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Two-Tier Crossed Beam Grid Damper with Beam-to-Beam Contact
Geometrically nonlinear 3D beam-to-beam contact analysis of a two-tier tubular steel grillage bumper with progressive gap closure.
Multi-tier protective grillages, wire-rope arrestors, and torsion-bar bumpers rely on sequential beam-to-beam contact to absorb impact energy and stiffen progressively under overload. In this model, three longitudinal upper tubular beams (Ø40 × 6 mm at z = +32 mm) are loaded downward above three orthogonal lower support beams (Ø44 × 6 mm at z = 0 mm) mounted in a 1.6 × 1.6 m perimeter box frame. Using WebCAE's closest-point cylinder-to-cylinder beam contact (nlgeom beamcontact), all 9 crossover junctions engage smoothly, transferring vertical force to the lower tier.
1. Geometry & FEA Mesh
- •72 nodes and 86 corotational 3D beam elements (348 active DOFs) in a 1.6 × 1.6 m steel frame (E = 205 GPa, ν = 0.30).
- •Upper tier: 3 longitudinal pipes (Ø40 × 6 mm, r_a = 20 mm), 8 segments each; lower tier: 3 transverse pipes (Ø44 × 6 mm, r_b = 22 mm), 8 segments each.
- •Perimeter box frame (60 × 60 × 5 mm hollow square section) on 4 corner columns.
- •Beam-to-beam contact (nlgeom beamcontact) with radii r_a = 20 mm, r_b = 22 mm, penalty = 5×10⁷ N/m.
2. Loads & Boundary Conditions
- •4 base column footings at z = -0.18 m and beam ends at x = ±0.8 m / y = ±0.8 m constrained.
- •Downward vertical impact forces applied to the mid-span crossover nodes of the upper longitudinal beams.
- •Closest-point cylinder-to-cylinder contact (nlgeom beamcontact) between all 24 upper and 24 lower beam segments.
3. Simulation Results & Findings
- ✓Full Newton-Raphson convergence in 6 load steps (19 iterations, 0 cutbacks) with 36 active beam segment contact pairs across all 9 crossover junctions.
- ✓Maximum contact penetration is controlled to 0.165 mm while transferring downward load to the lower transverse beams (central node u_z = -31.03 mm).
- ✓Fundamental natural frequency of the grillage frame is f₁ = 70.55 Hz.
Enables rapid parametric sizing of multi-layer bar grilles, pipe racks, and protective bumpers with beam-to-beam contact without meshing 3D solid tubes.
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