Simultaneous Topology and Path Optimization for 3D Concrete Printing Based on Discrete Frame Structures

Abstract A novel methodology is introduced for simultaneously optimizing both the structural topology and printing paths in 3D concrete printing (3DCP). Drawing inspiration from the inherent geometric characteristics of 3DCP, this approach anchors its optimization framework within discrete frame structures. Beyond conventional frame topology optimization, we introduced the concept of simultaneous path optimization, bridging the gap between optimal design conception and its seamless realization in manufacturing. Leveraging the mechanical anisotropy inherent to 3DCP, we strategically orient the printing directions such that each frame member is printed along its longitudinal axis, optimizing for strength and material efficiency. To ensure direct printability, we impose constraints whereby the width of each member must be an integer multiple of the nozzle size, and the printing path must traverse continuously, covering the entire design without any intersections or overlaps. An Eulerian circuit, rooted in graph theory, fulfills part of these requirements, with additional constraints introduced to rigorously eliminate intersections and overlaps. The comprehensive simultaneous optimization problem is then formulated as a Mixed-Integer Linear Program (MILP), which is readily solvable. The application of this methodology to various test problems has yielded successful outcomes, demonstrating the efficacy and practicality of our approach in achieving simultaneous optimization of both structural topology and printing paths in 3DCP.