Differences between bead optimization algorithms

The user may choose between two bead optimization algorithms in SIMULIA Tosca Structure.bead. The algorithms have different ways to find the solution and their differences will be discussed in this chapter.

In the attempt to avoid confusion the following chapters will be marked with either "BEAD_CONTROLLER" or "BEAD_SENSITIVITY" if it is only valid for the one algorithm. If the chapter is not marked the content applies to both algorithms.

The following figures show the same optimization task: maximizing first eigenvalue.



Time solved by the sensitivity-based optimization algorithm:



Time solved by the controller-based algorithm:



Some of the main differences between the two algorithms are the following:

  Controller-based algorithm Sensitivity-based algorithm
Bead pattern
  • creates nice bead structures because of its bead-filter.
  • A bead pattern generator is not implemented in the sensitivity-based solution, therefore the results do not show a distinct bead pattern.
Number of optimization iterations
  • always uses 3 optimization iterations.
  • usually needs 20 or more iterations to converge.
Analysis types
  • supports all analysis types which produces a stress tensor as output.

    Note: It is recommended to only use it for static analyses.
  • supports the responses of: linear static, linear eigenfrequency and frequency response analyses.

    Note: the better results are considered by the sensitivity-based optimization for dynamic problems.
Objective and constraint types
  • uses the compliance as objective and the BEAD_HEIGHT as an equality constraint.
  • can have one objective function and several constraints where the constraints are all inequality constraints.
  • The objective and the constraints can be based upon compliance, displacements, eigenfrequencies or frequency dependent displacements.
Supported element types
  • supports all plate and shell elements.
BEAD_HEIGHT  
  • all DRESP which can be used in the object function can also be used in the constraint definitions. The maximal nodal displacement is not considered as a design response but instead as a design variable constraint.

    Note: The DRESP of type BEAD_HEIGHT is not allowed with the sensitivity-based algorithm.

  • Use the following example to get a similar optimization displacement in sensitivity-based algorithm in a benchmark example against the controller algorithm: 
    DVCON_BEAD
  ID_NAME = name_of_dvcon_bead
  ND_GROUP = design_nodes
  CHECK_GROW = <BEAD_HEIGHT>
  CHECK_SHRINK = 0.0
END_

    where the <BEAD_HEIGHT> is equal to the bead height defined by the controller input deck.

    Note: The sensitivity-based algorithm can move the nodes in positive and in negative direction, thus the optimization parameter SCALE has no effect.