Defining a Displacement Constraint

You can define a Displacement Constraint to obtain the structure with maximal stiffness subject to the constraint on the difference of the displacements of two nodes.

This task shows you how to:

Before you begin: Five design responses are needed in this example: The displacements at two different nodes, their difference, the volume and the strain energy.

Define a Displacement Constraint in Tosca Structure.gui

  1. Define a design response (DRESP) for the displacement of the first node.

    For a list of existing types, see Overview of Displacement and Rotation.

    Note: The total absolute value cannot be used as design response.

  2. Define a design response for the displacement of the second node, similar to the first one.
  3. To define a design response with the difference of the nodal displacement from the two nodes, choose Command > DRESP.
  4. In the DRESP dialog, select DefType = Operator and Operator = SUB_ABS.

Common Steps for Tosca Structure.gui

  1. Define a second constraint for the relative material volume.

    Only a few elements will be removed in the short arm in order to obtain equal displacements of the two arms. In most cases, the intention is to have a structure with a given weight and the maximum stiffness.

  2. Define the objective function as minimization of the compliance of the whole model. This is defined as the sum of the strain energy of all elements (ALL_ELEMENTS element group).

SIMULIA Tosca Structure Parameter File

The commands in the parameter file for this problem look like follows: 


DRESP
 ID_NAME        = DISP_TIP_RIGHT
 TYPE           = DISP_Z
 DEF_TYPE       = SYSTEM
 LC_SET         = STATIC,1,
 GROUP_OPER     = Max
 ND_GROUP       = TIP_RIGHT
END_

DRESP
 ID_NAME        = DISP_TIP_LEFT
 TYPE           = DISP_Z
 DEF_TYPE       = SYSTEM
 LC_SET         = STATIC,1,
 GROUP_OPER     = Max
 ND_GROUP       = TIP_LEFT
END_

DRESP
 ID_NAME        = DISP_DIFFERENCE
 DEF_TYPE       = OPER
 VAR_OPER       = SUB_ABS
 VAR_A          = DISP_TIP_RIGHT
 VAR_B          = DISP_TIP_LEFT
END_

DRESP
 ID_NAME        = DRESP_SUM_ENERGY_LC1
 TYPE           = STRAIN_ENERGY
 DEF_TYPE       = SYSTEM
 LC_SET         = STATIC,1
 GROUP_OPER     = SUM
 EL_GROUP       = ALL_ELEMENTS
END_

OBJ_FUNC
 ID_NAME        = MY_OBJ_FUNC
 TARGET         = MIN
 DRESP          = DRESP_SUM_ENERGY_LC1
END_

CONSTRAINT
 ID_NAME        = DISP_DIFF_CONSTRAINT
 MAGNITUDE      = ABS
 DRESP          = DISP_DIFFERENCE
 LE_VALUE       = 0.1
END_

DRESP
 ID_NAME        = DRESP_VOL_TOPO
 TYPE           = VOLUME
 DEF_TYPE       = SYSTEM
 GROUP_OPER     = SUM
 EL_GROUP       = ALL_ELEMENTS
END_

CONSTRAINT
 ID_NAME        = VOL_CONSTRAINT
 MAGNITUDE      = REL
 DRESP          = DRESP_VOL_TOPO
 LE_VALUE       = 0.3
END_