Parametric reduced-order modeling enhancement for a geometrically imperfect component via hyper-reduction

In this paper, an improved nonlinear reduced-order modeling technique capable of describing the parameterized shape defect is presented. In the proposed framework, a set of defect-shapes are pre-determined based on a nominal configuration. Then, the reduced-order representation is created in a polynomial form comprising a set of reduced-tensor coefficients of defect and physical displacement fields. However, constructing reduced tensors using a large number of discretized elements usually requires enormous amounts of computational resources. Therefore, to reduce the computational expense, a quadratic-manifold-based energy-conserving sampling and weighting approach was employed to obtain the reduced tensors concerning only a few optimally selected elements. This approach can be used to conduct both time-transient and frequency response analyses on rotating mechanical components. It was found that the proposed approach can accurately estimate the broad defect-parametric variation. In particular, its computational efficiency demonstrated a significant improvement over that of existing approaches.