4. Conclusions
A topology optimization approach with geometric constraints is presented to design structures that possess strict minimum length scale. The constraints are formulated based on structural indicator functions, which are defined on the regularized filtered and physical fields in a three-field topology optimization scheme. They are computationally cheap and differentiable w.r.t. the design variable. The constrained optimization problem is solved using mathematical programming. No additional finite element analysis is required. In order to utilize this approach effectively, it is advised to provide a good initial guess for the constrained optimization. One pertinent way is by adding the constraints later into the standard topology optimization process after an initial topology has formed. It is found difficult to obtain efficient designs if the initial guess for the constrained optimization is far from an admissible feasible design. One limitation of the proposed method is that parameters c and ϵ must be chosen properly based on the level of numerical accuracy in representing the underlying structure. However, strategies based on numerical investigation are suggested to set those parameters. It is targeted as future work to formulate a scheme without parameter tuning.
