A thin plate element based on the combined arbitrary Lagrange–Euler and absolute nodal coordinate formulations

Abstract

The goal of this study is to expand the combination of the arbitrary Lagrange–Euler (ALE) and absolute nodal coordinate formulation (ANCF) to plate elements. In the ALE–ANCF method, nodal coordinates are not associated with any specific material points. This means that nodal positions in a finite element mesh can be varied during simulations forward in time. This article contains a description of the kinematics and equation of motion of a thin ALE–ANCF plate element. The element kinematics is described using C 1 continuous shape functions and elastic forces are evaluated using a combined membrane and curvature approach. The presented plate element formulation is validated by comparison with a conventional ANCF plate element.