T-Umbrella
PROJECT TITLE
T-Umbrella: a case study for an inflatable rigid-ruling curved folding mechanism
AUTHORS
Georg NAWRATIL*a, Clemens PREISINGER b, Kiumars SHARIFMOGHADDAM a, Tomohiro TACHI c, Yiwei ZHANG c, Rupert MALECZEK d
INSTITUTION
a Institute of Discrete Mathematics and Geometry & Center for Geometry and Computational Design, TU Wien
b Institute of Architecture, University of Applied Arts Vienna
c Department of General Systems Studies, University of Tokyo
d i.sd | Department of Design, University of Innsbruck
Proc. of IASS Annual Symposia, IASS 2025 Mexico (2026)
Read the full paper here.
The T-Umbrella is a lightweight structure (43kg) acting as demonstrator for a curved folding system, materialized by straight inflatable pouches along the generators of an underlying semi-discrete T-surface allowing a rigid-ruling folding. The project is designed as a cantilevering structure based on a single column. The entire structure consists of one continuous folded strip of material (two-sided TPU laminated textile) that can be fabricated and pre-assembled in a flat state. After inflation it can be deployed into its final shape, where it forms a closed loop that self stabilizes the structure.
Basics of the underlying geometry
The proposed design is based on a semi-discrete version of T-hedra, a special class of planar quad (PQ) meshes introduced by Sauer and Graf, which exhibit a controlled 1-degree-of-freedom motion despite being generally rigid. T-hedra can be understood as a generalization of discrete surfaces of revolution, where rotation occurs along a trajectory polyline and may be combined with axial dilation, resulting in planar trapezoidal faces. Replacing the discrete profile with a smooth curve yields semi-discrete T-hedra with cylindrical, developable strips. The system supports a flat-folded configuration for assembly and a deployable, overconstrained folding motion, becoming rigid once the boundary curves meet and are connected.
Basics of the air-pouch system
Recent studies show that thin flexible sheets can be stiffened through the use of straight, inflated air pouches aligned with ruling directions, enabling them to act as load-bearing developable strips. Fabrication methods based on flat sheet patterns allow air pouches of arbitrary geometry to be produced efficiently by controlling the 2D-to-3D transformation. When inflated, straight pouches form near-cylindrical tubes whose internal pressure provides structural stiffness. Although the stiffness of individual pouches is limited, assemblies of aligned pouches can represent the rulings of curved-folding origami systems. In the case of semi-discrete T-hedra, this configuration enables a controlled 1-DOF folding mechanism, requiring precise design of the folding angles between adjacent air-pouch caps along each crease.
As part of the extended research project Advanced Computational Design funded by the Austrian Science Fund (FWF), a large-scale architectural demonstrator was proposed to explore the application of flexible planar-quad surfaces. The “pleated flower” was identified as a modular element for a vault system, arranged in a regular triangular tiling. This configuration allows for compact packing, rapid on-site assembly, and increased structural stability when modules are connected into a continuous, weather-protective canopy.
Strategies for realization
The realization strategy was first explored through a single-module prototype, initially conceived as a plate-and-hinge system. While theoretically feasible, this approach revealed significant challenges related to layering, hinge control, predictability of structural behavior, and compact transport particularly when using thick materials.
To address these issues, a lightweight realization strategy was pursued. The design shifted from a discrete to a semi-discrete T-hedral geometry and explored bending-activated, compression-only systems using elastic elements. While promising, this approach required complex hinge solutions for crossing elements and was deferred for future research. Instead, the adoption of cylindrical air pouches provided an effective solution and enabled lightweight construction, compact transport, and reliable handling of crossing creases, leading to the final design proposal.
Design for the initial IASS 2025 pavilion proposal
To meet the constraints of the IASS 2025 pavilion competition, the module was simplified to four petals and resized to fit within a compact envelope. This adapted configuration, termed the T-Umbrella, is exhibited as a single module and therefore stabilized using a waterbag foundation with an integrated inflatable seating element. The profile curve was designed such that the deployed configuration corresponds to a flexion limit of the semi-discrete T-hedron, ensuring a well-defined and stable final geometry, which formed the basis for the subsequent structural analysis.
Detailed layout of the T-Umbrella based on structural analysis
Structural analysis guided the refinement of the T-Umbrella design toward a detailed layout for a 1:2 prototype and the final large-scale demonstrator, both fabricated in collaboration with schulteswien. Material choices and fabrication strategies were informed by prior experience with inflatable structures, leading to the use of TPU-laminated textiles with known mechanical properties. Using seam strength data and Barlow’s formula, tube dimensions and internal pressure were defined to balance aesthetic considerations and structural performance. With a tube radius of 10 cm, high internal pressure and low self-weight allowed the air pouches to be idealized as rigid cylindrical elements. This enabled a bar-structure model in Karamba3D, where tubes were assumed rigidly connected. The analysis revealed three key issues in the initial design: insufficient form stability of the developable strips, inadequate stiffness of inward-pointing creases, and limited stability of the central trunk.
Structural analysis of the updated design
Structural analysis of the refined T-Umbrella shows that, under self-weight, the highest bending stresses occur at the outer edges of the longest tubes, where outward deflection is most pronounced. Even in these critical regions, stress utilization remains below 11% of the allowable limit.
Given the sheltered courtyard setting of the IASS 2025 installation, wind effects are expected to be minor. Nevertheless, a simplified horizontal load case equal to twice the dead weight was considered. This resulted in a maximum lateral displacement of approximately 5 cm and a peak stress utilization of 35%. While these results provide a conservative estimate, they confirm adequate structural performance despite model simplifications, including linearized stiffness assumptions for the pressurized tubes.
