Free-form topology optimization for additive layer manufacturing

Data di pubblicazione






Data di priorità



International PCT patent application; Italian and US patent application


Politecnico di Milano, Thales Alenia Space - Italia


Department of Mathematics


Simona Perotto, Stefano Micheletti, Luca Soli


The invention consists of a mathematical algorithm, implemented in a computer-aided design (CAD) environment, for the topology optimization of structures. Typical applications are 3D printing and Additive Layer Manufacturing (ALM), which may greatly benefit from such an algorithm. Actually, these technologies allows one to overcome the limits of standard manufacturing techniques, based on material subtraction, designing objects and structures which could not even be figured out so far. The present algorithm helps the designer in realizing free-form structures, thanks to a sophisticated finite element procedure, suitably devised to yield intrinsically smooth structures. In particular, with a view to the aerospace applications of interest, a light but sufficiently rigid free-form structure is desirable. To this end, the standard SIMP (Solid Isotropic Material with Penalization) technique for topology optimization, based on the finite element approximation of the linear elasticity equation, is improved by means of a suitable choice of the computational grid. The resulting procedure allows, on the one hand, to reduce the computational costs, on the other hand, it produces intrinsically smooth structures that lead to a reduction of additional post-processing. The added value of this algorithm is to guide the choice of the computational grid with a sophisticated mathematical tool, i.e., an a posteriori estimator for the discretization error. This choice makes the global optimization procedure even more efficient. We name such an algorithm as SIMPATY, which stands for SIMP with Anisotropic adaptiviTY. The SIMPATY algorithm has been successfully validated on both 2D and 3D configurations.

Campo di applicazione

Design of mechanical structures with lightweight properties combined with good resistance to stationary loads. This procedure may be of interest to different sectors of industrial design, as well as space, such as biomedical, automotive and aerospace.


Reduced computational costs; Very smooth structures; Limited post-processing.

Stadio di sviluppo

Algorithm implemented using FreeFem++, validated on 2D and 3D test cases.