Dynamic analysis of large rotation and deformation can be carried out using the absolute nodal coordinate formulation. This formulation, which utilizes global displacements and slope coordinates as nodal variables, make it possible to avoid the difficulties that arise when a rotation is interpolated in three-dimensional applications. In the absolute nodal coordinate formulation, a continuum mechanics approach has become the dominating procedure when elastic forces are defined. It has recently been perceived, however, that the continuum mechanics based absolute nodal coordinate elements suffer from serious shortcomings, including Poisson’s locking and poor convergence rate. These problems can be circumvented by modifying the displacement field of a finite element in the definition of elastic forces. This allows the use of the mixed type interpolation technique, leading to accurate and efficient finite element formulations. This approach has been previously applied to two- and three-dimensional absolute nodal coordinate based finite elements. In this study, the improved approach for elastic forces is extended to the absolute nodal coordinate plate element. The introduced plate element is compared in static examples to the continuum mechanics based absolute nodal coordinate plate element, as well as to commercial finite element software. A simple dynamic analysis is performed using the introduced element in order to demonstrate the capability of the element to conserve energy.

The absolute nodal coordinate formulation (ANCF) is a nonlinear finite element approach proposed for the large deformation dynamics analysis of beam- and plate/shell-type structures. In the ANCF approach, elastic forces can be defined using three-dimensional elasticity-based continuum mechanics. This approach is often straightforward, and it makes it possible to use advanced material models in the ANCF framework. However, it has been pointed out in several studies that continuum ANCF-based elements with a full three-dimensional elasticity description can suffer from locking phenomena. In this study, a comparison between various combinations of locking alleviation techniques and their applicability to different ANCF beam variants is studied using numerical examples. Furthermore, the enhanced deformation gradient (EDG) technique, which has been proposed recently in finite element literature, is demonstrated for high-order ANCF beam elements. Based on the numerical tests, none of the currently available techniques are suitable for all types of ANCF elements. The paper also shows that the efficiency and accuracy of the techniques are case-dependent. For the ANCF beam element involving higher-order terms with respect to trapezoidal mode, however, the EDG-based techniques are preferable to reduce locking phenomena.