Controller- Versus Sensitivity-Based Topology Optimization

In SIMULIA Tosca Structure, two principle algorithms exist for solving topology optimization problems: The controller-based optimality criteria approach and the general, sensitivity-based approach.

Related Topics
Semi-Analytical Sensitivity Calculation

Both algorithms have the special application area and both are useful for different types of optimization tasks. The main difference is the method for solving the problem, and also the type of design responses which can be used to formulate the optimization problem. Depending on the optimization task defined by the user, SIMULIA Tosca Structure decides which algorithm is the best to solve the problem.

Some of the main differences between sensitivity-based optimization algorithm and controller-based algorithm are the following:

Property Sensitivity-based optimization Controller-based optimization
Elements with intermediate densities (gray elements)
  • Has some elements in the final design containing intermediate densities (gray elements).
  • Leads to the elements being either void (density very close to zero) or solid (density equal to one) in the final design.
Number of optimization iterations
  • The number of iterations is unknown before the optimization starts, but normally the number of optimization iterations is around 30 to 45.
  • Uses 15 optimization iterations by default.
Analysis types
  • Supports the responses of linear static (non-conservative forces) and linear eigenfrequency (not allowed to be prestressed) finite element analysis. Constant temperature loading is allowed for MSC Nastran® and Abaqus.
  • Supports geometrical nonlinearities (NLGEOM) and contact for Abaqus .
  • Some non-linear materials are also supported.
  • Prescribed displacements are allowed in the CAE model for static topology optimization. However, prescribed displacements are not allowed for modal and frequency response analysis. Generally, laminate materials (layup and layer orientation) cannot be designed in topology optimization. However, laminate materials as design elements (only the thickness of the element is used as design variable) are allowed for MSC Nastran® and Abaqus.
  • Supports non-linear static analysis such as contact simulation, even when the contact zones are on the surfaces of the design space.
Objective and constraint types
  • Can have one objective function and several constraints where the constraints are all inequality constraints.
  • The objective and the constraints can be based upon the stiffness, displacements, reaction forces, internal forces, eigenfrequencies and material volume (material weight).
  • Has the compliance as objective and the material volume as an equality constraint.

Objective Functions and Constraints for Controller-Based Algorithm

In topology optimization, a variety of combinations of objective functions and constraints can be selected. Standard formulation using the efficient controller-based optimality criteria algorithm is:

Objective function

Constraint

Maximize stiffness

Volume constraint

All other types of objective functions and constraints can be applied using the sensitivity-based algorithm.

Objective Functions and Constraints for Sensitivity-Based Algorithm

The following list shows which terms and response types are valid for the objective function and the constraints using the sensitivity-based algorithm:

  • Center of gravity
  • Displacement (absolute or relative)
  • von Mises Stress
  • Moment of inertia
  • Rotations
  • Reaction forces (absolute or relative)
  • Reaction moments (absolute or relative)
  • Internal forces (absolute or relative)
  • Internal moments (absolute or relative)
  • Eigenfrequencies
  • Material Volume
  • Total stiffness

Several constraints and several terms for the objective function can be specified.