دانلود رایگان مقاله مقیاس طول حداقل در بهینه سازی توپولوژی با محدودیت هندسی

Abstract

A density-based topology optimization approach is proposed to design structures with strict minimum length scale. The idea is based on using a filtering-threshold topology optimization scheme and computationally cheap geometric constraints. The constraints are defined over the underlying structural geometry represented by the filtered and physical fields. Satisfying the constraints leads to a design that possesses user-specified minimum length scale. Conventional topology optimization problems can be augmented with the proposed constraints to achieve minimum length scale on the final design. No additional finite element analysis is required for the constrained optimization. Several benchmark examples are presented to show the effectiveness of this approach.

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.