We present a method for designing and assembling modular, folded lattices based on numerically calculated triangular Ron Resch molecules. These lattices form stiff structural grids of beams capable of realizing both single- and double-curvature surfaces. Our work builds upon Ron Resch’s contributions to topology and geometry, where he first introduced folded tessellations as structural systems. His work laid the foundation for major advancements in architecture, structural engineering, and computational design, establishing him as a key figure in the emergence of Structural Origami as a distinct field. While much research has focused on the kinematic aspects of Resch’s work, we find a gap in its less explored potential for static structural applications. First, we describe how to compute triangular Ron Resch tripods to form a stiff and constrained unit cell, which we then assemble into a lattice. The resulting structure forms a woven hexagonal grid of beams with continuous second moment of inertia across the assembly, contributing to high stiffness. Next, we demonstrate how to numerically calculate developable unit cells to approximate target surfaces with single or double curvature. We believe this method—where global geometry and mechanical performance are encoded within the local crease pattern—offers significant potential for scalable structural folded shells, with applications from engineering to architecture.
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.
