Static damage identification in beams by minimum constitutive relation error with both full-field and finite-point displacement measurements

Abstract

A novel static identification approach to beam damage is presented. It is based on the minimum constitutive relation error (CRE) principle where the exact stiffness, the exact displacement and the exact bending moment are shown to make the CRE functional minimal. For practical implementation, two cases regarding full-field displacement measurements and finite-point displacement data, respectively, are considered. For full-field displacement measurements, the CRE functional is directly treated as the objective functional while in case of finite-point measurement data, the CRE functional along with additional penalty terms for treatment of the finite-point displacement measurements is defined as the objective functional. Multiple loads and associated sets of measurements are also considered to improve the identifiability and robustness of the procedure. Convergence is finally verified through numerical examples.