Damage Identification of Euler–Bernoulli Beams Using Static Responses

Abstract

AbstractThe paper presents two computational procedures to reconstruct the stiffness distribution and to detect damage in Euler–Bernoulli beams. A novel methodology of damage identification is developed using static deflection measurements. The first formulation is based on the principle of the equilibrium gap along with a finite-element discretization, and leads to an overdeterminate linear system. The solution is obtained by minimizing a regularized functional using a Tikhonov total variation (TTV) scheme. The second proposed formulation is a minimization of a data-discrepancy functional between measured and model-based deflections. The optimal solution is obtained using a gradient-based minimization algorithm and the adjoint method to calculate the Jacobian. Also discussed is a simple procedure to measure the deflection of beams using a close-range photogrammetry technique. An edge detection-based algorithm is devised for quasi-continuous deflection measurement. The proposed identification methodology ...