Enhanced model-order reduction approach via online adaptation for parametrized nonlinear structural problems

With regard to the parameterized projection-based reduced-order model, it is significant to consider the computational efficiency as well as its capability for the parametric variation. The proposed approach is based on the online adaptive procedure to improve the accuracy and stability of the reduced-order model. Achieving efficient computation in online adaptation, a matrix version of the discrete empirical interpolation method is employed to approximate the nonlinear finite element matrix, independently. The proposed approach is applied to analysis of a structure with geometric and material nonlinearities. As a result, the computational efficiency during the offline/online steps of the proposed approach is significantly improved, compared to other existing approaches. Moreover, within the present numerical examinations, it is found that the proposed approach is capable of accurately addressing broad parametric variations by using only ten percent of the number of data used in the conventional ROM from the preliminary computation.