Efficient spline design via feature-mapping for continuous fiber-reinforced structures

Abstract

We present a feature-mapping topology optimization approach, in which curved features are parametrized as piecewise linear splines smoothly rounded by arcs. The motivation for our contribution to the tool set of feature-mapping methods is the optimization of structures manufactured by variable angle continuous fiber-reinforced filaments. For this reason, the feature’s geometry should be able to represent long, curved fiber objects satisfying manufacturing constraints, such as minimum turning radius. The proposed model has been chosen with special care for rigorous continuous differentiability, as well as an efficient analytical evaluation of the signed distance field to the spline. The geometrical description and sensitivity analysis of the spline model are developed fully analytically and then mapped to a discretized pseudo-density field for finite element analysis. For the fiber-reinforced material formulation, we also present a new combine step for individual features, in which the best possible angle for the combined features is searched. The model and results are presented in a two-dimensional setting.