Application of higher order finite differences to damage localization in laminated composite plates

The localization of damage in composite plates and other structures is often performed based on mode shape curvatures. These curvatures are usually computed using finite differences. However, finite differences spread and amplify numerical and experimental errors. A technique based on the Ritz method allows to choose an optimal spatial sampling in order to minimize this problem. In the present work we apply this technique, along with the second and fourth order finite differences to compute the mode shape curvatures. To evaluate the successfulness of the damage localizations a quality evaluator is proposed in this paper. The need for the optimal spatial sampling is verified by analyzing two locations of a wide range of damage severities. Damage localizations obtained with second and fourth order finite differences were compared and it was found out that the results are better when one uses the highest order finite difference.