Search Results (17)

In this study, the seismic vulnerability of the Ferdowsi School building in Tabriz is investigated. The research began with comprehensive fieldwork, during which exploratory surveys and in-depth technical inspections of all structural components were performed. Experimental testing of prismatic masonry specimens was carried out to evaluate their mechanical characteristics, and the resulting properties were then incorporated as input parameters into the numerical model. The seismic vulnerability assessment was then carried out using nonlinear static (pushover) analysis, applying a lateral load pattern proportional to the first vibration mode of the structure. For numerical simulation, the building was modeled in the ABAQUS finite element software using the macro-modeling technique. The results of the nonlinear static analysis indicated that the building does not possess sufficient load-bearing capacity at the target displacement. Damage was primarily concentrated in the form of cracking in the masonry walls as well as in the dome-shaped sections of the roof, requiring the implementation of a seismic retrofitting scheme to enhance the structure’s seismic performance. To rehabilitate the structure, horizontal and vertical reinforced concrete beams were introduced as confining elements for the masonry walls and subsequently applied in the strengthening project. Furthermore, due to the presence of a domed roof at the first-floor level, it was strengthened using FRP composite materials to enhance tensile capacity and ductility. At the second-floor level, where the roof structure is made of timber elements, a steel cable system was employed to improve its strength and diaphragm action. As for the third-floor timber truss roof, the connections were upgraded and reinforced to provide reliable force transmission and to maintain the overall integrity of the structural system. Following the implementation of the retrofitting measures, the structural model was re-analyzed using nonlinear static analysis. The results demonstrated that the proposed strengthening scheme successfully increased the structural capacity up to the target displacement level and satisfied the intended performance requirements. In the final section of the paper, the implementation details of the retrofitting interventions, as well as the practical experiences gained during the implementation process, are presented and discussed. Full article

To overcome the limitations of conventional steel support systems in large-span concrete dome construction, this study proposes a novel prestressed modular aluminum alloy formwork system based on a radial–circumferential spatial truss configuration. A refined finite element model was established to simulate the staged construction process under the most unfavorable load combination (1.3G + 1.5Q), and the influences of prestress levels and concrete pouring sequences were systematically investigated. Results indicate that external prestressing significantly enhances structural stiffness and deformation control. Increasing the prestress level from 0.3fptk to 0.5fptk reduces the maximum vertical displacement by approximately 18%, while a prestress of 0.7fptk achieves a total reduction of about 31%. Radial support displacement decreases by up to 48%, demonstrating improved global stability. Considering both deformation control and material utilization efficiency, 0.5fptk is recommended as the optimal prestress level. Comparative analysis of construction schemes shows that the layered pouring method reduces maximum vertical displacement by approximately 15% compared with ring casting. Buckling analyses further confirm adequate stability reserve beyond code-required safety coefficients. These findings verify the feasibility and deformation control effectiveness of the proposed prestressed aluminum alloy dome formwork system for large-span construction applications. Full article

The objective of the article is the assessment of the sensitivity of the equilibrium path of structures susceptible to loss of stability due to node snap-through. Increasingly, architectural designs feature organic forms and structures with complex geometry, which makes it possible to create very large, column-free spaces. These developments lead to the design of structures with ever smaller rise while simultaneously increasing their span. Due to the parameters of structures of this type, it is justified to analyze such systems with consideration of nonlinear effects. The Newton–Raphson algorithm was used to determine the limit points on the equilibrium path, employing both load control and displacement control. To accurately determine the position of the limit point on the equilibrium path, the step length was defined adaptively. Four dome space trusses were analyzed. Individual load sets were differentiated in terms of load location. The developed algorithm was implemented in a proprietary finite element method program created in the Matlab R2025b software. The analysis showed that, despite significant differences in the critical force (P_ult), the global response of the structure at the moment of snap-through remains similar. The displacement of the apex node at the moment of snap-through remains similar across most of the proposed load sets. In the case of low-rise structures, a significant increase in the sensitivity of the load location to the critical load value and in the displacement of the apex node at the moment of snap-through was observed. Full article

The objective of the article is the quantitative assessment of the reliability index for a specific type of structure—trusses with node snap-through. The trends in contemporary geometric and structural design of architectural forms of rod domes are evolving towards increasing diameters and reducing rise. Therefore, it is justified to assess the safety of this type of structure. The Hasofer–Lind reliability index (β) was adopted as the reliability measure. In the reliability analysis, the FORM method was applied using the implicit form of the random variables function (combining external reliability software with the noncommercial finite-element method program) and using explicit forms of limit-state functions (neural networks were used and own original finite-element method module). In addition, the classical Monte Carlo method and the hybrid Monte Carlo method (combining with a neural network) were used. For dome loads in the range of 73–100%, the reliability index β can be estimated with reasonable accuracy (error) compared to standard methods. The obtained approximation functions allow for easy determination of the percentage of the maximum load that ensures safe operation. In addition, they allow us to indicate at what load level the reliability index reaches the standard level (at least β = 1.5 for the serviceability limit state). Full article

Incorporating frequency constraints into the optimum design of large-scale truss dome structures is crucial for maintaining seismic resilience, as the natural frequencies must remain within specified ranges. In this work, seven metaheuristic algorithms—including three variants of the Fitness–Distance–Balance-based Adaptive Guided Differential Evolution (FDB-AGDE), the Cheetah Optimizer (CO), the Bonobo Optimizer (BO), the Flood Algorithm (FLA), and the Lung Performance Optimization (LPO) are applied to solve high-dimensional truss sizing problems under strict frequency limitations. Their convergence characteristics and solution quality are systematically compared across multiple dome configurations. Besides traditional measures of computational efficiency and final weight minimization, a suite of statistical analyses is conducted: the Wilcoxon rank-sum test to assess pairwise performance significance, the Friedman test to establish overall rank ordering, and Cohen’s test to quantify effect sizes. The results reveal that LPO, BO, CO, and the first variant of FDB-AGDE consistently produce lighter feasible designs with lower variability, whereas FLA and other variants of FDB-AGDE exhibit heavier structures or higher dispersion. The findings underscore the value of robust, well-tuned metaheuristics and rigorous statistical evaluation in structural optimization, offering clear guidance for seismic-focused designers seeking both lightweight solutions and reliable performance across repeated runs. Full article

This study proposes an Index-Based Neural Network (IBNN) framework for the static analysis of truss structures, employing a Lagrangian dual optimization technique grounded in the force method. A truss is a discrete structural system composed of linear members connected to nodes. Despite their geometric simplicity, analysis of large-scale truss systems requires significant computational resources. The proposed model simplifies the input structure and enhances the scalability of the model using member and node indices as inputs instead of spatial coordinates. The IBNN framework approximates member forces and nodal displacements using separate neural networks and incorporates structural equations derived from the force method as mechanics-informed constraints within the loss function. Training was conducted using the Augmented Lagrangian Method (ALM), which improves the convergence stability and learning efficiency through a combination of penalty terms and Lagrange multipliers. The efficiency and accuracy of the framework were numerically validated using various examples, including spatial trusses, square grid-type space frames, lattice domes, and domes exhibiting radial flow characteristics. Multi-index mapping and domain decomposition techniques contribute to enhanced analysis performance, yielding superior prediction accuracy and numerical stability compared to conventional methods. Furthermore, by reflecting the structured and discrete nature of structural problems, the proposed framework demonstrates high potential for integration with next-generation neural network models such as Quantum Neural Networks (QNNs). Full article

This paper presents an innovative procedure for the stability assessment of masonry domes, aiming at simplifying the modelling and the computational stages of structural analysis. It exploits a macroscopic approach to discretise masonry, specifically using elastic bodies linked by nonlinear interfaces. The latter are made by axial and, when needed, tangential trusses—in turn characterised by an elastic perfectly plastic/brittle behaviour—which constitute the joints connecting homogenised elastic macroblocks. The objective is—by employing low-cost commercial Finite Element software—to predict the behaviour of a masonry curved structure up to failure, maintaining the computational complexity low and the approach accessible to a common user. The process enables not only the quantification of damage at failure but also the tracking of its evolution within the structure, by examining axial forces found in the trusses at each load step. The method allows the modelling of the response of any kind of masonry structure under imposed loads or displacements. Its efficacy is proven on a paradigmatic dome (Global Vipassana Pagoda, Mumbai, India) by comparing the results with limit analysis precedent studies. Finally, the major reliability of a 3D approach is demonstrated. Full article

This paper presents a new method to model the nonlinear behavior of double-curvature masonry structures, possibly reinforced by composite materials, by means of conventional elasto-plastic analyses. The method is meant to be used in professional design, especially for assessment and retrofitting purposes, based on the exploitation of the simplest nonlinear finite elements available in commercial software, namely, trusses with elasto-fragile and elasto-ductile behavior (Cutoff Bars, according for instance to the definition provided by Strand7 R3.1.3a). Numerical static nonlinear analyses are carried out by considering elastic hexahedral elements for bricks and by lumping nonlinearities on joints. These are assumed, in turn, to be elastic–brittle and elastic–plastic by using 1D elements, namely, Point Contacts, under the No-Tension Material hypothesis, and Cutoff Bars, respectively, assigning a small tensile resistance to the material. The reinforcement, realized with FRP hooping strips, is successfully modeled in a similar fashion, i.e., by applying perfectly bonded elastic–plastic Cutoff Bars at the extrados of the dome, where debonding is accounted for in a conventional way, limiting the tensile strength according to Italian Standards’ indications. The procedure is validated against benchmark models with the same geometry, using experimental data and more refined structural model results for comparison. After an in-depth analysis of the obtained results, in terms of capacity curves, the robustness and accuracy of the proposed approach are assessed. Full article

This study introduces a Radial Basis Function-Genetic Algorithm-Back Propagation-Importance Sampling (RBF-GA-BP-IS) algorithm for the multi-scale reliability analysis of Fiber-Reinforced Polymer (FRP) composite structures. The proposed method integrates the computationally powerful RBF neural network with GA, BP neural network and IS to efficiently calculate inner and outer optimization problems for reliability analysis with hybrid random and interval uncertainties. The investigation profoundly delves into incorporating both random and interval parameters in the reliability appraisal of FRP constructs, ensuring fluctuating parameters within designated boundaries are meticulously accounted for, thus augmenting analytic exactness. In application, the algorithm was subjected to diverse structural evaluations, including a seven-bar planar truss, an architectural space dome truss, and an intricate nonlinear truss bridge. Results demonstrate the algorithm’s exceptional performance in terms of model invocation counts and accurate failure probability estimation. Specifically, within the seven-bar planar truss evaluation, the algorithm exhibited a deviation of 0.08% from the established failure probability benchmark. Full article

A simple numerical approach to predict the efficacy of FRP hooping in historical masonry domes is presented. The dome is modelled with 8-noded elastic hexahedron elements connected by 1D trusses/springs on meridians and on parallels, where all the non-linearity takes place. The aim is to simulate the nonlinear behaviour of domes through every FE commercial software equipped only with non-linear 1D elements, namely point contacts and cutoff bars. The constitutive behaviour of the trusses is assumed to be either perfectly brittle or perfectly ductile. A possible orthotropic behaviour and the no-tension material case can be reproduced. External retrofitting is simulated using trusses with an elastic perfectly ductile behaviour, assuming a perfect bond between the substrate and the reinforcement and imposing an ultimate strength for the trusses, which takes into account the possible debonding/delamination from the substrate in a conventional way. The Italian code CNR DT200 and the existing specialized literature are used as references. The models are benchmarked on a masonry dome reinforced with three hooping FRP strips and experimentally tested at the University Architecture Institute of Venice IUAV, Italy. The procedure is validated through extensive comparisons with available experimental data and numerical results obtained in the literature with a variety of different models. Through the extensive comparisons that were made and discussed, the robustness and simplicity of the procedure are proven. Full article

The Cathedral of Florence is one of the largest churches in the world and is known for one of the most famous domes ever, which characterizes the skyline of the city. The dimensions of the building mean that the dimensions of the roof are equally large and so are the wooden structures that support it. The roof of the cathedral is organized on two levels: the roof of the large central nave and, at a lower level, those of the two lateral naves. The purpose of this paper is the identification of the wood species of which the structures are made. The sampling method of the 408 samples that have been identified is then described, the methods followed to reach a reliable identification and finally the results. The timbers most represented among the structural elements are those of silver fir, chestnut and elm. Other timbers are then found in the other components less directly linked to the main structural parts that make up the trusses. The paper then discusses the technological implications on the use of those woods within the wooden covering structures of the cathedral and the main sources of timber that the builders had available, in particular the Casentino forests that the Municipality of Florence had donated to the structure that managed the construction of the cathedral (Opera di Santa Maria del Fiore—OPA). OPA still exists today and is responsible for the maintenance of the cathedral and other annexed buildings. Full article

In this study, the newly developed Marine Predators Algorithm (MPA) is formulated to minimize the weight of truss structures. MPA is a swarm-based metaheuristic algorithm inspired by the efficient foraging strategies of marine predators in oceanic environments. In order to assess the robustness of the proposed method, three normal-sized structural benchmarks (10-bar, 60-bar, and 120-bar spatial dome) and three large-scale structures (272-bar, 942-bar, and 4666-bar truss tower) were selected from the literature. Results point to the inherent strength of MPA against all state-of-the-art metaheuristic optimizers implemented so far. Moreover, for the first time in the field, a quantitative evaluation and an answer to the age-old question of the proper convergence behavior (exploration vs. exploitation balance) in the context of structural optimization is conducted. Therefore, a novel dimension-wise diversity index is adopted as a methodology to investigate each of the two schemes. It was concluded that the balance that produced the best results was about 90% exploitation and 10% exploration (on average for the entire computational process). Full article

With changes in the city environment and advances in engineering technologies, there is an increasing demand for the construction of super-large span city domes that can cover a large area to create a small internal environment within a specific region. However, the structural design must overcome various challenges in order to break the current structural span limitations. Moreover, there is little research on structures achieving such large spans. The seismic performance of the selected Kiewitt-type, Geodesic-type, and Three-dimensional grid-type mega-latticed structures is further investigated upon previous studies of the model selection, static and stability analysis results of the 800 m span mega-latticed structures. Finite element models were established with ANSYS to analyze the modal properties and earthquake response of the structures. The study evaluated the impact of earthquake directionality on the structural response as well as the response pattern of the structure under frequent and rare earthquake actions. It was found that the overall integrity of the structures is good, with strong coupling effects in three directions. The multi-dimensional seismic input method should be applied to solve the structural response. Combining the plastic development of the structure under rare earthquakes, the top and the circumferential trusses of the third and fourth rings are relatively weak parts of the structures. According to this study, given the known static analysis results, the maximum displacement and maximum stress of the structures under frequent and rare earthquake actions can be estimated. Furthermore, the study highlights that Three-dimensional grid-type mega-latticed structures should be prioritized designing structures with spans of 800 m, providing helpful guidance for the practical application of this type of structure. Full article

The aim of the paper is to find the appropriate self-stress state of the tensegrity structures. The first approach provides exact solutions but is suitable for simple structures. In the second approach proposed in this research, it is assumed that the forces of the self-stressed state are a set of randomly selected values, which are then optimized by a genetic algorithm. This procedure is intended for more elaborate structures, for which the spectral analysis identifies many self-stress states that need to be superimposed. Two approaches are used, i.e., the spectral analysis of the compatibility matrix and the genetic algorithm. The solution procedures are presented on the example of a simple two-dimensional truss. Next, three different tensegrity domes are considered, i.e., Geiger, Levy and Kiewitt. The significant difference between these domes lies in the cable system. The obtained results are compared with those documented in the literature. It follows from the considerations that the self-stressed states found in the literature are not always accurate (forces do not balance themselves). The presented results confirm the effectiveness of the genetic algorithm for finding self-balanced forces of the existing structures. The method is relatively simple and provides sufficiently accurate results. Full article

Since the literature lacks an effective analysis method of collapse mechanisms and optimisation design theory for progressive collapse resistance of cable dome structure, a structural performance-based optimisation approach was proposed to improve the progressive collapse resistance for cable dome structures in this study. First, the dynamic response and collapse model of a cable dome structure were analysed after its members were removed using Ansys LS-DYNA and the full dynamic equivalent load-based instantaneous unloading method. Second, the importance coefficients of the members were calculated to determine the contribution of each member to the progressive collapse resistance of the structure. Finally, a stepwise optimisation solution was proposed by integrating a global optimisation model, which uses the mean of the importance coefficients of all members as the optimisation index, with a local optimisation model, which minimises the maximum member importance coefficient. The results indicated that different members exhibited varying levels of importance in the progressive collapse resistance of the structure, with the inner and outer hoop cables demonstrating the highest levels of importance, followed by the inner upper string of the tension hoop. The other members had low levels of importance. Compared with the cable dome structure based on the Geiger topology, the cable dome structure based on the Levy topology was more resistant to progressive collapse; such resistance decreased as the number of cable-truss frames decreased. Additionally, the local optimisation approach based on the genetic algorithm reduced the maximum member importance coefficient (i.e., that of the outer hoop cable) by 60.26%. Full article