Structural Panel Impact Example

Problem

A clamped steel panel (200 mm x 200 mm, 3 mm thick) is impacted by a 0.01 kg mass at 300 m/s. Estimate the permanent deflection assuming the kinetic energy is absorbed by membrane stretching.

Given

• Panel: 200 x 200 x 3 mm steel
• Clamped on all edges
• Impact: m = 0.01 kg, v = 300 m/s
• Steel: E = 210 GPa, sigma_y = 350 MPa

Solution

Kinetic energy:
  KE = 0.5 * 0.01 * 300^2 = 450 J

For a clamped square panel in the membrane regime,
the energy absorbed by membrane stretching is
approximately:
  W = (4/3) * sigma_y * t * delta^3 / L

where delta is the central deflection, L is the span.

Setting W = KE:
  450 = (4/3) * 350e6 * 0.003 * delta^3 / 0.200
  delta^3 = 450 * 0.200 * 3 / (4 * 350e6 * 0.003)
  delta^3 = 270 / 4.2e6 = 6.43e-5
  delta = 0.040 m = 40 mm

This is an illustrative estimate using a simplified
membrane model. A full explicit FEA analysis is
required for a defensible prediction.

Interpretation

The estimated deflection of 40 mm is large — 13x the plate thickness — confirming that membrane action dominates. This simplified estimate provides a physics check for an FEA model: if the FEA gives a very different deflection, the model should be investigated. The estimate is illustrative only; a full analysis is required for engineering decisions.