Analysis of Stress and Strain in the Absolute Nodal Coordinate Formulation with Nonlinear Material Behavior

Abstract

The present paper deals with the analysis of strain and stress in the absolute nodal coordinate formulation (ANCF). An accurate stress distribution is needed for the evaluation of comparative strains in nonlinear material behavior. The ANCF has been recently developed and studied by many investigators in the field of flexible multibody dynamics. The ANCF focuses on the modeling of beams and plates including large deformation and represents exact rigid body inertia. The derivation of the equations of motion for an ANCF element is usually based on a solid finite element formulation and thus leads to finite elements that show locking behavior. While the problem of locking in the ANCF might be solved by means of different techniques [1], [2], the accuracy of stress and strain quantities within the element is still poor and needs to be improved in order to incorporate nonlinear material behavior. In the present paper, a higher order element is presented where locking is prevented by means of standard selective reduced integration techniques and the improved order and accuracy of stress and strain quantities is shown in comparison with the original formulation. As an example of nonlinear material behavior, Prandl-Reuss plasticity is included to the absolute nodal coordinate formulation. The results of stress and strain components for the improved higher order element are compared to the solution of fully tree-dimensional computations performed with the commercial software ABAQUS. Good agreement of the ANCF is found with the results of ABAQUS as well as with examples of elasto-plastic multibody systems available from the literature.