Analysis of Higher and Lower Order Elements for the Absolute Nodal Coordinate Formulation

Abstract

A higher order and a reduced order element for the analysis of thin beams using the absolute nodal coordinate formulation are investigated. Additional shape functions are introduced for the existing spatial absolute nodal coordinate beam element in order to increase its accuracy. For thin structures where bending stiffness might be still desired, a cable element is introduced and compared with existing formulations using several examples. Cables that experience low tension or catenary systems, where bending stiffness has an effect on the wave propagation, are examples in which the low order element can be used. The cable element, which does not include torsional stiffness, can be very effective in numerous applications and problems such as the formulation of sliding joints in applications such as the spatial pantograph-catenary system.