Component-level proper orthogonal decomposition for flexible multibody systems

Abstract

Nonlinear finite element methods such as isogeometric analysis and absolute nodal coordinate formulation can be applied to modeling the flexible multibody systems (FMBS) subject to both large rotation and deformation. However, the computational expense is prohibitive for complex systems, especially for a parameterized FMBS. Proper orthogonal decomposition (POD), nonmodal model order reduction (MOR) technique, has been widely applied to nonlinear problems in order to reduce the computational expense of simulating the dynamic responses of FMBSs. This paper presents a component-level POD method, which applies the singular value decomposition process to snapshots of each component of an FMBS and utilizes constraint equations to satisfy the connecting conditions among the components. Furthermore, the paper provides a systematic study of the parameterized MOR (PMOR) for an FMBS, including the reduction of the constraint equations, energy conserving mesh sampling and weighting (ECSW), and the greedy-POD method. The ECSW method aims to further reducing the computational cost of matrix multiplications for evaluating the reduced stiffness matrix. Greedy-POD is applied to get a robust set of reduced order bases with parametric changes in simulation. Finally, three numerical examples validate the feasibility of the component-level POD as well as the whole PMOR process for an FMBS, thereby demonstrating that the component-level POD performs better numerical simulations in accuracy computational costs than the classical POD.