Identification of concentrated damages in Euler-Bernoulli beams under static loads

An identification procedure of concentrated damages in Euler-Bernoulli beams under static loads is presented in this work. The direct analysis problem is solved first by modeling concentrated damages as Dirac's delta distributions in the flexural stiffness. Closed-form solutions for both statically determinate and indeterminate beams are presented in terms of damage intensities and positions. On this basis, for the inverse damage identification problem, a nonquadratic optimization procedure is proposed. The presented procedure relies on the minimization of an error function measuring the error between the analytical model response and experimental data. The procedure allows to recognize "a posteriori" some sufficient conditions for the uniqueness of the solution of the damage identification problem. The influence of the instrumental noise on the identified parameters is also explored.