Group Operations for Displacements

The picture below shows a structure loaded at the nodes 15, 16 and 17. The y-displacement of these three nodes should be minimized or applied in a set of constraints using GROUP_OPER=MAX or GROUP_OPER=SUM.

Use in Objective Function

Initially, a node group is defined containing the nodes 15, 16 and 17 (see figure above) yielding:


GROUP_DEF
 ID_NAME = DISP_NODES
 TYPE    = NODE
 FORMAT  = LIST
LIST_BEGIN
 15, 16, 17
END_
GROUP_OPER = MAX

Based on the node group a design response for the displacements in y-directions are defined in a DRESP using GROUP_OPER=MAX yielding:


DRESP
 ID_NAME    = DRESP_DISP_MAX
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 LC_SET     = STATIC,1,
 ND_GROUP   = DISP_NODES
 GROUP_OPER = MAX
END_

Internally, SIMULIA Tosca Structure generates three DRESPs. One DRESP for the displacement of node 15, one DRESP for the displacement of node 16 and one DRESP for the displacement of node 17.

If one then applies the DRESP in the objective yielding:


OBJ_FUNC
 ID_NAME = MIN_DISP_MAX
 DRESP   = DRESP_DISP_MAX
 TARGET  = MIN
END_

SIMULIA Tosca Structure then sums up the three displacements like the following:


$minimize {Φ_{0}} = minimize {u_{15} + u_{16} + u_{17}}$

Remark: If you want to minimize the maximum of the three displacements you need to define an objective function with target MIN_MAX operating on three design responses (one for each node).


$minimize {Φ_{0}} = \max \{u_{15}; u_{16}; u_{17}\}$

GROUP_OPER = SUM

Based on the node group a design response for the displacements in y-directions are defined in a DRESP using GROUP_OPER=SUM yielding:


DRESP
 ID_NAME    = DRESP_DISP_SUM
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 LC_SET     = STATIC,1,
 ND_GROUP   = DISP_NODES
 GROUP_OPER = SUM
END_

Internally, SIMULIA Tosca Structure generates one DRESP consisting of the sum of the displacements of the nodes 15, 16 and 17.

If one then applies the DRESP in the objective yielding:


OBJ_FUNC
 ID_NAME = MIN_DISP_SUM
 DRESP   = DRESP_DISP_SUM
 TARGET  = MIN
END_

SIMULIA Tosca Structure then sum up the three displacements like the following:


$minimize {Φ_{0}} = minimize {u_{15} + u_{16} + u_{17}}$

Alternative Definition of Objective Function

Alternatively, one could also define three DRESPs for each node like the following:


DRESP
 ID_NAME    = DRESP_DISP_1
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 NODE       = 15
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

DRESP
 ID_NAME    = DRESP_DISP_2
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 NODE       = 16
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

DRESP
 ID_NAME    = DRESP_DISP_3
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 NODE       = 17
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

And then add the three design response in the objective function:


OBJ_FUNC
 ID_NAME = MIN_DISP_SUM
 DRESP   = DRESP_DISP_1
 DRESP   = DRESP_DISP_2
 DRESP   = DRESP_DISP_3
 TARGET  = MIN
END_

Meaning that the objective function minimizes the following:


$minimize {Φ_{0}} = minimize {u_{15} + u_{16} + u_{17}}$

Remark: Consequently, it can be concluded that all three ways of defining the optimization leads to the same objective function. In this case, it is strongly recommended that you combine the displacements using GROUP_OPER = SUM, which results in a better performance.

Use in Constraints

Initially, a node group is defined containing the nodes 15, 16 and 17 (see figure above) yielding:


GROUP_DEF
 ID_NAME = DISP_NODES
 TYPE    = NODE
 FORMAT  = LIST
 LIST_BEGIN
 15, 16, 17
END_

GROUP_OPER = MAX

Based on the node group a design response for the displacements in y-directions are defined in a DRESP using GROUP_OPER=MAX yielding:


DRESP
 ID_NAME    = DRESP_DISP_MAX
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 LC_SET     = STATIC,1,
 ND_GROUP   = DISP_NODES
 GROUP_OPER = MAX
END_

Internally, SIMULIA Tosca Structure generates three DRESPs. One DRESP for the displacement of node 15, one DRESP for the displacement of node 16 and one DRESP for the displacement of node 17.

If you apply the DRESP in a constraint yielding:


CONSTRAINT
 ID_NAME   = CONSTRAINT_MAX
 DRESP     = DRESP_DISP_MAX
 MAGNITUDE = ABS
 LE_VALUE  = <value>
END_

SIMULIA Tosca Structure then generates three displacement constraints like the following:


$u_{15} \leq u^{}$ $u_{16} \leq u^{}$ $u_{17} \leq u^{*}$

GROUP_OPER = SUM

Based on the node group a design response for the displacements in y-directions are defined in a DRESP using GROUP_OPER=SUM yielding:


DRESP
 ID_NAME   = DRESP_DISP_SUM
 DEF_TYPE  = SYSTEM
 TYPE      = DISP_Y
 LC_SET    = STATIC,1,
 ND_GROUP  = DISP_NODES
 GROUP_MAX = SUM
END_

Internally, SIMULIA Tosca Structure generates one DRESP consisting of the sum of the displacements of the nodes 15, 16 and 17.

If you apply the DRESP in a constraint yielding:


CONSTRAINT
 ID_NAME   = CONSTRAINT_MAX
 DRESP     = DRESP_DISP_MAX
 MAGNITUDE = ABS
 LE_VALUE  = <value>
END_

SIMULIA Tosca Structure then generates a single displacement constraint like the following:


$u_{15} + u_{16} + u_{17} \leq u *$

Alternative Definition of Constraints

Alternatively, one could also define three DRESPs for each node like the following:


DRESP
 ID_NAME    = DRESP_DISP_1
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 NODE       = 15
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

DRESP
 ID_NAME    = DRESP_DISP_2
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 NODE       = 16
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

DRESP
 ID_NAME    = DRESP_DISP_3
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 NODE       = 17
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

And then add the three design response in three constraints:


CONSTRAINT
 ID_NAME   = CONSTRAINT_1
 DRESP     = DRESP_DISP_1
 MAGNITUDE = ABS
 LE_VALUE  = <value>
END_

CONSTRAINT
 ID_NAME   = CONSTRAINT_2
 DRESP     = DRESP_DISP_2
 MAGNITUDE = ABS
 LE_VALUE  = <value>
END_

CONSTRAINT
 ID_NAME   = CONSTRAINT_3
 DRESP     = DRESP_DISP_3
 MAGNITUDE = ABS
 LE_VALUE  = <value>
END_

SIMULIA Tosca Structure then generates three displacement constraints like the following:


$u_{15} \leq u^{}$ $u_{16} \leq u^{}$ $u_{17} \leq u^{*}$

Consequently, it can be concluded that there is fundamental difference in the constraints if a node group (ND_GROUP) consisting of more than one node is applied and the choice of GROUP_OPER.