Concurrent Topology and Orientation Optimisation of 3D-Printed Concrete Under Drucker–Prager Strength Constraints: Numerical and Experimental Validation

Abstract

The layer-wise deposition process of three-dimensional concrete printing (3DPC) induces anisotropic behaviour, while cementitious materials exhibit pronounced tension–compression strength asymmetry. This study develops a concurrent topology and printing-direction optimisation framework for plain 3DPC under Drucker–Prager (D–P) strength constraints. Within a solid isotropic material with penalisation (SIMP) formulation, material density and printing orientation are updated simultaneously using the Method of Moving Asymptotes (MMA). A double-angle vector-field mapping regularises the π-periodic orientation field, while element-wise D–P failure indices are aggregated into a differentiable global constraint through P-norm aggregation with adaptive scale correction. Numerical studies on a four-corner pinned plate, a T-shaped bracket and a perforated deep beam show that the strength constraint reshapes load paths, suppresses local strength violations and increases ultimate load capacity by approximately 200%, 176% and 42%, respectively, relative to compliance-based optimisation. The optimised deep-beam layouts are reconstructed, converted into continuous printing paths, fabricated and tested under three-point bending. Experimentally, the mean ultimate load increases from 8.13 to 9.54 kN, corresponding to an increase of 17.39%, while the mean displacement at peak load and pre-peak energy are 20.58% and 41.16% higher, respectively. The experimental and finite element comparisons show closely similar ultimate-load increases of 17.39% and 17.43%, respectively. The framework provides a strength-aware route from concurrent numerical optimisation to the fabrication and structural assessment of plain 3DPC components.