A Space-Time Absolute Nodal Coordinate Formulation Cable Element and the Study of Its Accuracy and Efficiency

Abstract

In this paper, a space-time absolute nodal coordinate formulation cable (SAC) element forming technique based on the Lagrange family of shape functions is proposed. Two distinct SAC elements, each with a distinct spatial shape function, have been generated by this method. Moreover, the external forces such as the bending moment and the air resistance formula have been accounted for. The Lagrange multiplier method, along with the concepts of replacement constraint and supplementary constraint, has been employed to provide a solution for the dynamics of constrained mechanical systems. Additionally, a constraint conversion strategy has been suggested. The solver has been constructed through Hamilton’s law of varying action. The space-time finite element method is used to solve dynamic problems, employing the Newton algorithm and quasi-Newton algorithm. The accuracy and efficiency of the solution has been verified by three simulations and one experiment. The circle-bending static simulation and the double-ended velocity impact dynamic simulation demonstrate the accuracy of the two elements. The correlation between statics and dynamics has been studied for different discretization methods and different solvers’ calculation accuracy and efficiency. Different modeling methods, time steps, order and the application of the quasi-Newton method all have a bearing on the efficiency of the solution. Finally, a comparison with an experiment in the free-pendulum simulation reveals the capability of this model to simulate dynamic problems with air resistance.