Group Operations for Displacements | ||
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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.
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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 upon 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:
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).
Based upon 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:
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:
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 to combine the displacements using GROUP_OPER = SUM which results in a much 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 upon 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 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:
GROUP_OPER = SUM
Based upon 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 one then applies 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:
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:
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.