An integral equation for damage identification of Euler-Bernoulli beams under static loads

A damage identification procedure for Euler-Bernoulli beams under static loads is proposed. Use is made of an integral formulation for the static problem of damaged Euler-Bernoulli beams. This formulation originates from the observation that a variation in the bending stiffness of a linear elastic beam can be modeled as a superimposed curvature depending on damage parameters as well as on the actual bending moment distribution. Using the superposition principle, the problem is reduced to the solution of a Fredholm integral equation of the second kind characterized by a Pincherle-Goursat kernel. It is shown that the solution of this equation can always be obtained in an analytical form that may be used to set up a damage identification procedure based on the minimization of a nonlinear function of damage parameters.