Identification of Concentrated Damages in Euler-Bernoulli Beams under Static Loads

By G. Buda, Salvatore Caddemi. 2007

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Physically-based Dirac’s delta functions in the static analysis of multi-cracked Euler–Bernoulli and Timoshenko beams (2011, methodology): “The reason is that, as stressed by Buda and Caddemi (2007), the bending stiffness of the cracked beam is represented in their approach by a distribution, rather than by a classical function.”
Exact closed-form solution for the vibration modes of the Euler-Bernoulli beam with multiple open cracks (2009, methodology): “The cracks are modelled by means of the introduction of a sequence of Dirac’s delta generalised functions in the flexural stiffness, which is equivalent to a sequence of concentrated elastic rotational springs [45–48].”
Exact solution of the multi-cracked Euler–Bernoulli column (2008, background): “Recently the model of flexural stiffness with singularities, represented by Dirac’s deltas, has been shown to be equivalent to an internal hinge endowed with a rotational spring (Biondi and Caddemi, 2005, 2007), hence it can be adopted to model concentrated cracks (Buda and Caddemi, 2007).”