Validation Case: Cantilever Beam

Explicit Dynamics Elastic Vibration Contact Release Transient Response

This benchmark is a transient explicit cantilever beam case used to assess elastic wave propagation, contact release, and the free-vibration response after tip loading is removed.

Reference paper

A Material Point Method for Simulating the Thermomechanical Response of Elastic Solids Undergoing Large Deformations

Fraser, UQAC thesis PDF

Model setup

  • The leftmost end of the beam is fixed and the rightmost end is free.
  • An initial deformation equal to 10% of the beam thickness is imposed at the tip.
  • The total simulation time is 0.02 s to capture the transient elastic deformation.
  • The beam material is AA6061-T6 with elastic modulus 70.0 GPa, density 2700 kg/m3, and Poisson ratio 0.33.
  • The rectangular cross section is 24 mm thick and 12 mm wide.
  • The total beam length is 100 mm.
  • The particle and finite element grid size is 2 mm.

Loading sequence

  • A rigid plate presses downward on the beam tip.
  • The plate displacement is 2.4 mm applied over 0.005 s.
  • From t = 0.005 s to t = 0.01 s, the plate is held fixed.
  • At t = 0.01 s, contact between the plate and the beam is disabled.
  • After release, the beam vibrates freely.

What this benchmark checks

  • Transient deformation under explicit time integration
  • Contact enforcement during tip loading
  • Release behavior when contact is removed
  • Free-vibration response of the elastic body

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