Allying topology and shape optimization through machine learning algorithms

Abstract

Structural optimization is part of the mechanical engineering field and, in most cases, tries to minimize the overall weight of a given design domain, subjected to functionality constraints given in terms of stresses or displacements. The most relevant techniques are topology and shape optimization. Topology optimization provides the optimal material distribution layout into a given, static, design domain. On the other hand, shape optimization provides the optimal combination of the parameters that define the required parametrization of the domain's boundary. Both techniques have strengths and weaknesses, thus a hybrid optimization approach that combines the former techniques will define a more general structural optimization framework that will take advantage of their synergistic combination. The difficulty arises when communicating both techniques for which, in this paper, we propose a machine learning-based methodology. • We proposed a methodology that allies topology and parametrized shape optimization algorithms, obtaining an hybrid optimization algorithm. • We studied the strengths and weaknesses of topology and shape optimization algorithms, which justified its combination to obtain a synergetic effect. • The use of manifold learning techniques, such as the Locally Linear Embedding (LLE), to extract the principal geometrical modes from a set of material distributions that topology optimization algorithm provides. • In order to properly use the LLE technique, the quasi-boolean material distribution provided by the topology optimization algorithm must be transformed into a richer level-set with the distance information. • The geometrical modes, extracted with the LLE algorithm, may be used to generate brand new geometries, as they define a parametric geometrical model. • The parametric space of geometrical modes may be considered by a shape optimization algorithm as its design space.