Closing the gap towards super-long suspension bridges using computational morphogenesis

The paper addresses the challenge that conventional orthotropic closed steel box-girders for suspension bridges, largely unchanged since the 1950s, face fatigue issues and impose weight limits that constrain the feasibility of future super-long spans (>3 km). As self-weight dominates (>90% of total loads) for such bridges and the construction sector contributes substantially to global CO2 emissions, the study seeks new, material-efficient girder concepts. The research question is whether computational morphogenesis (topology optimization with unrestricted design freedom) can reveal a viable, manufacturable girder concept that significantly reduces weight while maintaining performance, thereby enabling longer spans and reduced environmental impact.

Prior work has focused mainly on mitigating fatigue problems in orthotropic steel decks and welded joints, with limited efforts on fundamentally new girder concepts or explicit weight/CO2 reduction. A gradient-based parametric optimization of conventional girders showed limited improvement potential without changing the geometric concept. Topology optimization has seen widespread use in automotive and aerospace but relatively few applications in civil engineering due to conservative practice, complexity, low volume fractions, and multi-scale challenges. Recent advances demonstrated giga-voxel computational morphogenesis (e.g., aircraft wing with 1.1 billion voxels), suggesting feasibility for large civil structures.

The study applies a giga-scale topology optimization (computational morphogenesis) to a three-section (75 m × 30.1 m × 4.75 m) finite element model of a suspension bridge girder based on the 2682 m Osman Gazi Bridge (1550 m main span). Due to periodicity and symmetries, a quarter of the center 25 m section (12.5 m × 15.05 m × 4.75 m) is the active design domain, mapped to adjacent sections. The outer aerodynamic profile is retained; walkways are neglected. The road surface top layer and hanger anchorage regions are fixed as solid; material is otherwise free to distribute. Boundary conditions include a fixed end and global section forces (N, My, Mz, Vy, Vz, and Mx) applied at the opposite end via a stiff end surface. Local loads include uniformly distributed deck load and hanger forces. From an initial set of 14 critical load cases (traffic, wind, temperature, seismic per Eurocode/UK NA), five representative static load cases (1, 5, 10, 13, 14) were selected for optimization. Material is linear-elastic steel (E=210 GPa, ν=0.3). Objective: maximize stiffness of the center section for a given material volume by minimizing the weighted sum of center-section compliances across the load cases. The domain is discretized into 2.1 billion 8-node hexahedral elements (mesh 4384 × 1760 × 272, max element size 17 mm). Allowable volume fraction is V=3.0% to reveal details at this resolution. A density-based SIMP interpolation with penalization and image-convolution density filtering (filter radius 1.5× element size) is used. The optimization employs a fully parallel MMA algorithm with a continuation on the penalization parameter from 1 to 3 in 0.25 steps over 400 design cycles. Because the objective targets only the center section, an adjoint formulation is used for sensitivities. Computation was performed on the Joliot-Curie supercomputer (~16,000 CPU cores). Each design cycle solves ten large linear systems (five load cases plus five adjoints) with ~6.3 billion DOF; average 35 s per solve; total runtime ~85 h. Interpretation: The optimized volumetric result (with double-curved diaphragm-like panels and longitudinal supports) was qualitatively distilled into a manufacturable shell-model design using solid plate diaphragms: six diaphragms per 25 m section (vs five conventional), with four curved toward hangers, plus longitudinal panels (“hanger steel plates”) connecting hangers to diaphragms. Conventional and interpreted designs were modeled with Abaqus shell elements (identical material volumes); performance measured by center-section weighted compliance over the five representative and all 14 load cases. Parametric optimization: Using iSight with the Abaqus shell model of the interpreted design, plate thicknesses (lower bound 4 mm) were optimized via sequential quadratic programming to minimize center-section compliance without increasing material volume. Estimation of knock-on effects: Based on Osman Gazi Bridge quantities, reductions in girder weight were propagated through main cables, towers, anchor blocks, and tower foundations with conservative assumptions to compute total steel and concrete savings and associated CO2 emission reductions using ICE v3.0 emission factors.

• The giga-scale topology optimization revealed a radically different internal girder structure with double-curved diaphragm-like panels and longitudinal supports that provide more direct load paths from deck to hangers, reducing zig-zag load transfer seen in conventional designs.
• A practical interpreted design (six diaphragms per section with four curved toward hangers plus longitudinal panels) achieved a 12.7% improvement in stiffness at equal material, which corresponds to an estimated 12.7% weight reduction relative to the conventional design for equivalent stiffness, across five representative load cases; similar improvement was confirmed over all 14 load cases.
• Subsequent plate-thickness parametric optimization of the interpreted design achieved a total weight saving of 28.4% compared to the conventional design, exceeding the 13.8% improvement previously reported for refined parametric optimization of the conventional layout.
• Stress assessment showed small changes in maximum von Mises stresses, indicating fatigue demand is not worse than for the conventional design.
• For a bridge comparable to Osman Gazi, a 28.4% girder weight reduction corresponds to about 8,200 tonnes of steel saved in the girder, leading via knock-on effects to approximately 13,000 tonnes total steel and 19,000 m³ concrete savings in the whole bridge.
• The material savings translate to an estimated 43,000 tonnes CO2 emissions reduction (using ICE v3.0 factors), equivalent to roughly 358 million km of car driving (~9000 times around the globe).

The findings demonstrate that introducing design freedom via computational morphogenesis can uncover non-intuitive, yet manufacturable changes to the girder topology—specifically, adding a sixth diaphragm and curving most diaphragms toward hangers with longitudinal panels—that substantially improve structural efficiency. The interpreted, simplified design offers significant weight reductions while maintaining comparable peak stress levels, suggesting fatigue performance is not degraded. Although the optimized topology itself is too complex for direct construction, the distilled concept achieves large gains with moderate changes compatible with current fabrication methods. The authors note the need for comprehensive follow-up on dynamics (wind-induced vibrations), fatigue, buckling, and detailed load cases, especially given the reduced self-weight. Constructability aspects of curved diaphragms and uneven skin plate spans require detailing (e.g., redistributing trough and plate material), but modern digital production and repetition between sections make the changes feasible. The approach potentially accelerates progress toward super-long spans by alleviating self-weight constraints and indicates broader applicability to other civil structures with significant environmental benefits.

Applying giga-scale computational morphogenesis to a modern suspension bridge girder reveals a new diaphragm layout that, when interpreted into a practical plate-based design and sized parametrically, reduces girder weight by 28.4% relative to a state-of-practice orthotropic box. This yields substantial knock-on reductions in cables, towers, and foundations and an estimated 43,000 tonnes CO2 emissions reduction for a reference bridge. The work underscores the value of early-stage free-form topology exploration to guide simple, constructible design adaptations in civil engineering. Future research should integrate full dynamic, fatigue, buckling, and aero-structural assessments, refine manufacturability and cost analysis of curved diaphragms, and explore application to other large-scale civil structures to further enhance weight and emission savings.

• The topology and parametric optimizations did not include explicit fatigue, buckling, aeroelastic effects, or full dynamic behavior; only static, linear-elastic responses were considered.
• Five representative load cases were used for optimization, reduced from an initial set of 14; although checked post hoc, some scenarios may remain unaddressed.
• The mesh resolution (max element size ~17 mm) is coarser than the smallest plate thickness (6 mm), chosen to reveal trends rather than final details; results are qualitative for topology.
• The SIMP-based problem is non-convex and susceptible to local minima; a continuation strategy was used, but global optimality is not guaranteed.
• The optimized volumetric topology is too complex for direct construction and required subjective interpretation into a manufacturable design.
• The parametric shell model simplifies the complex stress state near hangers, potentially biasing local thickness increases.
• Aerodynamic optimization was not included; walkways were neglected in the design domain.
• Volume fraction was set at 3.0% (vs ~1.3% in the reference bridge) to ensure detail at the chosen resolution; the study aims for qualitative concept identification rather than a finalized optimal structure.
• Constructability and cost implications of curved diaphragms and uneven skin plate spans were not quantified and require further study.