Big public aquariums are multipurpose structures that provide not only leisure or touristic services but are also very useful for marine biology research, species conservation, and educational campaigns [1–4]. In addition to their educational and ecological missions, modern aquarium facilities are increasingly required to satisfy strict operational, maintenance, and research-related criteria associated with large zoological infrastructures [5].

Moreover, the circulation systems and seawater treatment processes in aquaria are further constrained by engineering issues, especially in larger aquatic environments [6]. Over the past three decades, there have been significant advancements in structural and architectural planning for aquaria, from basic reinforced-concrete rectangular tanks to large-span structures with advanced geometry [2], [4].

In addition to the above changes, there have been significant advances in the materials used for aquarium construction. Traditional glass panels are increasingly being replaced by acrylic PMMA panels owing to their high optical quality, reduced weight, increased shock resistance, and durability under hydrostatic loads [7], [8]. Modern research indicates that large-span acrylic structural members exhibit favorable behavior under hydrostatic loads and do not exhibit creep; therefore, they are highly applicable for modern aquarium construction [8]. Large-span translucent acrylic systems have become increasingly popular for aquatic architecture due to technological advances [8]. Although this technology is now available, the engineering challenges of designing a large aquarium are significant, particularly when nontraditional geometries are considered.

Out of various geometric configurations possible, there is a definite structural benefit associated with the use of spheres, since the distribution of hydrostatic pressure in such geometric configurations tends to be more uniform, hence lowering stress concentration. Spherical aquariums can thus save on material requirements and increase rigidity compared to rectangular or cylindrical counterparts. Although several public aquariums use complex shapes, including curved panes, no study has been conducted on a completely spherical structure with a cubic tunnel inside.

To support such geometrically complex systems, spatial structures are considered among the most efficient structural solutions. Space-frame systems are three-dimensional truss structures capable of distributing loads effectively in multiple directions while providing high stiffness-to-weight ratios, excellent seismic resistance, and significant architectural flexibility [9]. Geodesic domes are better suited than any other spatial structure for designing spherical storage tanks because they accurately depict the spherical form, distribute forces uniformly, and are efficient in material use [10], [11]. Optimizations of geodesic domes and space trusses have been carried out in recent years, ranging from topological to structural optimizations [10-13].

In addition, generative design approaches and variable-frequency dome configurations have demonstrated significant potential for improving structural efficiency in large-span spatial systems [10]. The structural assessment of such structures subjected to hydrostatic load requires an advanced modeling method. This issue cannot be solved using classical methods because the problem statement contains multiple nonlinearities. For this reason, the Finite Element Method (FEM) is widely used today to analyze the behavior of acrylic panels and steel space frames under realistic loading conditions [8–11]. Finite Element modeling enables accurate prediction of stress and strain distributions within the structure. Nonetheless, FEM computations are rather costly, particularly when many design variables need to be analyzed.

To address these shortcomings, surrogate modeling using Artificial Neural Networks (ANNs) has been widely used in structural engineering optimization problems [14]. Finite element-based ANN models can accurately capture nonlinear structural responses while significantly reducing computational costs. Recently, it has been shown that deep learning neural network models can generate accurate predictions for nonlinear structural systems and could be used in the optimization process [14].

Once an appropriate surrogate model is created, optimization algorithms can be applied to optimize the structure design. One of several popular optimization methods used in structural engineering due to its ability to handle both discrete and continuous variables simultaneously, avoid getting stuck in local optima, and solve multi-objective optimization problems is the Genetic Algorithm (GA) [11-13]. Successful implementation of hybrid optimization strategies involving FEM, ANN, and GA was observed during the optimization of trusses, geodesic domes, and cable-supported spatial structures [13–16]. For instance, Lu and Ye [11] examined the optimization of space dome design with respect to buckling using GAs. At the same time, Lu and Ye [12] proposed a new guided GA approach to optimize space domes with discrete variables. On the one hand, Khodadadi et al. [13] presented a thorough review of metaheuristic optimization methods for large-scale space trusses. On the other hand, Yücel et al. [15] proposed an innovative hybrid approach in optimizing the structure's weight under displacement and stress constraints.

While important progress has been made in the field of structural optimization and surrogate-assisted structural optimization [11-16], the problem of a combined analysis of a spherical public aquarium with a cubic tunnel using the FEM, ANNs, and genetic optimization has been neglected to date. The existing literature mostly focuses on either conventional dome shapes, instability control problems, or light-weight structural systems [10-13]. At the same time, little is known about the mechanical properties of the full-spherical public aquarium with hydrostatic pressure loads and construction materials such as acrylic glass panes, steel spatial members, and reinforced concrete supports. Another area that requires thorough investigation is the creation of reliable ANN surrogate models to predict nonlinear correlations between geometric design variables and structural response parameters, such as maximum stresses, displacements, and structural weight [14].

In addition, although GAs have been successfully employed for the optimization of truss and dome structures [11-16], their application to the simultaneous minimization of structural weight and stress in large-scale aquarium systems under hydrostatic loading conditions has not been reported. In addition, validation of optimized configurations through thorough analysis of full finite element simulations has received little attention in the existing literature.

Hence, the current research study aims to propose an integrated computing methodology for the design and optimization of a large-scale spherical public aquarium with a cubic tunnel within the spherical structure. The initial step would be to formulate a geodesic space-frame configuration, coupled with acrylic view panels and reinforced concrete support structures, to develop the finite element model. Hydrostatic and loading conditions would then be imposed on the structure. The geometry of the space frame and the addition of acrylic viewing panels and reinforced concrete support systems are first carried out to form an FEM model, followed by the application of loadings related to the hydrostatic environment and the structure's operation. The numerical results from extensive parametric finite element analyses are then used to train an ANN to approximate the relationship between the principal design variables and structural performance indicators. Furthermore, the trained surrogate model will be linked to a multi-objective GA to determine the optimal design parameters that achieve both structural safety and reduced material use. Lastly, the optimal design for the structure is validated through finite-element modeling analysis.

The spherical aquarium proposed herein is a massive spatial structure whose loads will primarily be determined by hydrostatic pressure and stability requirements. Because of the high stiffness-to-weight ratio and optimal force transmission associated with spatial systems, geodesic dome-like configurations are adopted as the primary structural forms. Spatial structures, especially geodesic domes, have been recognized for decades for their good stiffness-to-weight ratio, optimal force-transmission characteristics, and ability to handle multi-load directions within spheres [9–11]. New research proves that they also perform efficiently in multi-objective structural systems optimization [11-13].

First, the structure's geometry is created in CATIA and then imported into ANSYS Workbench for structural analysis. The complete layout of the structure is shown in Fig. 1, and its finite element model is illustrated in

Every story is 3 meters high. Steel circumferential members are oriented with the floors.

Geometric view of the designed spatial steel framework.

The discretization of the sphere in terms of geometry was performed by splitting the surface into 10 equal angular sectors (36°). The inner observation passage of about 21 m long is split into five equal sectors to limit local deformations and enhance the stiffness continuity. The first level consists of a reinforced concrete base (8m x 8m) that serves as the main load-transfer component, accommodating hydraulic and mechanical systems. Acrylic panels enclose only the uppermost six levels of the sphere. The model configuration and assumptions are shown in Fig. 2.

To accurately consider the interaction between the structural elements, a hybrid finite element modeling approach is applied. Steel members are considered as beams (line bodies), while acrylic panels are modeled as shell elements. The reinforced concrete base is modeled using solid elements. This multi-material Finite Element Analysis (FEA) provides an adequate representation of the actual stiffness distribution and load-transfer processes under hydrostatic loading [7], [8]. The resulting finite element mesh comprises about 220,000 finite elements (Fig. 3).

The most important optimization task here is to minimize the structure's total mass while maximizing the safety factor. Since the weight of the steel space frame remains constant throughout the optimization process, the total mass of the structure can be expressed as a function of the thickness of the acrylic panels. Therefore, three geometric parameters are selected as optimization variables:

I. Thickness of the acrylic panels in the lowest level of the aquarium II. Thickness of the acrylic panels in the higher levels of the aquarium III. Thickness of the acrylic panels of the visitor tunnel The system's response during optimization includes the structure's total mass and its minimum safety factor. To optimize the current structural configuration, a multi-objective GA will be coupled with FE simulations of the model. However, as there is no direct relationship between the input geometric parameters and the structure's performance, an ANN model must be created.

I. Carrying out extensive finite element simulations for various combinations of acrylic thickness.

II. Creating a dataset for structural responses such as stress, displacement, mass, and safety factor; III. Developing an ANN approximation of the nonlinear mapping of the input and output variables; and IV. Integrating the trained ANN with a multi-objective GA to identify the best design parameter values.

The optimal structural solutions obtained from the GA are illustrated in the Pareto front shown in Fig. 6. Selected Pareto-optimal points are summarized in Table 3.

The optimization results indicate that increasing the thickness of the lower acrylic panels has a relatively limited effect on total structural weight because the number of these panels is comparatively small. However, this parameter significantly improves the safety factor in critical regions subjected to high hydrostatic pressure. Conversely, the upper acrylic panels account for a large portion of the aquarium's total surface area. Therefore, reducing their thickness considerably decreases the total structural weight. The tunnel panels exhibit an intermediate influence on both structural mass and safety factor.

The optimization process further demonstrates that the hydrostatic pressure acting on the tunnel panels remains close to the static pressure distribution, indicating that slightly lower safety factors may still satisfy the structural requirements without compromising reliability. The final optimized dimensions are 31.98 cm of acrylic thickness for the bottom panels, 21.54 cm for the top panels, and 30.46 cm for the tunnel panels. The respective safety factors are approximately 8.2, 6.81, and 7.18. Recalculating the optimized design against the full FEM design indicates that the total optimized structural weight is 9569 tons.

The final optimized configuration corresponds to acrylic thicknesses of 31.98 cm for the lower panels, 21.54 cm for the upper panels, and 30.46 cm for the tunnel panels. The corresponding safety factors are approximately 8.2, 6.81, and 7.18, respectively. Reanalysis of the optimized structure using the full FEM model confirms that the total optimized structural weight is approximately 9569 tons and that all structural safety requirements are satisfied.

In this research, an innovative computational methodology was formulated and applied for the design optimization of the structural system of a public aquarium sphere with an internal observation tunnel. Using FEM, an analytical model of a geodesic steel frame with acrylic panels and reinforced concrete supports was developed to study structural performance under hydrostatic pressure, the influence of visitor loads, and dynamic impact loads from marine animals. According to the simulation results, hydrostatic pressure was found to be the most critical loading condition affecting the structural performance.

To enhance the efficiency of the structural optimization process, an ANN model was built based on FEM simulation results. After training, the ANN model was employed together with a GA to optimize its structure, minimizing mass and maximizing the safety factor. The results of the optimization procedure showed that a hybrid computational approach involving FEM, ANN, and GA enables the determination of optimal acrylic panel thicknesses that satisfy all safety conditions.

The optimized design has safety factors above the required minimum, with a total structural mass of approximately 9569 tons. The results show that the proposed technique is an effective approach for designing and optimizing large-span aquariums and similar structural systems dominated by hydrostatic pressure.

The authors declare that they have no competing interests.

The data supporting the findings of this study are available within the article.

This research did not receive any external funding.