Nonlinear dynamic response of a Pazy wing variant using the Koiter-Newton model reduction

Kurzfassung

Nonlinear structural analyses in the finite element (FE) framework are often computationally expensive due to their utilization of incremental predictor-corrector solvers. Application of reduced order models for such cases has proven to be beneficial, especially for dynamic loading conditions. Recent developments in the novel Koiter-Newton (K-N) model reduction technique enable us to study large deflection behaviour in cantilevered structures. The K-N approach is a reduced basis method which describes a system of nonlinear governing equations comprising quadratic and cubic stiffness terms. The higher order stiffness terms are evaluated as derivatives of the in-plane strain energy. In the case of extremely large deflections, to ensure that the foreshortening effect is accounted for, the reduced order model is updated at fixed load intervals. Linear eigenmodes of the deformed structure are used to formulate the reduction subspace at the different load steps. The objective of this work is to assess the effectiveness of the K-N method with the intended application to a nonlinear benchmark highly flexible wing. Investigations are carried out pertaining to nonlinear static and dynamic characteristics of the wing. Comparisons are made to the solutions from MSC Nastran for verification purpose. The results show that the K-N method requires a significantly small number of degrees-of-freedom to reproduce the Nastran solutions with a marginal loss in accuracy.