Detection of Cracks in Structures Using Two Crack Transfer Matrix

Abstract

Abstract A novel damage detection scheme for multiple crack detection in a beam like structures is presented, based on a transfer matrix (TM) derived from the beam element with two cracks. Based on Linear Elastic Fracture Mechanics (LEFM) principles, a crack is modelled as a hinge which provides an additional flexibility to the element. Each element is assumed to have two open edge cracks and a new TM called Two Crack Transfer Matrix (TCTM) is developed using the Finite Element method. Using an inverse approach, the TCTM is used to predict cracks in a beam. The state vector at a node includes displacements, forces and moments at that node; when it is multiplied with the TM the state vector at the adjacent node can be obtained. The state vector formed at the starting node, known as initial state vector needs to be estimated, from which state vectors at adjacent nodes are predicted using the TM. Displacement responses are measured at a few adjacent nodes in the structure. The mean square error (MSE) between measured and predicted responses is minimized using a heuristic optimization algorithm, with crack depth and location in each element as the optimization variables. Two numerical examples, a cantilever and a sub-structure (SS) of a frame with nine members are solved with two cracks in each element. The damage detection method is also validated experimentally by local identification of a SS of a fixed beam where the initial state vector is measured using strain gauges and accelerometers. Using this method, maximum of two cracks per element were successfully identified. The TCTM method is suitable for local damage identification in large structures.