Group Operations for Internal Forces

The picture below shows a structure where the internal forces in the y-direction of the two nodes 65 and 66 for elements 33, 34, 37 and 38 should be applied in a set of constraints using GROUP_OPER=MAX or GROUP_OPER=SUM.

For the use in CONSTRAINTs is, initially, a node group defined containing the nodes 65 and 66 (see figure above) yielding:


GROUP_DEF
 ID_NAME = FORCE_NODES
 TYPE    = NODE
 FORMAT  = LIST
 LIST_BEGIN
 65, 66
END_

and a element group is defined containing the elements 33, 34, 37 and 38 (see figure above) yielding.

GROUP_DEF
 ID_NAME = FORCE_ELEM
 TYPE    = ELEM
 FORMAT  = LIST
 LIST_BEGIN
 33, 34, 37, 38
END_

GROUP_OPER = MAX

Based upon the node group and the element group a design response for the internal force in y-directions are defined in a DRESP using GROUP_OPER=MAX yielding:


DRESP
 ID_NAME    = DRESP_FORCE_MAX
 DEF_TYPE   = SYSTEM
 TYPE       = INTERNAL_FORCE_Y
 LC_SET     = STATIC,1,
 ND_GROUP   = FORCE_NODES
 EL_GROUP   = FORCE_ELEM
 GROUP_OPER = MAX
END_

Internally, SIMULIA Tosca Structure generates two DRESPs. One DRESP for the internal force of node 65 for element 33 and 34, and one DRESP for the internal force of node 66 for element 37 and 38.

If one then applies the DRESP in a constraint yielding:


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

SIMULIA Tosca Structure then generates two internal force constraints like the following:


$F_{65} \leq F^{}$ $F_{66} \leq F^{}$

GROUP_OPER = SUM

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


DRESP
 ID_NAME    = DRESP_FORCE_SUM
 DEF_TYPE   = SYSTEM
 TYPE       = INTERNAL_FORCE_Y
 LC_SET     = STATIC,1,
 ND_GROUP   = FORCE_NODES
 EL_GROUP   = FORCE_ELEM
 GROUP_OPER = SUM
END_

Internally, SIMULIA Tosca Structure generates one DRESP consisting of the sum of the internal forces of the nodes 65 and 66 for the elements 33, 34, 37 and 38.

If one then applies the DRESP in a constraint yielding:


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

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


$F_{65} + F_{66} \leq F *$

Alternative Definition of Constraints Function

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


GROUP_DEF
 ID_NAME = FORCE_ELEM_1
 TYPE    = ELEM
 FORMAT  = LIST
 LIST_BEGIN
 33, 34
END_

DRESP
 ID_NAME  = DRESP_FORCE_1
 DEF_TYPE = SYSTEM
 TYPE     = INTERNAL_FORCE_Y
 NODE = 65 
 EL_GROUP = FORCE_ELEM_1
 LC_SET   = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

GROUP_DEF
 ID_NAME = FORCE_ELEM_2
 TYPE    = ELEM
 FORMAT  = LIST
 LIST_BEGIN
 37, 38
END_

DRESP
 ID_NAME    = DRESP_FORCE_2
 DEF_TYPE   = SYSTEM
 TYPE       = INTERNAL_FORCE_Y
 NODE       = 66
 EL_GROUP   = FORCE_ELEM_2
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

And then add the two design response in two constraints:


CONSTRAINT
 ID_NAME   = CONSTRAINT_1
 DRESP     = DRESP_FORCE_1
 MAGNITUDE = ABS
 LE_VALUE  = <value>
END_

CONSTRAINT
 ID_NAME   = CONSTRAINT_2
 DRESP     = DRESP_FORCE_2
 MAGNITUDE = ABS
 LE_VALUE  = <value>
END_

SIMULIA Tosca Structure then generates two internal force constraints like the following:


$F_{65} \leq F^{}$ $F_{66} \leq F^{}$

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.