Defining a Displacement Constraint

Aim of this optimization task is to obtain the structure with maximal stiffness subject to the constraint on the difference of the displacements of two nodes.

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

This task shows you how to:

Define the Displacement Constraint in Tosca ANSA® environment

  1. In CONSTRAINT_ITEM dialog, create a COMBINED_ITEM design response with VAR_OPER = SUB_ABS.

  2. To create the individual design response for each of the two displacements, press "?" key in the VARIABLE_1 field.

  3. Press New in the appeared dialog, then choose TOSCA_DRESP.

  4. In the DRESP dialog, choose TARGET = NODE and TYPE = DISP_Z (in case of the displacement in z-direction).

  5. Enter the node ID in the NID field and the load case(s) in the LC_SET field.

  6. Double click on the name of the design response in TOSCA HELP window so that this design response is entered in VARIABLE_1 field of the COMBINED_ITEM design response.

  7. Repeat the steps for the second displacement entered in VARIABLE_2 field.



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.

Define a Displacement Constraint in Tosca Extension for ANSYS® Workbench

  • Differences between displacements (OPER) are not available yet.

Common Steps for Tosca ANSA® environment and 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_