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Buckminster Fuller Double-Layer Geodesic Dome
Montreal Biosphère style double-layer icosahedral geodesic dome (Ø 48 m, H = 20 m) with inner shell dome and outer space-truss connected by 3D radial and diagonal struts.
Buckminster Fuller's geodesic dome for Expo 67 in Montreal revolutionized architectural engineering by maximizing enclosed volume per unit mass through an omni-triangulated double-layer space truss. The double-layer topology pairs an outer geodesic grid with an offset inner grid linked by 3D tetrahedral struts, preventing local cell oil-canning and providing enormous flexural and shear rigidity. This model captures a Ø 48 m dome (height 20 m) comprising 1,274 tubular struts coupled to an inner MITC4 shell skin. WebCAE computes extreme rigidity under self-weight, snow, high fundamental vibration frequencies, and massive buckling safety margins.
1. Geometry & FEA Mesh
- •Geometry: double-layer spherical cap (outer sphere R = 24.0 m, inner sphere R = 23.0 m, base diameter 48.0 m, crown height 20.0 m).
- •Truss structure: 1,274 tubular steel struts (chords Ø 140×8 mm, inter-layer diagonals Ø 100×6 mm) forming a rigid triangulated spatial lattice.
- •Skin cladding: 144 MITC4 quad shell elements (t = 8 mm polycarbonate/acrylic glazing) attached to inner layer nodes.
- •System discretization: 337 joints, 1,274 beam elements, 144 shell quads, totaling 1,734 system DOFs with verified node coincidence.
2. Loads & Boundary Conditions
- •Fixed boundary conditions (all 6 DOFs constrained) at all perimeter base foundation nodes around the circumference (z = 0).
- •Permanent gravitational self-weight of steel framing (density 7,850 kg/m³, E = 205 GPa) and lightweight glazing.
- •Uniform downward snow load (-1.2 kPa) distributed across the projected dome surface.
3. Simulation Results & Findings
- ✓Exceptionally low maximum static deflection |u| = 1.00 mm at the dome crown under full dead and live load, demonstrating outstanding structural efficiency.
- ✓Fundamental mode frequency f₁ = 16.49 Hz reflects the extraordinary stiffness-to-weight ratio of the double-layer space truss.
- ✓Critical elastic buckling factor λ₁ = 490.9 confirms complete immunity to localized snap-through or general buckling under design loads.
WebCAE validates the supreme structural economy of double-layer geodesic space frames for planetariums, bio-domes, and exhibition pavilions, delivering instant natural frequencies and buckling factors in the browser.
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