Merging nonlinear finite element models and the floating frame of reference formulation

Abstract The current state of the art floating frame of reference formulation is used for flexible multibody dynamics simulations. In this formulation, the flexibility is modelled using linear finite element models with respect to a moving frame. Nevertheless, taking into account higher order terms locally can be important for the purpose of modelling moderate to large strains within a body. Nonlinear finite element models contain such terms. In this work, it is explained how the floating frame of reference formulation and the nonlinear finite element formulation can be merged to obtain the best of both worlds. A new nonlinear finite element formulation is developed relative to a body’s floating frame. This is used to find expressions for the internal elastic loads and tangent stiffness matrix. Both expressions contain all possible higher order terms and can be used in the incremental solution procedures for static and dynamic simulations. The new formulation is developed such that when these higher order terms are neglected, a floating frame formulation is obtained in terms of the absolute interface coordinates. Hence, this work enables inclusion of carefully selected higher order terms in the floating frame formulation for specific applications. In this way, the floating frame of reference formulation allows for higher order terms while at the same time model order reduction techniques can still be applied.