Deflection-constrained topology optimization of ribbed reinforced-concrete slabs: a verification-driven density-to-design framework

Density-based topology optimization can identify efficient rib layouts for reinforced-concrete floor systems, but the resulting density fields are rarely ready for conventional detailing, structural verification, or carbon benchmarking. This paper presents a verification-driven Optimize–Extract–Verify workflow for ribbed reinforced-concrete slabs at a prescribed overall floor-system depth. The method combines density-based topology optimization with in-loop elastic deflection control, manufacturability controls, deterministic density-to-rib extraction, and topology-preserving rib-width sizing to recover the deflection target after discretization. The in-loop objective is concrete mass, while reinforcement quantities, Ultimate Limit State (ULS) compliance, and A1–A3 embodied CO2e are evaluated downstream after geometry extraction through an explicit verification-driven feedback rule. The extracted layouts are re-analysed as explicit rib-and-topping models, checked for ULS and long-term Serviceability Limit State (SLS) requirements, detailed for reinforcement, and benchmarked for embodied CO2e, restricted to modules A1–A3. Five cases are studied, including irregular support conditions and a transfer-slab stress test. For the four floor-slab cases, translation from the manufacturable density optimum to the final detailed geometry requires less than 3% additional concrete; relative to deflection-matched solid slabs, these designs reduce concrete by 37.4–42.7% and A1–A3 embodied CO2e by 33.1–38.5%; relative to a deflection-matched waffle-slab baseline, where one is defined, they reduce A1–A3 embodied CO2e by 20.9–23.6%. In the transfer-slab stress test, the verification branch triggers a strength-driven topping-depth update before reaching a 43.4% concrete and 31.9% A1–A3 reduction. Representative shear, local punching/load-introduction, crack-width, and first-mode vibration checks are included for governing configurations. The framework provides a repeatable, verification-ready route from continuum topology optimization to explicit ribbed reinforced-concrete slab candidates with quantified structural and product-stage carbon performance.