Enhancing the shape-optimization of submerged arches using Bézier curves

Submerged arches play a significant role in marine and hydraulic structures, due to their structural capacity to withstand environmental loads. Effective arch design, particularly in submerged environments, is crucial for achieving economy, durability and safety. Thus, submerged arches have been traditionally designed based on funicular equilibrium. Recognizing the convenience of a multiobjective optimization strategy, recent research has approached submerged arch design using conic-shape parameterization methods and metaheuristic algorithms. To simplify the mathematical formulation in polar coordinates of previous works, and addressing thus practical construction considerations, this article introduces a new shape optimization method, via CRO-SL evolutionary algorithm, based on Bézier curves. To this aim, a hybrid strategy is performed, parameterizing each arch candidate by a Bézier curve, and evaluating its structural response through a geometrically nonlinear finite element model of the submerged arch. Additionally, Bézier curves provide a compact and flexible set of algebraic curves defined through control points in Cartesian coordinates, enabling a comprehensive geometric exploration of the arch shapes domain and facilitating the implementation of the geometric design conditions for the submerged arch to be built. The effectiveness of Bézier curves is validated through a detailed comparative analysis. As result, the structural design obtained with previous parameterizations is improved for all the depth ranges. Moreover, in the case of shallow waters, where the second-order structural behaviour of the submerged arch represents a key issue, Bézier curves achieve a global improvement of the arch design (that is, not only regarding its mechanical design, but also in terms of its functionality). • The geometrical design of submerged arches in shallow and deep waters is tackled. • Bézier curves are presented as a more compact and practical alternative to conic curves. • The application of Bézier curves is also feasible in the context of a geometrically nonlinear finite element analysis. • Improvements in the geometric and mechanical design of shallow un- derwater installations are validated.