Model order reduction of multibody system dynamics based on stiffness evaluation in the absolute nodal coordinate formulation

Abstract

Although various studies on reduced-order modeling (ROM) of flexible multibody dynamics have been conducted, the issue of efficiency still exists. Significant computational resources are required in order to handle rigid body motions and inertia forces along with the flexibility of each body. The absolute nodal coordinate formulation (ANCF) uses only the absolute values in global coordinates to describe the flexible motions of multibody dynamics. While the other conventional formulations have nonlinearities in mass matrices and inertia forces, the nonlinearities are concentrated in the internal forces in the ANCF formulation, which is analogous to the equations of nonlinear structural dynamics. This enables ANCF approaches to embrace the various ROM techniques that have been developed for nonlinear structural analysis. This paper adopts stiffness evaluation methods, which represent nonlinear internal forces as the sums of third-order polynomial displacements, in order to enhance the efficiency of the ANCF approach. A stiffness evaluation method based on element connectivity is proposed to improve the low efficiency of the conventional method and is combined effectively with an ROM technique without loss of accuracy. The proposed reduction method, which is referred to as SEECROM, is utilized smoothly with ANCF beam elements. A number of examples including a four-bar mechanism are demonstrated to verify the efficiency and accuracy of the proposed method.