Structural topology optimization with smoothly varying fiber orientations

In recent years, the field of additive manufacturing (AM), often referred to as 3D printing, has seen tremendous growth and radically changed the means by which we describe valid 3D models for production. In particular, it is now conceivable to produce composite structures consisting of smoothly varying oriented anisotropic constitutive materials. In the present work, we propose a sensitivity driven method for the generation of transverse isotropic fiber reinforced structures having smooth spatially varying orientations. Our approach builds upon finite element analysis (FEA) and density-based topology optimization (TO). The local material orientations are formulated as design variables in a stiffness maximization problem, and solved with a non-convex gradient-based optimization scheme. Length-scale control is achieved through the use of filters for regularization. We demonstrate the ability of the proposed approach to handle large-scale 3D problems with synchronous optimization of material densities and orientations yielding millions of design variables on multiple load case scenarios. The method is shown to be compatible with compliant mechanism optimization as well as local volume constraints. Finally, the approach is extended with an additional design variable dictating the ratio of anisotropy for each element, thereby delegating the choice of material type to the optimization scheme.