Analysis of high-order quadrilateral plate elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

• Main Authors: Henrik Ebel, Marko K Matikainen, Vesa-Ville Hurskainen, Aki Mikkola
• Format: Article
• Language: English
• Published: SAGE Publishing 2017-06-01
• Series: Advances in Mechanical Engineering
• Online Access: https://doi.org/10.1177/1687814017705069

The absolute nodal coordinate formulation is a computational approach to analyze the dynamic performance of flexible bodies experiencing large deformations in multibody system dynamics applications. In the absolute nodal coordinate formulation, full three-dimensional elasticity can be used in the definition of the elastic forces. This approach makes it straightforward to implement advanced material models known from general continuum mechanics in the absolute nodal coordinate formulation. As, however, pointed out in the literature, the use of full three-dimensional elasticity can lead to severe locking problems, already present in simple, static tests. To overcome these drawbacks and to get a better understanding of these behaviors in the case of absolute nodal coordinate formulation elements, this study introduces and carefully analyses several high-order three-dimensional plate elements based on the absolute nodal coordinate formulation, primarily in meaningful static scenarios. The proposed elements are put to test in various numerical experiments intended to bring forward possible locking phenomena and to evaluate the accuracy attainable with the considered element formulations. The proposed eight- and nine-node elements that incorporate polynomial approximations of second order in all three directions prove to be advantageous both with respect to the actual performance and with regard to the numerical efficiency when compared to other absolute nodal coordinate formulation plate elements. A comparison with a four-node high-order element corroborates the supposition that the usage of in-plane slopes as nodal coordinates has a negative effect on numerical convergence properties in thin-plate use cases. An additional example showcases the functioning of two of the higher-order elements in a dynamic simulation.