Optimize the Plastic Plate Model

The actual model shows the main parts of a sizing optimization task: Definition of design variables, constraints, and objective function.

  1. Define the Design Area.
  2. Define the Objective Function.
  3. Define the stress constraint.
  4. Define clustering elements.
  5. Set the Optimization Task.

  1. Define the Design Area (DV_SIZING): 
    DV_SIZING
 ID_NAME  = Opt_Plate_DESIGN_AREA_
 EL_GROUP = ALL_ELEMENTS
END_
  2. To define the Objective Function, do the following:
    1. Define a Design Response (DRESP) with the volume of the model: 
      DRESP
 ID_NAME    = Vol
 LIST       = NO_LIST
 DEF_TYPE   = SYSTEM
 TYPE       = VOLUME
 EL_GROUP   = ALL_ELEMENTS
 GROUP_OPER = SUM
END_
    2. Reference the Design Response in the Objective Function (OBJ_FUNC) and set the TARGET to MIN: 
      OBJ_FUNC
 ID_NAME = Min_Vol
 DRESP   = Vol
 TARGET  = MIN
END_
  3. To define the stress constraint, do the following:
    1. Define a Design Response (DRESP) that contains the absolute von Mises stresses appearing in the model: 
      DRESP
 ID_NAME    = mises_stress
 LIST       = NO_LIST
 DEF_TYPE   = SYSTEM
 TYPE       = SIG_SENS_MISES
 EL_GROUP   = ALL_ELEMENTS
 GROUP_OPER = MAX
 LC_SET     = ALL, 1, ALL
END_
    2. Reference the Design Response in a constraint (CONSTRAINT) and restrict it to 425 MPa: 
      CONSTRAINT
 ID_NAME   = Max_stress
 DRESP     = mises_stress
 MAGNITUDE = ABS
 LE_VALUE  = 425
END_
  4. Set up the optimization
    1. Define an element group (Cluster1, Cluster2,... (predefined in the example model)) for each of the clustering areas and assign them to a clustering design variable constraint as follows: 
      DVCON_SIZING
 ID_NAME    = CLUSTERING
 EL_GROUP   = Cluster1
 EL_GROUP   = Cluster2
 EL_GROUP   = Cluster3
 EL_GROUP   = Cluster4
 EL_GROUP   = Cluster5
 EL_GROUP   = Cluster6
 EL_GROUP   = Cluster7
 EL_GROUP   = Cluster8
 EL_GROUP   = Cluster9
 EL_GROUP   = Cluster10
 EL_GROUP   = Cluster11
 EL_GROUP   = Cluster12
 EL_GROUP   = Cluster13
 EL_GROUP   = Cluster14
 EL_GROUP   = Cluster15
 EL_GROUP   = Cluster16
 EL_GROUP   = Cluster17
 EL_GROUP   = Cluster18
 EL_GROUP   = Cluster19
 EL_GROUP   = Cluster20
 EL_GROUP   = Cluster21
 EL_GROUP   = Cluster22
 EL_GROUP   = Cluster23
 EL_GROUP   = Cluster24
 CHECK_TYPE = CLUSTER
END_
    2. Define a DVCON_SIZING to increase the upper and lower bounds of the element thicknesses: 
      DVCON_SIZING
 ID_NAME     = THICK_BOUNDS
 EL_GROUP    = ALL_ELEMENTS
 CHECK_TYPE  = THICKNESS_BOUNDS
 MAGNITUDE   = ABS
 LOWER_BOUND = 0.5
 UPPER_BOUND = 2
END_
    3. Reference the Design Variables, Objective Function, and constraints in the OPTIMIZE command: 
      OPTIMIZE
 ID_NAME    = Opt_Plate
 DV         = Opt_Plate_DESIGN_AREA_
 OBJ_FUNC   = Min_Vol
 CONSTRAINT = Max_stress
 DVCON      = CLUSTERING
 DVCON      = THICK_BOUNDS
 STRATEGY   = SIZING_SENSITIVITY
END_
    4. Define specific settings for optimization in OPT_PARAM command: 
      OPT_PARAM
 ID_NAME                  = Plastic_Plate_OPT_PARAM_
 OPTIMIZE                 = Plastic_Plate
 AUTO_FROZEN              = LOAD
 THICKNESS_UPDATE         = CONSERVATIVE
 THICKNESS_MOVE           = 0.25
 STOP_CRITERION_LEVEL     = BOTH
 STOP_CRITERION_OBJ       = 0.001
 STOP_CRITERION_THICKNESS = 0.005
 STOP_CRITERION_ITER      = 4
END_
      Here it is important to mention that optimization with nonlinearities should run with THICKNESS_UPDATE = CONSERVATIVE to improve convergence.
  5. The optimized results including nonlinear kinematics (NLGEOM=ON):
    1. Optimum with elastic material:



      Optimum when ignoring nonlinear effects limits the optimizer from removing the material if one of the element reaches the stress constraint value.

    2. Optimum with elastic-plastic material:



      Optimum when considering nonlinear effects contains more regions with yield stress, allowing the optimizer to remove more material compared to the elastic case.