FRep can be successfully combined with level-set methods for topology optimization. This is a mesh-free approach and it has several advantages. There are two pipelines of topology optimization algorithms shown below. The first one is for the FRep-based technique, and the second one is for the widely used SIMP topology optimization algorithm.

Figure 1 Pipelines of FRep-based optimization and SIMP

SIMP is an example of mesh-based algorithms. The result of the optimization that it provides is density distribution under space partitioning (mesh). SIMP can exploit cubic or tetrahedral meshing. It works quite well for many applications, but still, it returns just an approximation of a modelled solid body with a polygonal surface. Usually, designers use the geometry constructed by SIMP as the starting point for further modelling. That happens because such a geometry requires some changes before manufacturing. Smoothing is one of these changes. It is needed since the obtained polygonal surface can have undesired sharp features. Sometimes this revision of the optimized body becomes modelling from scratch.

The topology optimization approach based on FRep modelling allows designers to obtain bodies ready for manufacturing. Choosing different forms of FRep functions for shape approximation leads to different properties of the resulting geometry. In our research, we used a free-form FRep defining function. This kind of function defines bodies with the piecewise second-order surface. Such a surface is much smoother than a polygonal approximation.

The topology optimization approach based on FRep modelling allows designers to obtain bodies ready for manufacturing. Choosing different forms of FRep functions for shape approximation leads to different properties of the resulting geometry. In our research, we used a free-form FRep defining function. This kind of function defines bodies with the piecewise second-order surface. Such a surface is much smoother than a polygonal approximation.

Fifure 2 Results of the mesh-free FRep-based topology optimization