On profile reconstruction of Euler–Bernoulli beams by means of an energy based genetic algorithm

Abstract

This paper studies the inverse problem related to the identification of the flexural stiffness of an Euler Bernoulli beam to reconstruct its profile starting from available response data. The proposed identification procedure makes use of energy measurements and is based on the application of a closed form solution for the static displacements of multi-stepped beams. This solution allows to easily calculate the energy related to beams modeled with arbitrary multi-step shapes subjected to a transversal roving force, and to compare it with the correspondent data obtained through direct measurements on real beams. The optimal solution which minimizes the difference between the measured and calculated data is then sought by means of genetic algorithms. In the paper, several different stepped beams are investigated, showing that the proposed procedure allows, in many cases, to identify the exact beam profile. However, it is shown that, in some other cases, different multi-step profiles may correspond to very similar static responses, and, therefore, to comparable minima in the optimization problem, thus complicating the profile identification problem.