A component-level co-rotational 3D continuum finite element framework for efficient flexible multibody analysis

Abstract

This paper proposes a systematic and novel component level co-rotational (CR) framework, for upgrading existing 3D continuum finite elements to flexible multibody analysis. Without using any model reduction techniques, the high efficiency is achieved through sophisticated operations in both modeling and numerical implementation phrases. In modeling phrase, as in conventional 3D nonlinear finite analysis, the nodal absolute coordinates are used as the system generalized coordinates, therefore simple formulations of the inertia force terms can be obtained. For the elastic force terms, inspired by existing floating frame of reference formulation (FFRF) and conventional element-level CR formulation, a component-level CR modeling strategy is developed. By in combination with Schur complement theory and fully exploring the nature of the component-level CR modeling method, an extremely efficient procedure is developed, which enables us to transform the linear equations raised from each Newton-Raphson iteration step into linear systems with constant coefficient matrix. The coefficient matrix thus can be pre-calculated and decomposed only once, and at all the subsequent time steps only back substitutions are needed, which avoids frequently updating the Jacobian matrix and avoids directly solving the large-scale linearized equation in each iteration. Multiple examples are presented to demonstrate the performance of the proposed framework.