Reduced Order Modeling for the Nonlinear Geometric Response of Cracked Panels

Abstract

The focus of this investigation is on a first assessment of the predictive capabilities of nonlinear geometric reduced order models for the prediction of the large displacement and stress fields of cracked panels. First, a comparison of the basis functions employed for virgin and cracked panels revealed clearly visible crack effects but only on the transverse components of the “dual” modes, i.e. the part of the basis modeling primarily the in-plane displacements. Next, it was demonstrated that the reduced order models of both virgin and cracked panels provided a close match of the displacement field obtained from full finite element analyses of the cracked panel for moderately large static responses (peak displacement of 2 and 4 thicknesses). In regards to stresses, it was found that the cracked panel reduced order model led to a close prediction of the stress distribution obtained on the cracked panel as computed by the finite element model. Finally, two “enrichment” techniques, based on superposition of the crack effects on the virgin panel stress field, were proposed to permit a close prediction of the stress distribution of the cracked panel from the reduced order model of the virgin one. A very good prediction of the full finite element results was achieved with both enrichments.