A novel model order reduction scheme for fast and accurate material nonlinear analyses of large-scale engineering structures

摘要

A new framework is developed for the fast and accurate analysis of large-scale engineering structures considering material nonlinearity. A fundamental linear model is constructed first by assigning nominal linear material parameters for each of the potentially nonlinear elements, and then, for each nonlinear element, a Nonlinear Deviation Force Vector (NDFV) is defined as the difference between the true nonlinear nodal force vector and the vector calculated using the nominal linear material parameters. In this way, the displacement of the nonlinear model can be expressed as a linear combination of a set of basis solutions of the fundamental linear model. These basis solutions include nodal displacement solutions due to the applied load and all unit components of NDFVs of nonlinear elements. Therefore, the values of these NDFVs, as combination coefficients in the displacement expression are the only unknowns for the whole structure and can be determined by considering a much smaller nonlinear equation system. It is noteworthy that no approximation is introduced in the proposed model order reduction scheme and the new scheme can be applied to the iterative solution process of both static and dynamic problems. Numerical examples are presented to show the effectiveness of the proposed scheme.