Link and Coupling Conditions Overview

Shape optimization involves determining the displacement of each design node to homogenize the stress on the surface based on the optimization criteria. The displacement of the neighboring nodes is not coupled; thus, each of the design nodes can move independent from the other design nodes. For example, during optimization free-form surfaces might develop from flat surfaces. By coupling the design nodes the optimization can maintain the regularity of planes. To take functional and manufacturing restrictions in shape optimization into account , certain link conditions can be set with the command LINK_SHAPE.

This page discusses:

See Also
In Other Guides
LINK_SHAPE
  • In Tosca Structure.gui, select Command > LINK_SHAPE.

Each link condition has a name (ID_NAME parameter). A criterion for determining the main node (MAIN parameter) is defined as well as a rule for the displacement of the client nodes (CLIENT parameter).

A typical LINK_SHAPE command appears as follows:


LINK_SHAPE
  ID_NAME = name_of_link_shape
  MAIN    = ...
  CLIENT  = ...
  ...
END_

Depending on the selected CLIENT parameter, other parameters are also required. In some circumstances, a coordinate system (CS parameter) or tolerances (TOL parameter) must be specified. These parameters of a LINK_SHAPE command might appear as follows:


LINK_SHAPE
  ...
  CS  = name_of_coord_system
  TOL = <tol_1>, <tol_2>, <tol_3>
END_

In the following subsections, the MAIN and CLIENT parameters are described in detail. The CS and TOL parameters are also described when applicable.

Link conditions basically only define a coupling rule without referencing a specific node group. The coupling condition is assigned to a node group after activation with CHECK_LINK in the DVCON_SHAPE command.

  • In Tosca Structure.gui, the link condition is assigned in the menu of the DVCON_SHAPE command.

Important:

  • The definition of coupling conditions can require a great deal of time and effort. To be able to estimate the best possible potential of an optimization, one optimization should be performed with as few restrictions as possible and only a few coupling conditions at the beginning of a project.
  • Coupling conditions restrict the range of solutions for the system and reduce the optimization potential.

Determining the Main Node (MAIN)

The MAIN parameter is used in each definition of a link condition to specify how to determine the main node. This node prescribes the displacement of the nodes affected by the link condition. It can be set explicitly by the user:


MAIN = NODE, node_nr

This causes the main displacement to be determined from the same node during the entire optimization.

In addition, the main node might be determined from a main node group. This allows the user to define a components edge to be the main edge for optimization. The algorithm determines the main node automatically from the main node group. In this case, the main node group must contain exactly one node of each link group.


MAIN = NDGR, <nodegroup>

Another way is to have the system automatically determine the main node according to two different criteria:


MAIN = MAX

or


MAIN = MIN

In this case, the main node is redetermined in every cycle. When the main node is automatically determined, the critical factor is identifying which node displacement (determined by the stress) for the coupling group is relevant. Principally, there exist four different cases of how the largest and smallest node displacements relate to the reference value within the node group:

  • Case 1: The stress everywhere is greater than the reference value; a positive displacement is determined for all design nodes of the coupling group. All design nodes grow out of the component.
  • Case 2: The stress everywhere is less than the reference value; for all design nodes of the coupling group a negative displacement is determined. All design nodes shrink inwards.
  • Case 3: There are nodes with greater and less stress than the reference value and the absolute shrinkage is greater than the absolute growth (abs(max_neg) > abs(max_pos)).
  • Case 4: There are nodes with greater and less stress than the reference value and the absolute shrinkage is less than the absolute growth (abs(max_neg) < abs(max_pos)).

Case 1

Case 2

Case 3

Case 4

ALL_GROWTH

ALL_SHRINK

MORE_SHRINK

MORE_GROWTH








lab1 =

Selected Main Displacement Value

MAX

max_growth

min_shrink

max_growth

max_growth

MIN

min_growth

max_shrink

max_shrink

max_shrink

The two criteria MAX and MIN, respectively, select different main nodes corresponding to the selected displacement values:

  • MAX: The MAX-Criterion is the conservative option. Here, the maximum growth (as in the cases 1, 3, 4) or the smallest shrinkage (as in case 2) is always used to select the main node. This is the standard criterion for shape optimization.
  • MIN: The MIN criterion moves the component surface inward as far as possible. This criterion must be used when linking conditions are required while optimizing contact surfaces.
Note:

  • CHECK_LINK in the DVCON_SHAPE command assigns the link condition to a node group. For MAIN=NODE, node_nr, the explicitly declared node must not necessarily be contained in the node group. For MAIN=MAX or MAIN= MIN , the main node is always determined from the nodes of the node group.
  • Older parameters CRIT_1 and CRIT_2 correspond to MAX and MIN respectively. With Tosca Structure 2023, these older definitions are still supported.

Displacement of the Client Nodes (CLIENT)

The CLIENT parameter is used in each definition of a link condition to set a rule for determining the displacement of the client nodes based on the displacement of the main node. The client nodes are moved relative to the main node. The following rules can be selected:

The individual rules for determining the client displacements are described in detail in the linked chapters.

Not all link conditions are applicable for both, the controller and the sensitivity-based shape optimization approach. The table below shows which types are usable with which approach.

CLIENT / Applicable for SHAPE_CONTROLLER SHAPE_SENSITIVITY
PLANE_SYM OK -
SURF_PLANE_SYM OK OK
SURF_CYCLIC_SYM OK OK
SURF_CYCLIC_PLANE_SYM OK OK
POINT_SYM OK -
ROTATIONAL_SYM OK -
VECTOR OK -
DIRECTION OK -
LENGTH OK -
DISP_CS OK -
SURF_STAMP OK OK
SURF_TURN OK OK
SURF_DRILL OK -
SURF_DEMOLD OK OK
FREE_FORM OK -

Example: Link Condition with Fixed Main Node

All nodes of the previously defined node group node_rigid should have the same displacement with respect to the global Cartesian coordinate system as the design node with the number 46. Node 46 need not be a part of the node group node_rigid. The link condition should have the name link_rigid. The link condition is then used in the restriction with the name dvcon_rigid.


LINK_SHAPE
 ID_NAME = link_rigid
 MAIN    = NODE, 46
 CLIENT  = VECTOR
 CS      = CS_0
END_

DVCON_SHAPE
 ID_NAME    = dvcon_rigid
 ND_GROUP   = node_rigid
 CHECK_LINK = link_rigid
END_

Example: Coupling Condition with Automatic Determination of the Main Node

All nodes of the node group ndgr_left should have the same displacement as the node from ndgr_left that has the greatest outward displacement. In the same way, all nodes of the node group ndgr_right should have the same displacement as the node from ndgr_right that has the greatest outward displacement. This requires a link condition and two restrictions.


LINK_SHAPE
 ID_NAME = link_left_or_right
 MAIN    = MAX
 CLIENT  = VECTOR
 CS      = CS_0
END_

DVCON_SHAPE
 ID_NAME    = dvcon_left
 ND_GROUP   = ndgr_left
 CHECK_LINK = link_left_or_right
END_

DVCON_SHAPE
 ID_NAME    = dvcon_right
 ND_GROUP   = ndgr_right
 CHECK_LINK = link_left_or_right
END_

In each design cycle the system identifies which nodes in each of the node groups, ndgr_left and ndgr_right, has the greatest positive displacement (in the growth direction). Usually, these are the nodes with the largest stress difference between the effective value and the targeted value. These displacements are then applied to all nodes of the node groups ndgr_left and ndgr_right, respectively. The following command can be used instead of the two individual DVCON_SHAPE commands:


DVCON_AUTO_SHAPE
 ID_NAME         = dvcon_*
 ND_GROUP_FAMILY = ndgr_*
 CHECK_LINK      = link_left_or_right
END_

The naming left and right is determined automatically from the complete name of the node groups and added to the root name of the automatically generated DVCON_SHAPE entries. However, this requires that only these two node groups begin with the name ndgr_ otherwise other node groups are taken into consideration.