Damage detection based on the internal force or deformation variation

The presence of damage in an intact structure leads to the change in internal force and deformation due to stiffness deterioration in the region of damage. This study proposes modelbased damage detection methods by deriving the mathematical formulation to describe such changes. The force and deformation variations between the undamaged and damaged systems are derived by minimizing the variation in dynamic strain energy with respect to the internal force and deformation vectors, respectively. They are expressed by the product of a coefficient matrix and the external force vector, and the product of a coefficient matrix and the displacement vector, respectively. Taking singular value decomposition (SVD) on the coefficient matrices of rank-deficiency, this study identifies the damaged elements as belonging to the set of elements whose internal forces or deformations between two adjacent nodes of finite element model are not changed. The validity of the proposed methods is illustrated in a simple application.