Topology of grids is a key aspect in the design of architectural structures: the beams’ connectivity is related to the structure’s geometry and influences its performance. This article proposes a new method for generating a space of quad mesh topologies controlled by continuous parameters on the boundary. It uses gradient and contour lines on minimal surfaces; this surface and network are chosen for the properties of the resulting architectural grids: beams converge to the support are aligned to the boundary and intersect at right angles. The types of generated topologies (number and indices of singularities and poles) as well as the conditions of application are detailed. The potential of this method is illustrated using various types of architectural boundaries (convex and non-convex, with one or multiple boundary components). Finally, the design of a timber pavilion demonstrates how this tool can be integrated into a design process subject to fabrication constraints.
Original hub-shape inlay joint constitutes a crucial joint kind for reticulated shell. However, due to its relatively low joint rigidity and design tend to be conservative, limits its application in single-layer reticular shell with smaller spans. Based on this, this study improves the original hub-shape inlay (OHI) joint, and proposes an innovative semi-rigid joint, namely improved hub-shape inlay (IHI) joint. FE models are created for the OHI and IHI joints using ABAQUS package, with a total of 126 numerical joint models investigated. This study systematically examines IHI joint’s mechanical properties under five types of single loads as well as coupled action of axial load along with moment, followed by parametric analysis. Subsequently, nonlinear fitting of key joint parameters established a bilinear model for IHI joint’s strong axis load-displacement relationship. Computational results indicate: (i) Compared with the OHI joints, the IHI joints exhibit significantly enhanced bending capacity about strong axes, with initial rigidity increasing by 97% as well as ultimate moment rising by 29%; (ii) As the depth of the inlay tenon decreases, various joint rigidities improve to different degrees, with the most pronounced effect observed when the joint undergoes axial tension; and (iii) Under coupled action of moment along with axial load, IHI joints’ bending resistance gradually decreases with increasing axial tension, and initial stiffness as well as ultimate moment are inferior to their corresponding values under pure bending.
The utilization of large deployable space membrane structures has the potential to offer substantial cost reduction in space programmes and systematically creased membrane structures exhibiting fascinating folding patterns provide exceptional compaction capabilities by facilitated movement along predefined paths for packaging and deployment. This study used experimental and numerical techniques to investigate the minimum load requirements for efficient and controlled deployment of single-creased Kapton membrane. The experimentally determined crease stiffness was incorporated into numerical modelling where the crease was idealized as Join + Rotation type connector. The creased membrane begins to unfold upon applying the actuation load, attains its fully deployed state, and the corresponding displacement data were recorded using a laser displacement sensor for multiple stages. Numerical results aligned quite well with experimental findings, though slight deviations were observed and acknowledged in this study. The investigation demonstrated that an external force of 1.12 × 10 −3 N was sufficient to deploy the creased membrane from an initial folded area of 500 mm² to an effective area of 972.48 mm². Stress analysis revealed peak levels localized within a 1.55 mm range on both sides of the crease line. Significantly, the maximum induced stress remained below the membrane’s yield strength, thereby averting additional permanent deformations and reducing the risk of structural failure or uncontrolled motion. The validated methodology was further extended to a 3 crease configuration, demonstrating consistent deployment efficiency with 3.1 times higher area expansion from the folded state, enabling an efficient 4:1 compaction ratio for large-scale deployable structures. Multi-crease deployment exhibits sequential crease opening from the actuated to fixed edge, maintaining all stresses below 30% of yield strength. The multi-crease configuration requires a force of 0.1 N at near-complete deployment, with a wavelength and amplitude of 74.94 mm and 12.64 mm, respectively, and uniform membrane tension confirmed throughout the deployed configuration.
Current modular design approaches often rely on numerical optimization to satisfy fabrication constraints, which can be computationally intensive and sensitive to initial geometric conditions. This work introduces a parametric design algorithm based on Conformal Principal-Asymptotic (CPA) networks on Minimal Surfaces (MS). This “pre-rationalized” approach enables the rapid generation of diverse shell morphologies while ensuring that construction logic, such as developability and node-orthogonality, is constantly preserved. The method provides a versatile design space for both surface geometry and beam configurations, while also facilitating geometric analyses of assembly-induced stresses. Our methodology is validated through a full-scale experimental timber model, providing a physical proof-of-concept that demonstrates a streamlined workflow for the design and modular assembly of complex elastic gridshells.
The AlgoRhythms project on curve-folded sheet metal provided a model for the industrial production of mass-customized designs of simple architectural products (columns, walls, and ceilings). It was extended to mass-customization of emergent forms shown with one example of Morphing Platters presented here. Based on a new automaton, it provided an example of mass-customized designs, each different, with the same cost of producing identical designs. This challenged the economy of scale principle, the staple of production since the Industrial Revolution. This example also showed each platter weighed the same. Same mass was redistributed by the algorithm within the same area showing conservation of mass in design. The conceptual underpinning of mass-customization based on three twin phenomena—design-production, infinity-eternity, and unity-diversity—is suggested as the overarching design strategy for producing infinite variations of form. Due to the affinity of these concepts with biology, the term “endless forms” is adopted from Darwin from his classic work on evolution. The production of endless forms, forever, provides an aspirational upper limit for physical production of our designs. Combined with another triad—form-material-process—an integrated universal design tool, when invented, can support endless creativity by humans to aid our natural drive to make physical objects and structures.
The Improved Bolt-Column (IBC) joint is a kind of novel semi-rigid connections in spatial structures. By modifying the cone section of the bolt-column joint, the bending capacity of the joint is enhanced. However, in-depth research on its mechanical behavior under the combined action of bending moment and axial force remains limited. This study first investigates the failure modes and mechanical properties of IBC joints under eccentric loading. Moment-rotation curves and axial load-axial displacement curves under different plate thicknesses and eccentricities are obtained, and the stress distribution of the joints is analyzed using ABAQUS package. The results indicate that increases in both plate thickness and eccentricity result in greater initial stiffness and ultimate moment capacity of the joints. The critical eccentricity is identified as e = 200 mm; beyond this value, the mechanical behavior of the joints under eccentric loading becomes similar to that under pure bending. Furthermore, as the plate thickness increases, the failure mode gradually shifts from yielding of the conical section to yielding and fracture of the bolts. By analyzing the ultimate moments of four groups of joints with different plate thicknesses under eccentricities ranging from 10 to 200 mm, a predictive formula between eccentricity and ultimate moment is established. When the joints are subjected to combined axial force and bending moment, an increase in axial tension significantly reduces both the initial bending stiffness and the ultimate moment capacity. In contrast, an increase in axial compression also leads to a decrease in the ultimate moment capacity; however, the initial bending stiffness first decreases and then increases. A parametric analysis is conducted on the bending capacity of the joints under different magnitudes of axial force, and a formula is developed to quantify the influence of axial force on the bending capacity.
Fractal geometries, inspired by patterns found in nature, offer a powerful framework for generating complex and adaptive forms through simple recursive rules. The application of these geometries in architectural design may enhance the structural efficiency. In this regard, this paper aims to evaluate the behavior of fractal grid-shell structures under both symmetric and asymmetric loading conditions. In order to assess the influence of different generation methods on the structural performance, the assumed fractal pattern is created based on three different strategies, including (a) a fully stochastic approach, (b) a deterministic approach with constant ratios in all iterations, and (c) a deterministic approach with independent ratios in each iteration. A conventional grid-shell structure with square cells is also adopted for comparison purposes. The generated planar patterns are mapped to three surfaces with different characteristics (i.e., spherical, hyperboloid, and hyperbolic surfaces) to form grid-shell structures. To achieve the optimal design of the considered structures, both single and multi-objective optimization approaches are used. Structural mass and maximum deflection are considered as two main goals to be minimized. The results highlight the effectiveness of fractal grids, in particular those created through the third strategy, in achieving optimized, lightweight structural systems under both loading conditions. The finding is confirmed through the comparison of structural mass in constant deflections and evaluating their stress and deflection distribution contours.
The purpose of the present paper is to demonstrate how the script components of Grasshopper, the user-programming platform of the geometry program Rhinoceros 7/8, can be used to create a software tool for the generation of two complex semi-regular polyhedra, namely, the snub dodecahedron and its dual, the pentagonal hexecontahedron. The snub dodecahedron is an Archimedean polyhedron whose geometric construction is not as simple or direct as that of other polyhedra. The dual of this polyhedron is the Catalan polyhedron known as the pentagonal hexecontahedron, a convex polyhedron with 60 identical, axially symmetric, semi-regular, pentagonal faces. The intricacy of deriving and specifying the geometric particulars of these two polyhedra might be a reason for their infrequent application in dome-like architectural envelopes, such as the “Amazon Spheres” in Seattle (2018). A numerical method for the geometric specification of the snub dodecahedron based on the regular icosahedron is used in this article to illustrate its formulation in Grasshopper (GH). The successive GH implementation of the duality principle to obtain the pentagonal hexecontahedron completes the formulation exercise. Here, the geometric construction method and its algorithm, as well as the data organization and its handling within the data tree structure in Grasshopper, pose the actual challenge for an efficient formulation. The practical outcome of the present discussion is provided by the GH-script that generates the mentioned polyhedra, which can be used in further design and construction processes.
Spatial structures in architecture are popular. The origin of popularity of space frames, dome structures was Surrey. Tensile structures were developed in Stuttgart. Free Form Structures often are more sculptural than structural. Tensegrity structures were the most complicated structures. In all hubris, very complicated tensegrity projects were designed and proposed, almost impossible to build. Yet structural design of more simple tensegrity systems ended in stabilizing systems in Delft for frameless glass facades and roofs with extreme visual super-slender appearance. To realize innovative spatial structures a design and build approach is absolutely an advantage.
The article deals with material testing for the research of shell timber structures constructed using active bending. These structures belong to a category in which the elastic properties of the material are directly involved in the construction process during the design stage. It is therefore essential to determine the material properties that govern both the elastic capacity of the material (modulus of elasticity) and the structural resistance (flexural strength). The paper presents the standardized procedure for determining flexural strength by means of a four-point bending test, carried out on 41 pine specimens with a cross-section of 10 × 40 mm. The results of this test serve as calibration data for the numerical models of ongoing research on active bending at the Slovak University of Technology. Within this framework, experimental testing represents a fundamental requirement for numerical model verification, encompassing both material testing and investigations performed on a scaled experimental shell model. The tests provide the mean flexural strength, the 5th percentile, and the characteristic flexural strength. The results indicate that the value of characteristic flexural strength, after applying the relevant correction factors, may reach up to more than twice as low as the minimum flexural strength obtained from the four-point bending test. The aim of the article is, in addition to obtaining the necessary material parameters, to highlight the potential to increase design efficiency by utilizing the full capacity of the material through knowledge of its actual properties.
The mechanical behavior of the SLO joint with a separated joint body is investigated under bending shear and axial eccentric loading. The validity of the finite element model of the SLO joint is verified through a comparison with pure bending test results. Six groups of joints with varying parameters are designed to analyze the effects of end plate thickness, bolt size, axial eccentricity, and lever arm on the mechanical performance. The failure mode of the joint under axial eccentric loading is obtained. The following conclusions are obtained: under the action of axial eccentric force, the axial eccentricity has little impact on the initial rotational stiffness of the joint, but a significant impact on the ultimate bending moment. Under shear bending, the thickness of the end plate has little effect on the initial rotational stiffness and ultimate bending moment of the joint. But as the bolt size and lever arm increase, the initial rotational stiffness and ultimate bending moment of the joint both increase. The calculation formulas for initial rotational stiffness and ultimate bending moment under axial eccentric and bending shear actions are derived by introducing stiffness ratio and moment ratio based on pure-bending formulas. The formulas proposed in this study can be applied to the design of SLO joints with the separated joint body.
3D chain mail assemblies have recently emerged as a promising class of self-transforming structural systems, yet their behaviour at larger scales remains poorly understood. In particular, it is unclear whether geometric outcomes observed in small prototypes persist when the same interlocking assembly is enlarged. This study investigates the multiscale behaviour of a gravity-actuated 3D chain mail curved-beam configuration realised at three geometric scales (1:10, 1:2 and 1:1). Using physical prototyping and 3D scanning, global form is evaluated through span–height outcomes and curvature-profile fitting, while local interaction is characterised through intermodular opening angles as an indicator of how jamming develops along the beam during self-transformation. Results show that, despite increased weight and changes in surface friction with scale, the global curvature profile remains consistently well described by the Catenary model across all scales tested. In contrast, dimensional proportions and intermodular opening angle distributions vary with scale, with greater non-uniformity at full scale. Together, these findings show that robust global curvature can coexist with scale-sensitive local interaction behaviour, highlighting comparative geometric trends and scale-dependent interaction patterns across scales and providing insight into the multiscale behaviour of 3D chain mail beam assemblies.
The conventional triangular cross-arm configuration for V-string insulators in transmission systems, while it is necessary to satisfy stringent electrical clearance requirements, results in excessively large tower heads. This geometric necessity elevates wind loads on both conductors and tower structures, consequently increasing risks of wind-induced insulator string dropouts that degrade overall system reliability. To address these limitations, this study proposes an innovative wing-shaped cross-arm design. Using a 500 kV double-circuit V-string tangent tower as a case study, two structurally distinct tower head configurations (triangular vs wing-shaped cross-arms) were engineered with identical electrical clearances to enable a comparative structural performance analysis. Key design parameters, including cross-arm layer spacing, cross-arm height, line spacing, string length, tower weight, and foundation forces, were systematically compared. The results demonstrated that the wing-shaped cross-arm scheme achieved significant reductions in all the aforementioned design parameters compared to the conventional triangular design. Subsequently, a full-scale test was conducted on a 500 kV double-circuit V-string tangent tower featuring a wing-shaped cross-arm. Seven critical load cases, including those caused by broken wires, installation loads, and strong winds, were evaluated. The study further analyzed the discrepancies between the experimental results and the FEM analysis of the tower’s displacement and member internal forces, along with the underlying causes of these differences. Despite these differences, the experimental results demonstrated that the overall displacement and internal force behavior was well-captured by the FEM model. This indicates that the computational model for the wing-shaped cross-arm, utilizing bar elements, provides a reasonably accurate representation of the structural response under the actual loading cases. Notably, a tower with a wing-shaped cross-arm demonstrated outstanding structural performance, offering significant economic benefits.
A novel six-bar tetrahedral tensioned stringed cylindrical lattice shell was proposed based on the structural configuration of the six-bar tetrahedral cylindrical lattice shell which can be assembled by rhombic projection plane six-bar tetrahedral units. A self-balancing structural system is formed with the counterbalance between the horizontal thrust at the support and the tension from the added tensioned stringed part. The internal force distribution of the overall structure is more reasonable. Meanwhile, the advantages of standardized design, industrial production and prefabricated construction are inherited. The configuration of six-bar tetrahedral tensioned stringed cylindrical lattice shell was analyzed. A parameterized modeling program with visualization was developed. Completeness and effectiveness of the parameters were verified. The construction path of the structure was discussed. Based on the test model of six-bar tetrahedral cylindrical lattice shell, a tensioned stringed test model was built by the addition of struts and steel tie rods and the change of bearing properties along span direction from fixed bearing to sliding bearing. Static tests of the model were conducted. Reliability of the structure was verified by the experimental research.
This paper presents an integrated approach to the design, fabrication, and structural analysis of wide-spanning concrete structures by combining bending-active formwork with conformal 3D printing. Traditional large-scale additive manufacturing in construction is constrained by horizontal layer deposition, limiting applications to vertical elements such as walls. To extend 3D printing capabilities to roofs, floors, and other spanning elements, this study proposes using elastically deformed timber strips as lightweight formwork substrates onto which concrete is robotically deposited along non-planar, structurally informed toolpaths. The methodology is validated through a systematic experimental campaign progressing from material characterization and small-scale tests to a full-scale prototype spanning 4.6 meters. Complementing the physical investigations, a voxel-based finite element simulation framework is developed to evaluate the influence of toolpath strategies and interlayer timing on structural stability during the printing process. Results demonstrate that toolpaths aligned with the global span reduce formwork buckling and promote uniform stress distribution, while short interlayer pauses enhance printing stability. This research contributes a novel fabrication and analysis framework for sustainable, material-efficient construction of curved, long-span architectural elements.
Isogeometric formulations of thin shells provide accurate geometric descriptions and deformation fields with higher-order continuity. They use only translational degrees of freedom and require smaller-sized models than standard finite elements with bilinear shape functions, which include both displacement and rotational degrees of freedom. This paper analyses the folding of a prototypical thin-shell deployable structure, a tape spring, using both NURBS-based and bilinear Reissner-Mindlin finite elements available in the software LS-DYNA. It is found that the analysis with isogeometric elements is three times slower than the analysis with bilinear Lagrange polynomial elements. Use of high aspect ratio meshes in the regions of the tape spring that do not deform significantly during folding leads to significant improvements in speed for both types of elements, but the difference in performance remains.
The evaluation of mechanical properties for the analysis of existing masonry buildings still represents a current problem, especially when retrofit interventions have to be planned on the historical-artistic heritage. Due to the huge cost of laboratory destructive tests, the need of knowledge is today often achieved through the combined use of investigations carried out with different methodologies. The actual tendency should be to increasingly privilege, to the point of almost exclusive use, non-destructive investigations, which can be easily and widely used on buildings, replacing destructive or partially destructive tests. At present, however, relationships among mechanical characteristics (modulus of elasticity, strength) to be reliably estimated using on site measurements are not available. This is especially true for natural stone masonry like those widely diffused in Southern Italy. In this context, an extensive set of experimental data obtained on yellow tuff masonry from the Campania Region is presented and discussed in this paper.
The excavations conducted in the triangular terrace on the Acropolis of Cumae, Pozzuoli (Italy), since 2019 by the Scuola Superiore Meridionale together with the Università della Campania “L. Vanvitelli,” and the scientific direction of Prof. Carlo Rescigno, have unveiled the ruins of a medieval church. Its remains show an almost square-plan single nave church with apse constructed with masonry made of blocks of squared tuff and mortar. Its nearly 2 m above ground level walls tell little about its original architectural layout, and in particular whether its roof structure was vaulted or duo-pitched. To reach a plausible hypothesis of how the roof structure of the medieval church may have been made, a multidisciplinary approach has been adopted, comparing data coming from the stratigraphic interpretation of the excavation, from the architectural reading of its ruins, and from the study of the in-plane and out-of-plane responses of the masonry walls through nonlinear analyses performed using Finite Element Macro-modeling approach. The purpose of the paper is to reconstruct the most creditable reconstructive hypothesis of the roof structure of the medieval church, integrating data deduced from the results from an archeological, architectural, and structural point of view.
The study provides an advanced non-linear approach to assess the structural capacity of strengthened masonry buildings. The numerical approach aims to optimize the efficiency of strengthened systems made of inorganic matrix and synthetic fiber. The strengthening contribution was evaluated considering a non-linear stress-strain relationship of composite both under compression and in tension. Finally, the proposed approach was applied on a case study comparing the classical method with the proposed approach.
The prestress optimization of cable dome structure holds significant practical importance in engineering applications. However, the intricate relationship between prestress levels and structural responses in complex structures renders the optimization process challenging. To address this, a surrogate model of structural response was first developed in this study based on a Backpropagation (BP) neural network, enabling the establishment of a nonlinear mapping between prestress and both structural displacements and support reactions. This approach markedly reduces the reliance on computationally expensive finite element analyses during the optimization process. Building upon this, an Artificial immune algorithm (AIA) and an improved Genetic–artificial immune algorithm (GA-AIA) were employed to conduct multi-objective prestress optimization of the structure. Considering the multi-objective nature of the problem, a Pareto-based optimization framework was adopted to obtain the Pareto front solutions that simultaneously account for vertical displacement, support reaction, and prestress levels. The optimal solution was then selected from the Pareto set using the coefficient combination method. The results demonstrate that the proposed neural network surrogate model exhibits high accuracy and computational efficiency, and that the presented optimization strategy possesses excellent global search capability and strong engineering applicability.
