Damage Localization and Quantification from the Image of Changes in Flexibility

AbstractAn approach to interrogate changes in flexibility regarding the severity of damage is presented. The approach is built on two results. The first shows that the influence lines of stress resultants at damage locations are a basis for the difference in the displacement field between the damaged and reference states for arbitrary loading. The second result shows that the coefficients that combine the basis are the magnitudes of discontinuities in the differential displacement field at the damage locations. The approach quantifies the damage severity by finding changes in sectional stiffness that justify, over reasonable smearing distances, the computed discontinuities. It is shown that at damage locations where the relevant stress resultant is statically determinate the solution is in closed form, while in the indeterminate case it is the fixed point of a nonlinear function.