Topology Optimization of Components With Embedded Objects Using Discrete Object Projection

Abstract

Although traditional free-form topology optimization typically addresses monolithic structures, a recently developed method termed Discrete Object Projection extended topology optimization to design problem of optimizing the layout (and shape) of discrete, non-overlapping objects within a predefined domain. This domain may be the unit cell of a composite, where (for example) stiff inclusions are embedded in a compliant matrix material, or component of pre-defined geometry. The current work extends this recently developed methodology to three-phase design problems consisting of void phase and two material phases, one of which is a discrete object, essentially enabling the simultaneous optimization of component topology and object layout within that topology. This is achieved by combining the Heaviside Projection Method (HPM) with multi-phase Rational Approximation of Material Properties (RAMP) method. The proposed algorithm is demonstrated on benchmark problems in structural design where the elastic stiffness of structures is to be enhanced by optimizing the layout of embedded reinforcement.