Abstract
The number of measured degrees of freedom for detecting the damage of any structures is usually less than the number of model degrees of freedom. It is necessary to expand the measured data to full set of model degrees of freedom for updating modal data. This study presents the expansion methods to estimate all static displacements and dynamic modal data of finite element model from the measured data. The static and dynamic methods are derived by minimizing the variation of the potential energy and the Gauss's function, respectively. The applications illustrate the validity of the proposed methods. It is observed that the numerical results obtained by the static approach correspond with the Guyan condensation method and the derived static and dynamic approaches provide the fundamental idea for damage detection.