A defect identification problem for elastic plates with damages is studied in this paper. The classical theory of thin plates in bending is applied for the modelling of the mechanical structure. Bonded piezoelectric sensors and actuators are considered in a simplified way. Within classical finite element discretization, cracks and other defects are modelled in a smeared-crack sense by reducing the stiffness of the corresponding element. According to the simplicity of the model, only the position of the possible crack is considered to be the unknown. The most general case of dynamical excitations is considered. The identification is based on dynamic non-destructive loading. A suitable error norm is used to transform the defect identification problem to a nonconvex output error optimisation problem [
]. The difference between the dynamic response of the plate in bending with and without cracks demonstrates the areas of the plate where the influence of the cracked element is higher. The position of the defect, which is unknown in real applications, can be computed from the solution of the arising optimisation problem. This problem has been solved by a genetic algorithm. The investigation includes the effect of different types of boundary conditions. In all cases the error function, which depends on the boundary conditions and the position of the defect, may have local minima and one global minimum, exactly at the position of the real crack.
As a general observation, the boundary conditions, the loading and the shape of the structure, as well as the position of the measurement points and the duration of the considered time interval influence the shape of the error function. Numerical results show that by using the genetic algorithm the crack position can be found. Moreover, for a relatively high population size (about 15-20) the probability of finding the crack position on the first few steps is very large.