Analysis of Stress and Strain in the Absolute Nodal Coordinate Formulation

Abstract

Accurate values of stress and strain are required for the evaluation of comparative stresses in nonlinear material behavior. The absolute nodal coordinate formulation (ANCF) has been recently developed and focuses on the modeling of beams and plates under the presence of large deformation. 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 standard techniques, the accuracy of stress and strain quantities within elements is still poor and needs to be improved in order to incorporate nonlinear material behavior. In the present paper, a higher order ANCF 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 integrated in the absolute nodal coordinate formulation. Results of stress and strain components for the improved higher order element are compared to the solution of fully three-dimensional computations performed with the commercial software ABAQUS. Static and dynamic spatial examples are used to investigate the accuracy. 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.