Adaptive ANCF method and its application in planar flexible cables

• Published in: Acta mechanica Sinica 2018-02, Vol.34 (1), p.199-213
• Main Authors: Zhang, Yue, Wei, Cheng, Zhao, Yang, Tan, Chunlin, Liu, Yongjian
• Format: Article
• Language: English
• Subjects: Accuracy; Cables; Classical and Continuum Physics; Computational efficiency; Computational Intelligence; Computer simulation; Computing time; Continuity (mathematics); Deformation mechanisms; Efficiency; Engineering; Engineering Fluid Dynamics; Finite element method; Flexible bodies; Interpolation; Mathematical models; Model accuracy; Research Paper; Simulation; Theoretical and Applied Mechanics
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-017-0721-4

In the conventional absolute nodal coordinate formulation (ANCF), the model is pre-meshed, the number, distribution and type of elements are unchangeable during the simulation. In addition, the deformations of a flexible body are space-varying and time-varying, one cannot predict when, where, and how the deformations will occur. Therefore, in order to obtain a satisfactory accuracy during the whole simulation, the model is usually densely meshed, but it will result in a loss of computational efficiency. In this study, an adaptive absolute nodal coordinate formulation (AANCF) is proposed to optimize the accuracy and efficiency of flexible dynamics. The movement features of flexible bodies are analyzed, and the conventional and adaptive ANCF methods are compared. Then the adaptive computation strategy is presented. The discretization errors come from the inability of interpolation functions of individual elements to capture the complexity of the exact solution, so the mesh can be adaptively optimized by changing the element sizes or the orders of interpolation functions during dynamic computation. Important issues of AANCF, including error estimation, mesh updating, and performance of the AANCF model, are analyzed and discussed in detail. A theoretical model of a planar AANCF cable is presented, where the strategies of dividing and merging elements are discussed. Moreover, the continuity of dynamic variables is deduced, and the mean factors that affect the continuity are obtained, which is very important for the subsequent continuity optimization. The simulation results indicate that the distribution of elements varies with time and space, and the elements are denser in large-deformed domains. The AANCF model improved the computational accuracy and efficiency, but the system energy is discontinuous when the elements are merged. Therefore, a continuity-optimized AANCF model is given based on the previous continuity analysis, the results show that the accuracy and continuity of energy are further improved by the continuity-optimized AANCF model.