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

This article presents a novel methodology for the simultaneous optimization of both structural topology and printing path in 3D concrete printing (3DCP), addressing a critical gap between digital design and physical manufacturability. Unlike conventional sequential approaches, our framework is grounded in discrete frame structures, which inherently reflect the filament-based nature of 3DCP, thereby enhancing geometric and mechanical fidelity. The proposed formulation strategically leverages the inherent anisotropy of printed concrete by aligning the printing direction along the longitudinal axis of each frame member to maximize strength and material efficiency. Key manufacturing constraints are integrated directly into the optimization process: member widths are restricted to integer multiples of the nozzle size, and the printing path is enforced as a globally continuous, non-intersecting, and non-overlapping Eulerian circuit through a mixed-integer linear programming model. The efficacy of this simultaneous optimization approach is demonstrated through a series of benchmark problems, which confirm that the resulting designs not only satisfy strict structural displacement and stress constraints with minimal material usage but are also readily manufacturable via direct “one-stroke” printing. This work establishes a foundational integration of structural performance and manufacturability, paving the way for more efficient and reliable 3DCP applications.