Damage evaluation of Timoshenko beams using invariant stress resultants

This paper presents an explicit damage evaluation methodology that utilizes the fundamental principles of mechanics to relate the changes in the physical properties of an undamaged and damaged structure to measurable response quantities. The proposed methodology is based on the principle of invariant stress resultants and the Timoshenko beam theory. First, damage in a structure is expressed in terms of local decreases in the bending stiffnesses of structural members. These stiffness decreases are in turn related to appropriate response quantities utilizing the Timoshenko beam theory. Next, a set of numerical experiments using results from two dimensional finite element models of cantilever and fixed–fixed beams are introduced to evaluate the performance of the proposed damage evaluation scheme. Results indicate that the proposed methodology can identify the location, the extent, and the severity of the local stiffness degradations in beams of arbitrary aspect ratios.