An optimization algorithm for automatic structural design

Abstract

We propose a new algorithm to design lightweight and stiff structures exhibiting free-form features, with the aim of minimizing the compliance under a volume inequality constraint. The procedure is based on the coupling of geometric shape optimization with topology optimization. We start from a full-mass body corresponding to a given material occupying entirely the initial design domain. The first phase of geometric shape optimization acts as an out-of-the-box paradigm. It allows one to modify the initial design domain by acting only on its boundary, keeping the same volume and topology. With respect to the full-mass body, this phase reduces the compliance to a large extent. The successive step of topology optimization does actually change the topology of the structure, e.g., by introducing holes, reduces the volume according to the volume constraint, but does not affect the boundary of the structure, which is fixed by the previous phase. Overall, the combined approach allows us to design a new structure, that is lighter and stiffer with respect to the full-mass body. Additionally, the employment of a structure-tailored computational mesh, via an anisotropic mesh adaptation procedure during topology optimization, yields an intrinsically smooth final layout characterized by free-form features. An extensive numerical assessment corroborates both qualitatively and quantitatively the performances of the proposed optimization algorithm.