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Design Concept of Variable, Flat Cut Bending-Active Shells Cover

Design Concept of Variable, Flat Cut Bending-Active Shells

Open Access
|May 2025

Figures & Tables

Figure 1.

Schematic of the structural concept design, and proposed aspects to be consider in the concept design of sustainable bending active structures

Figure 2.

Curvature of a curve on a surface. a) the curve and its curvature frame; b) the Darboux frame of a curve lying on a surface; c) a curve of zero geodesic torsion on a surface; d) a curve of zero geodesic curvature on a surface

Figure 3.

Case study of a barrel shell with anticlastic surface and pointed arch cross section

Figure 4.

Comparison between three bending active gridshells having the same bounding area but different designs. Considering the geometry moving from the edges of the structure to its centre: (a) a structure composed of transversal elements of progressively larger width; (b) a structure composed of longitudinal elements of progressively larger width; (c) a structure composed of transversal elements of progressively smaller width

Figure 5.

Comparison of two bending active gridshells in the erection process, composed of the same main elements but having secondary elements of smoothly variable width (a) and of discontinuous width (b). Map of the principal stress (above), originally flat surface (bottom left) and deform

Figure 6.

Torsion deformation of a plate of variable width

Figure 7.

(a) Active bending gridshell in the erection process when constructed in plywood made with the same design (b) Active bending grid-shell made of NFRP under a uniform distributed gravity load (c) gridshell system created with plywood under a uniform distributed gravity load

Figure 8.

A timber physical model was constructed at a 1:5 scale. (a) The CNC process utilized for the flat timber sheet, (b, c) the top view and side of the timber grid shell after the erection process, respectively, (d) The front view, highlighting the height in the middle of the span point (23.4 cm), (e) a perspective view of the timber model, and (f) the span of the model after the erection process measures 50 cm

Figure 9.

Plywood grid shell under uniform horizontal loads, (a) uniform wind loads along the transversal direction, (b) uniform wind loads along the longitudinal loads

Material Properties and Environmental Impact

MaterialFlexural Strength/Modulus Ratio (MPa/GPa)Manufacturing TechniquesEmbodied Carbon (kgCO2e/kg)Already employed in Bending-active StructuresDensity (kg/m3)
NFRP10–503D Printing, CNC DrillingVariable; lower than GFRPYes – furniture scale800 to 1500
Plywood4–11.13CNC Cutting, Molding1.07yes500–800
Glulam2.07–2.45Lamination CNC0.512yes400–700
Timber, bamboo1–11Cutting, Shaping0.493yes400–700
GFRP10–12.5CNC Cutting2.63 to 6.72yes1800 to 2100

Installation Feasibility comparison-based rating of FPMBSs

CRITERIUMPlywoodNFRP
Material Ratio (R)9.0913.25
Manufacturing challengesProduction of wasteFiber alignment sensitivity
Embodied Carbon (kgCO2) - temporary usage869 – 13901133 to 2124
Embodied Carbon (kgCO2) - permanent usage1001–16021287 to 2413
Erection challengesVery slow erection process, especially for thick structures; risk of ruptureSucceeded at small scale and large curvature, no available data from architectural projects
Usage challengesMay require maintenanceHumidity, may require protection from agents
RecyclabilityMechanicalMechanical or chemical (emerging)

Results of the simulation of temporary and prolonged usage for the design already in Figures 7 and 9, made in plywood and NFRP

ScenarioPlywoodNFRP
Temporary usage qh,t = 0.5 kN/m2 ΔbentΔloaded=1/125t=4.85cm \begin{matrix} \frac{\Delta \text{bent}}{\Delta \text{loaded}}=1/125 \\ \text{t}=4.85\ \text{cm} \\ \end{matrix} ΔbentΔloaded=1/131t=4.05cm \begin{matrix} \frac{\Delta \text{bent}}{\Delta \text{loaded}}=1/131 \\ \text{t}=4.05\ \text{cm} \\ \end{matrix}
Prolonged usage qv = 0.5 kN/m2 qh,p = 0.5 kN/m2 ΔbentΔloaded=1/277t=5.60cm \begin{matrix} \frac{\Delta \text{bent}}{\Delta \text{loaded}}=1/277 \\ \text{t}=5.60\ \text{cm} \\ \end{matrix} ΔbentΔloaded=1/277t=4.60cm \begin{matrix} \frac{\Delta \text{bent}}{\Delta \text{loaded}}=1/277 \\ \text{t}=4.60\ \text{cm} \\ \end{matrix}

End of life options

MaterialMethodsOptionsCostBarriesMarkets drivers
NFRPMechanicalRecoverLowDegraded mech. proprietiesAutomotive industry, consumer goods, energy production
ThermalRepurposeMediumResearch uncertaintiesAutomotive components, industrial applications
PlywoodMechanicalReuse, Repurpose, RecoverLowDegradation from exposureConstruction industry, furniture manufacturing, energy production
GlulamMechanicalReuse, Repurpose, RecoverLow Medium LowAdhesives complicate separationBuilding and construction, energy production
Timber, bambooMechanicalReuse, Repurpose, RecoverLowPossible degraded mech. proprietiesBuilding and construction, consumer industry, energy production
GFRPMechanicalReuse, RepurposeLowPossible degraded mech. proprieties Potential for harmful emissionsConstruction industry, energy production, energy production
Thermal, ChemicalRepurpose, RecoverHighHigh energy consumptionAerospace, automotive, sports equipment
DOI: https://doi.org/10.2478/acee-2025-0008 | Journal eISSN: 2720-6947 | Journal ISSN: 1899-0142
Language: English
Page range: 97 - 111
Submitted on: Jul 4, 2024
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Accepted on: Mar 5, 2025
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Published on: May 10, 2025
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Armin Fathollahi, Valentina Beatini, published by Silesian University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.