Review of Available Options and Possibilities

This section reviews useful options and possibilities regarding nonlinearities in topology optimization.

This page discusses:

General Information for Topology Optimization

  • Since the design variables for topology optimization are the elemental pseudo densities, the elemental stiffness is changes during the optimization process. This can lead to larger deformations and strains compared to the initial simulation. Therefore, the material laws need to be defined for all material states, especially plasticity laws. Continuous material laws such as Johnson-Cook are preferred for nonlinear optimizations since they are defined for all strain values.
  • As the structure softens during the optimization, the recommendation is to adapt applied loads in such a manner that they are reasonable for the final, softer structure with less material, for example 20% of the original material. Otherwise, too much plastic deformation occurs.
  • If possible, convert loading to prescribed displacements to improve the robustness of the optimization.

Tosca Structure Options

In Tosca Structure, all the following described options are set in the OPT_PARAM block of the *.par file.

Option: Description:
DENSITY_MOVE This option decides the maximum possible change of the pseudo density values within each optimization iteration. Smaller values of this parameter help to overcome convergence issues. But at the same time, the convergence rate can be slower when compared to the default settings. The default value is DENSITY_MOVE=0.25. In cases where it is observed that either the objective function or some of the constraints are oscillating, the recommendation is to set DENSITY_MOVE=0.1.
DENSITY_UPDATE This option affects the behavior of CSA (Algorithm based on Convex Separable Approximations). The two available schemes of density update are CONSERVATIVE and NORMAL. Conservative update method is considered to be more stable. The default is DENSITY_UPDATE=NORMAL. In cases where it is observed that either the objective function or some of the constraints are oscillating, the recommendation is DENSITY_UPDATE=CONSERVATIVE.
DENSITY_INITIAL Material properties of design elements are scaled (solid and void properties are interpolated) based on the pseudo density values. Different material interpolation schemes like SIMP and RAMP are available in Tosca Structure. The initial pseudo density values can be set by the DENSITY_INITIAL option. If one of the constraints is based on volume design response, then the initial density is set equal to the value of the volume constraint by default. In all other cases, the initial density value is set equal to 0.5. Note, to compare the DRESP value of Tosca Structure with the solver results set DENSITY_INITIAL = 1 and use the DRESP value from design cycle 0.
DENSITY_LOWER In topology optimization, the voids are not created by deleting the finite elements from the mesh, but are simulated scaling the stiffness of the design elements to a very low value. Zero elemental stiffness would lead to the loss of positive definiteness of the global structural stiffness matrix. The corresponding system of equations would not be solved. Hence, a minimum value of pseudo density is used within topology optimization. The default value is DENSITY_LOWER=0.001 but can be modified by the user.
SOFT_DELETE_METHOD In a topology optimization process, the structure consists of hard (filled) and soft (void) elements. The soft elements have a negligible influence on the stiffness of the resulting structure but they are still relevant for the solution of the system of equilibrium equations. The soft delete option activates a procedure that looks for elements that could be potentially distorted during the optimization procedure based on the user-defined criteria and deletes them from the finite element mesh. The deleted elements are reactivated if required, in case that the force flow changes during the optimization. Note, this procedure is useful to stabilize the optimization in the context of nonlinear structural analysis and helps to overcome solver instabilities. By default, it is not activated.
AUTO_FROZEN This option is used to keep elements with loaded nodes and boundary conditions from being optimized. There are four settings available: LOAD, SPC, BOTH, and OFF. LOAD and SPC constrain elements with loaded nodes or boundary conditions, respectively, from being optimized, while BOTH simultaneously freezes all elements with either load and boundary condition. The default setting is AUTO_FROZEN=LOAD.

Solver Settings: Abaqus

The Abaqus solver gives the possibility to define settings to improve the convergence for nonlinear models. See Guide for Nonlinear Models.