Comparison of the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation by Means of a Simplified Strain Formulation

Abstract

The floating frame of reference (FFR) formulation and the absolute nodal coordinate (ANC) formulation are often used for the modeling of multibody systems. In the present work a simplified strain model is derived for the ANC formulation which is equivalent to the (small strain) FFR formulation. The simplified strain model is based on a co-rotated reference configuration and the deformation is assumed to be small with respect to this configuration. This configuration is described by a translation vector and a rotation matrix which are both determined from the motion of the body with respect to its fixed reference. The ANC formulation with simplified strain leads to a constant mass matrix. The stiffness matrix consists of two parts: One part depends on the small-strain stiffness matrix of the body in the fixed reference configuration which is rotated by the rotation matrix and a second nonlinear part which depends quadratically on small strains. Both formulations represent displacements and deformations differently but lead to exactly the same results in the case of equivalent floating reference configurations. The relationship of both formulations is compared in a 2D example problem of a rotating hinged plate. A detailed description of the modelling in both cases as well as numerical results are presented.