Summary of Guidelines

This section summarizes the guidelines for optimization of structures with nonlinear behavior.

Check List

The following table contains tips that can be helpful to set up a more robust topology optimization problem.

Check case: Check before optimization: Check after optimization:
Is the objective to minimize volume/mass?
  • Check the displacement boundary conditions with respect to:
    • 3rd direction is fixed in cases of 2D models,
    • unwanted deformations,
    • out of plane buckling.
  • If there is a displacement constraint in the model:
    • impose the displacement constraint at the load application,
    • choose the regions around the displacement constraint to be frozen.
  • Check if:
    • the results are converged,
    • constraints are satisfied,
    • the resulting structure does not represent mechanism design.
  • If any of the above is not satisfied, impose additional constraints on the structural stiffness to stabilize the optimization.
  • Alternatively, set DENSITY_LOWER = 0.01, which can help to get better result, but it can also aid the creation of mechanism design, which is not a favored result in most cases.
Is a volume/mass constraint used in the model?
  • The recommendation is to set a feasible volume constraint suitable for the FE mesh.
  • Set the DENSITY_INITIAL = 0.5 for a very low volume constraint (for example relative volume constraint equal to 0.05) to begin the optimization with a feasible design.
  • In the case of mass constraint, verify if the material density is specified.
  • Check if:
    • the results are converged,
    • optimized structure contains no unconnected regions.
  • If any of the above is not satisfied, refine the finite element mesh of the structure.
  • If the same issue retains, maybe there is no feasible solution for the given constraint, hence try increasing the value of the volume constraint.
Is there geometric or material nonlinearity in the model? The following are considered to be stable settings and set in:
  • Tosca Structure parameter file: 
    
DENSITY_MOVE    = 0.1
DENSITY_UPDATE  = CONSERVATIVE
DENSITY_INITIAL = 1.0
  • Abaqus input file: 
    
*STEP, NLGEOM: YES, INC=10000, extrapolation=NO
*STATIC
0.1, 1.0, 1e-14, 1.0
  • Check if the results are converged.
  • If no, look for warnings in the *msg and *dat files:
    • ELEMENTS ARE DISTORTING EXCESSIVELY
    • SYSTEM HAS 'n' NEGATIVE EIGEN VALUES
  • If the above warnings are found, activate the soft delete procedure: 
    
SOFT_DELETE_METHOD = AGGRESSIVE, 0.1
SOFT_DELETE        = <element group>, 0.0
  • Alternatively, setting DENSITY_LOWER=0.01 can help to improve convergence. This method is only preferred if soft delete could not solve the issue.
  • If the convergence issue still retains, impose additional constraints on the displacement or stiffness of the structure to stabilize the optimization procedure.
Are there manufacturing restrictions in the model? Check if the origin of the co system and the axis corresponding to the restrictions are set correctly in the parameter file. In the case of nonlinear problems, if the optimization fails because of solver convergence issues then the recommendation is to remove the manufacturing constraints and solve the convergence issues. After obtaining the converged result, impose the restrictions one after the other.