCE_Z_ABS REACTION_MOMENT_X_ABS REACTION_MOMENT_Y_ABS REACTION_MOMENT_Z_ABS	MAX MIN	---
* For these, `VAR_A` and `VAR_B` must have the same `DRESP` type. For example, the `DRESP` type for `VAR_A` and `VAR_B` is `TYPE = REACTION_FORCE_ABS` yielding $Δ R = \sqrt{{(R_{x 1} - R_{x 2})}^{2} + {(R_{y 1} - R_{y 2})}^{2} + {(R_{z 1} - R_{z 2})}^{2}}$

Internal Forces


TYPE The allowable types for internal forces	GROUP_OPER The allowable definition types for internal forces	VAR_OPER The allowable operators for internal forces
INTERNAL_FORCE_X INTERNAL_FORCE_Y INTERNAL_FORCE_Z INTERNAL_MOMENT_X INTERNAL_MOMENT_Y INTERNAL_MOMENT_Z	MAX MIN SUM	SUB SUB_ABS COMBINE ADD_ABS
INTERNAL_FORCE_ABS INTERNAL_MOMENT_ABS	MAX	SUB_ABS*
INTERNAL_FORCE_X_ABS INTERNAL_FORCE_Y_ABS INTERNAL_FORCE_Z_ABS INTERNAL_MOMENT_X_ABS INTERNAL_MOMENT_Y_ABS INTERNAL_MOMENT_Z_ABS	MAX MIN	---
* For these, `VAR_A` and `VAR_B` must have the same `DRESP` type. For example, The `DRESP` type for `VAR_A` and `VAR_B` is `TYPE = INTERNAL_FORCE_ABS` yielding $Δ R = \sqrt{{(F_{x 1} - F_{x 2})}^{2} + {(F_{y 1} - F_{y 2})}^{2} + {(F_{z 1} - F_{z 2})}^{2}}$

Modal Eigenfrequencies


TYPE	GROUP_OPER The allowable definition types	VAR_OPER The allowable operators
DYN_FREQ	MAX MIN	SUB SUB_ABS COMBINE KSO

Note that with the operator KSO the Kreisselmeier-Steinhauser formulation can be constructed from single eigenfrequency DRESPs in context of sensitivity-based topology and sizing optimization. It is given by $- \frac{1}{k} ln (\sum_{j} e^{- k f_{j}})$ .

Frequency Spectrum Responses


TYPE The allowable types for frequency response	GROUP_OPER The allowable definition types for frequency response	VAR_OPER The allowable operators for frequency response
FS_DISP_X_ABS FS_DISP_Y_ABS FS_DISP_Z_ABS FS_DISP_ABS	MAX MIN	SUB_ABS*
FS_PHASE_X FS_PHASE_Y FS_PHASE_Z FS_VELOCITY_X FS_VELOCITY_Y FS_VELOCITY_Z FS_ACCEL_X FS_ACCEL_Y FS_ACCEL_Z	MAX MIN	---
* For these, `VAR_A` and `VAR_B` must have the same `DRESP` type. For example, the `DRESP` type for `VAR_A` and `VAR_B` is `TYPE = FS_DISP_X_ABS` yielding $Δ A_{x} = \sqrt{{(u_{R, x 1} - u_{R, x 2})}^{2} + {(u_{I, y 1} - u_{I, y 2})}^{2}}$

Temperature


TYPE The allowable types for thermal analysis	GROUP_OPER The allowable definition types for thermal analysis	VAR_OPER The allowable operators for thermal analysis
TEMPERATURE REACTION_HFLUX INTERNAL_HFLUX	MAX SUM	SUB SUB_ABS COMBINE

A maximum of 5000 Design response definitions (DRESP) is allowed.