Analytically derived matrix end-form elastic-forces equations for a low-order cable element using the absolute nodal coordinate formulation

Abstract

Abstract In everyday, practical, multibody, dynamic simulations, any savings in computational time are welcome. The aim of this paper is to develop an analytical mathematical approach to be used on a low-order element to reduce the computational costs. In this paper the Bernoulli-Euler beam energy formulation is expressed with an absolute nodal coordinate formulation (ANCF) and the general integral equation due to internal strain and bend generalized elastic forces is derived and expressed with the pre-computed matrices. The derived matrices, together with the Gauss quadrature integration, minimize the number of numerical operations when performing a dynamic time simulation. The equations are general and can be used for a cable element, without any restrictions on the strain-bend-displacement relationship. The proposed equations are implemented in the ANCF dynamic model, and the presented numerical results show that savings in the computational time can be achieved.