Beam Elements with Trapezoidal Cross Section Deformation Modes Based on the Absolute Nodal Coordinate Formulation

In this study, higher order beam elements are developed based on the absolute nodal coordinate formulation. The absolute nodal coordinate formulation is a finite element procedure that was recently proposed for flexible multibody applications. Many different elements based on the absolute nodal coordinate formulation are introduced, but still the beam elements are not able to describe the trapezoidal cross section mode. This leads to the locking phenomena, and therefore, the beam elements based on the absolute nodal coordinate formulation with three dimensional elasticity converge to an inexact solution. In order to avoid the locking phenomena, the trapezoidal cross section deformation mode is included in the beam elements based on the absolute nodal coordinate with additional degrees of freedom. The proper description for the trapezoidal cross section deformation is important for the continuum beam elements based on three‐dimensional elasticity where the material model is often based on general continuum mechanics.