Asymptotic analysis of a von Koch beam

Fractal geometry is used in diverse research areas, being an useful tool in describing the mechanical behaviour of natural and man-made structures. In this paper, the structural behaviour of a von Koch cantilever beam is analyzed in the small deformations regime. Analytical recursive formulae for the strain energy scaling are derived, which have been found in good agreement with numerical simulations. Energy considerations suggest a peculiar scaling for the beam rigidity in order to prevent compliance divergence. The results are then extended to evaluate the stiffness matrix of a von Koch beam.