Damage identification of truss structures based on force method and free vibration analysis

The improved structural analysis is presented to determine the sites and extents of multiple damages of truss structures. The algorithm uses the mathematical programming of the finite element technique based on the force method and the free vibration analysis. The equilibrium matrix is generated through the finite element analysis, while the compatibility matrix is obtained directly using the force-displacement relations and the singular value decomposition technique. The governing equations with the element nodal forces as variables are presented by combining the equilibrium and compatibility matrices with the force-displacement relations. Next, the genetic algorithm is used to properly identify the sites and extents of multiple damage cases in truss structures. In order to verify the accuracy and superiority of the proposed damage detection technique, numerical solutions are presented for the planar and space truss models. The numerical results indicate that the combination of the force method and genetic algorithm can provide a reliable tool to accurately and efficiently identify the multiple damages of truss structures.