Direct optimization of continuous non-intersecting toolpaths for extrusion-based 3D printing

Abstract

We present a novel framework for the direct optimization of continuous, non-intersecting toolpaths in extrusion-based additive manufacturing. The toolpath parameterization serves both as an explicit representation of the geometry and as the optimization design variables, eliminating the need for intermediate design representations and post-processing for generating a manufacturable toolpath, thereby closing the gap between design and fabrication. The toolpath is represented by a continuous piecewise-linear centerline that is controlled by shape design variables. Finite element analysis for evaluating structural and thermal responses is achieved by a distance-based embedding technique within a fixed grid. Physical manufacturability is enforced throughout the optimization using differentiable geometric constraints that ensure minimum filament spacing, prevent self-intersections, control local toolpath angles, and preserve prescribed material-free regions. Inspired by potential applications in 3D printing of cementitious materials, the efficacy of the framework is demonstrated primarily by applications in cross-section layout design of masonry blocks and walls, considering structural and thermal performances. The numerical examples show that the proposed approach generates toolpath-based layouts that are straightforward to manufacture, while providing systematic control over structural stiffness and thermal insulation.