The article proposes a method developed for model order reduction in a Finite Element (FE) framework that is capable of computing higher order stiffness tensors. In the method, a truncated third order asymptotic expansion is used for transformation of an FE model to a reduced system. The basis matrix in the formulation of the reduced-order model (ROM) is derived from linear mode shapes of the structure. The governing equations are derived using Hamilton's principle and the method is applied to geometrically nonlinear vibration problems to test its effectiveness. An initial validation of the numerical formulation is obtained by comparison of results from time domain nonlinear vibration analyses of a rectangular plate using Abaqus. Subsequently, a stiffened plate is modeled to test a more complex structure and a continuation algorithm is used in combination with the ROM to compute nonlinear frequency response curves. The validation of the stiffened plate has been performed through comparisons with the results of nonlinear vibration experiments. The experiments are conducted with Polytec Laser Doppler Vibrometer and PAK MK-II measurement systems for large amplitude vibrations to validate the nonlinear vibration analyses.@en

Wing structures subjected to large deflections are prone to nonlinear load-deflection behavior. Geometric nonlinearities can arise due to the accompanying large rotations and in-plane deflections that manifest in the form of stiffening effects in the nonlinear static response. To account for these nonlinearities, reduced-order modeling techniques in combination with nonlinear finite element formulations have been previously proposed. However, these methods often have a limited range of validity due to linear eigenmode-based formulations with assumptions of small rotations. In this paper, a large deflection analysis framework based on the Koiter–Newton model reduction technique is presented. It is demonstrated that the reduced model in its basic form is ineffective for large deflection analysis. To resolve this, an incremental updating procedure is used for the reduced-order model that incorporates the necessary nonlinear effects. The model updating enables the computation of nonlinear response for a large range of deflections.@en