DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION

The objective of this study is to develop simple and accurate elastic force models that can be used in the absolute nodal co-ordinate formulation for the analysis of two-dimensional beams. These force models which account for the coupling between bending and axial deformations are derived using a continuum mechanics approach, without the need for introducing a local element co-ordinate system. Four new different force models that include different degrees of complexity are presented. It is shown that the vector of the elastic forces can be significantly simplified as compared to the elastic force model developed for the absolute nodal co-ordinate formulation using a local element frame [1]. Despite the simplicity of the new models, they account for elastic non-linearity in the strain–displacement relationship. Therefore, they lead to more accurate results as compared to the more complex models developed using the local frame method which does not account for the non-linearities in the strain–displacement relationships. Numerical results are presented in order to demonstrate the use of the new models and test their performances in the analysis of large deformations of flexible multibody systems.