Reduced order modeling with local enrichments for nonlinear geometric vibration of a notched panel

This paper revisits the reduced order modeling of structures with local defects undergoing large deformations, i.e., within the nonlinear geometric range. More specifically, its focus is first on the formulation of local enrichments of the displacements basis functions that complement those of the virgin structure to accurately capture not only the displacements but also the stresses of the structure with defect. It is shown that such functions can be constructed from the linear static analysis of the zone affected by the defect subjected to an imposed far field displacement derived from the virgin structure basis functions. The second objective of this investigation is on assessing which parameters of the reduced order model would need to be updated if the defect, and thus the enrichments, were to change. A validation effort on a beam-like panel suggests that only the linear stiffness and stress coefficients relating to the enrichments would need to be updated which represents the lowest possible computational effort.