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Dynamic Snap-Through Inversion of Rib-Stiffened Shallow Arch Vault on SO(3)
Shallow parabolic roof vault (span L = 1,200 mm, width B = 600 mm, rise f = 80 mm) stiffened by 5 longitudinal arch ribs and 3 transverse ties undergoing dynamic snap-through inversion into its inverted equilibrium state.
Shallow arch roofs and curved aerospace panels subjected to sudden blast or impulse loads can undergo catastrophic dynamic snap-through, inverting through the plane of their supports into a reversed curvature state. Linear or small-rotation solvers completely miss the softening membrane-bending transition and post-buckling inversion. Here, a 1,200 × 600 mm aluminum vault (rise f = 80 mm, skin thickness t = 4 mm) stiffened by 5 longitudinal arch ribs (8 × 14 mm) and 3 transverse ties (8 × 12 mm) is solved using WebCAE's geometrically exact SO(3) beam-shell transient solver over 150 steps (387 Newton iterations, zero cutbacks).
1. Geometry & FEA Mesh
- •Coupled rib-stiffened shell grid: 128 4-node MITC4 shell elements (t = 4 mm) + 104 3D spatial beam elements (5 arch ribs 8 × 14 mm + 3 transverse struts 8 × 12 mm), 153 nodes, 864 active DOFs.
- •Aluminum alloy 6061-T6 / D16T (E = 70 GPa, ν = 0.33, ρ = 2,700 kg/m³).
- •25 saved transient frames capturing pre-buckling flattening, snap-through passage across z = 0, peak inverted excursion, and post-snap ringing.
2. Loads & Boundary Conditions
- •Longitudinal thrust abutments at x = −600 mm and x = +600 mm pinned in all three translational DOFs (ux = uy = uz = 0) while allowing free support rotation.
- •Vertical impulse load (−6,000 N per crown node) applied across the central arch ridge with pulse profile amplitude="0:0,0.001:1,0.015:1,0.020:0".
3. Simulation Results & Findings
- ✓The crown (initially at z = +80 mm) snaps dynamically through the support plane to a peak downward displacement uz = −192.99 mm (snap-through inversion ratio |uz|/f = 2.412 > 2.0, putting the crown 113 mm below the support line).
- ✓After impulse release at t = 20 ms, the inverted vault oscillates around its second stable equilibrium configuration (uz = −176.73 mm at t = 30 ms).
- ✓150 time steps completed in 387 Newton-Raphson iterations (2.58 iterations/step) with 0 step cutbacks.
WebCAE's geometrically exact SO(3) beam-shell solver captures large-rotation buckling, snap-through inversion, and post-buckling dynamics of stiffened roofs, domes, and aerospace skins.
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