Topological optimization. Design for additive manufacturing

By definition, topological optimization enables us to optimize the material distribution of a part subject to various objectives, such as mass, mechanical, thermal, chemical or electromagnetic constraints.

This mathematical technique is already used in many CAD and finite element modeling software packages.

Topological optimization differs from historical methods of dimensional optimization (i.e. beam length or diameter, plate thickness), or shape optimization (connection radius, shape of an edge or opening), methods which generally concern a fairly limited number of parameters to be optimized ( $\le$ 10 - 100). Material optimization, on the other hand, is a generalization that allows the characteristics of materials to evolve freely at any point on the part, particularly with non-isotropic materials.

Topological optimization is mainly applied to the fields of solid mechanics, thermics and fluid mechanics, but also sometimes to chemistry, electromagnetism and piezoelectricity. The objectives are most often to lighten structures subjected to mechanical stress, but also to optimize fluidic, thermal and other mono or multiphysical performances [BM 7 940] .

In order to exploit this method, which is generally based on iterations of finite element (FE) calculations, it is first necessary to ensure that such a model is feasible and can be run dozens or hundreds of times.

It is also important to ensure that the boundary conditions of the problem are well known, and that the criteria for dimensioning the structure are explicitly formulated. Without this, the robustness of the result obtained, or even the convergence of the optimization, is generally highly compromised.

You then need to identify the CAD quality you are aiming for, as the results can sometimes be disappointing (e.g. roughly defined part contours, or areas that are difficult to interpret).

Finally, depending on the process in question (most often additive manufacturing [BM 7 017] ), the part's manufacturability must be taken into account, including problems of support or closed volumes, for example. Any post-processing, such as polishing (mechanical or chemical) or machining, must also be anticipated,...