On the stable mode selection for efficient component mode synthesis of geometrically nonlinear beams

Abstract

A large-scale structural system containing a substantial amount of degrees of freedom requires many computations to achieve the optimum of the system. In particular, nonlinear structural analysis compels a recursive calculation in limited computational resources. Thus, a powerful tool, which improves the efficiency of analysis in the limitations, may be required. In structural dynamics, various methods related to model order reduction have been developed in the past decades [1–15]. In addition, several mode selection methods to enhance the rate of reduction have been reported in the Refs. [16–19]. Most of them are focused on dynamic analysis. In this paper, we focus on the nonlinear static response of reduced order model with a proper mode selection criterion. To construct the nonlinear reduced order model, modal derivatives [10–14], which are the quadratic enhancement of modal basis, have been employed. The degrees of freedom used to the model reduction have been selected via the singular value decomposition (SVD). Finally, the performance of the selection scheme for the static problem is verified via numerical examples.