Absolute Nodal Coordinate Formulation Method Research Articles

Dynamics modeling and experiment of a large space umbrella truss structure

This paper studies the dynamics of a large space umbrella truss structure (SUTS) by using a flexible multibody dynamic method. The SUTS is treated as a rigid-flexible multibody system that consists of a number of horizontal and vertical elastic rods, and connecting rigid joints. A SUTS model is established by the absolute-coordinate-based (ACB) modelling strategy, which is composed of the methods of natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF). The NCF method is adopted to describe the global motions of the rigid joints, while the ANCF method accounting for the large displacement and large deformation is utilized to establish the dynamic model of the elastic rods. The method of Lagrangian multipliers is used to obtain the dynamic equations of the system, which are solved based on the generalized-alpha method. The accuracy of the established SUTS model is verified via the ground air-bearing vibration experiment. Finally, numerical case studies are presented for investigating the dynamics of the SUTS model by comparisons.

Numerical and Experimental Study on the Dynamics of the Tendon/Top Tension Riser System of a Tension-Leg Platform

In this study, the dynamics of the tendon/top tension riser (TTR) system of a tension-leg platform (TLP) are investigated through an experiment and by using absolute nodal coordinate formulation (ANCF). First, the model test of the TLP system is conducted in the water tank of Harbin Engineering University to examine the motion response of the TLP and the dynamic response characteristics of the tendon and TTR. The test scale ratio is set to 1: 66.3. Then, on the basis of the ANCF, the stiffness, external load, and mass matrices of the element are deduced to establish the motion equation of the tendon/riser. Finally, the static and dynamic characteristics of the tendon/TTR system of TLP are analyzed systematically by using the ANCF method. The results are compared with commercial software and test results. The motion response of tendon/TTR is affected by the TLP movement and environmental load simultaneously. The analysis proves the effectiveness and accuracy of the ANCF method despite the low number of riser units, suggesting the superiority of the ANCF method for calculating the dynamics of tendon/riser in the field of ocean engineering.

Application of Absolute Nodal Coordinate Formulation in Calculation of Space Elevator System

The space elevator system is a space tether system used to solve low-cost space transportation. Its high efficiency, large load, reusability and other characteristics have broad application prospects in the aerospace field. Most of the existing mechanical models are based on “chain-bar” and a lumped mass tether model, which cannot effectively reflect the flexible behaviour of the rope of space elevator system. To establish an accurate mechanical model, the gradient deficient beam elements of the absolute nodal coordinate formulation (ANCF) are used to build the mechanical model of the space elevator system. The universal gravitation and centrifugal force in the model are derived. The calculation results of the ANCF model are compared with the results of the finite element method (FEM) and lumped mass (LM) models. The results show that the calculation results of the ANCF method are not very different from the results of the FEM and LM models in the case of axial loading. In the case of lateral loading, the calculation results of the ANCF method are basically the same as the results of the FEM and LM models, but can better reflect the local flexible deformation of the space elevator rope, and have a better calculation stability than FEM. Under the same calculation accuracy, the ANCF method can use fewer elements, and the speed of convergence is faster than the FEM and LM models.

Numerical Investigation of Dynamics of the Flexible Riser by Applying Absolute Nodal Coordinate Formulation

Abstract In this paper, the dynamics of the flexible riser are investigated based on the absolute nodal coordinate formulation (ANCF). The stiffness, generalized elastic force, external load, and mass matrixes of the element are deduced based on the principle of energy conversion and assembled with the finite element method. The motion equation of the flexible riser is established. The influence of the environmental load conditions on the flexible riser model is studied in the MATLAB environment. Moreover, the accuracy and reliability of the programs are verified for a beam model with theoretical solutions. Finally, the static and dynamic characteristics of the flexible riser are analyzed, systematically adopting the ANCF method, which in turn proves the effectiveness and feasibility of the ANCF. Therefore, the proposed method is a powerful scheme for investigating the dynamics of flexible structures with large deformation in ocean engineering.

A Response Spectrum Analysis of Wind Deflection in Railway Overhead Contact Lines Using Pseudo-Excitation Method

The wind deflection of overhead contact lines (OCLs) challenges the stable and safe operation of electrified railways. The steady wind causes the static deflection of the contact line, while the fluctuating wind leads to the OCL buffeting. This paper performs a response spectrum analysis of the wind deflection caused by the combined effects of steady and fluctuating winds. Considering the initial configuration of OCL, an absolute nodal coordinate formulation method is employed to model the OCL. A spatial wind field including the fluctuating wind in three directions is constructed and the aerodynamic forces on the OCL are derived. A nonlinear solution procedure is proposed to include the geometrical nonlinearity and dropper slackness in the evaluation of static wind deflection. The pseudo-excitation method is utilised to evaluate the buffeting response of the OCL with stochastic wind load. The analysis results indicate that the dropper slackness has a significant effect on the vertical static deflection. Under an extreme wind speed of 40 m/s, the contact line is always within the safe working range of pantograph head when only the steady wind load is considered. However, the stochastic wind load causes non-negligible fluctuation of OCL, and the contact line may be outside of the pantograph working range under the same wind speed. Sensitivity analyses on the effects of some key parameters to the OCL buffeting suggest that the increases of damping ratio and the tension class are effective measures to improve the wind-resistance capability of OCL.

Dynamics of a tethered satellite formation for space exploration modeled via ANCF

This paper studies the dynamics of a spinning three-body tethered satellite formation by a flexible multibody dynamics method. The tethered system is specially designed to constitute a Space Infrared Interferometric Telescope for a space exploration mission. Two sub-satellites are deployed from the main-satellite by using long flexible tethers and moving along trajectories of Archimedes spirals. Both of the large displacement and large deformation of the variable-length tethers are described by utilizing the Absolute Nodal Coordinate Formulation method in a framework of Arbitrary Lagrange-Euler (ANCF-ALE) description. The Natural Coordinate Formulation (NCF) method is used for describing the overall rigid motions of the three satellites. Considering the mass flow of tether element, the dynamic equations of tether element are derived by using the D'Alembert's principle. The governing dynamic equations of the system are obtained with a method of Lagrange multipliers. The tether deployment is achieved by regulating deployed velocity and applied jet forces. Numerical case studies are presented for investigating the parametric influences on the deployment dynamics of the tethered system by comparisons.

Nonlinear Large Deformation of Graphene Sheets Using a Nonlocal-Based ANCF Method

A novel nonlinear model of single-layered graphene sheets (SLGSs) subject to large deformation is proposed using the absolute nodal coordinate formulation (ANCF) and the nonlocal elasticity theory. The geometrical definition of SLGSs is described by ANCF thin plate element while the strain energy is expressed by nonlocal theory. Then, the formulation of elastic force and the Jacobian of the elastic force is derived. We verify the proposed model by comparing the results with other published results and conduct corresponding numerical case study to clarify the influence of boundary conditions (BCs), nonlocal parameters, side length and aspect ratio. Large deformation problem of SLGSs with several BCs and different loading modes are simulated to study the mechanical nonlinearity of the SLGSs.

Large Deformation and Vibration Analysis of Microbeams by Absolute Nodal Coordinate Formulation

This investigation uses the absolute nodal coordinate formulation (ANCF) method to solve statics and dynamics of microbeams for the first time. A comprehensive model for the investigation of statics and dynamics of microbeams by using gradient deficient elements of the ANCF and modified couple stress theory (MCST) is developed. The vibration equations of a planar hub-microbeam system with constant angular rotations are derived considering the static equilibrium. Accuracy of the ANCF method for microbeams is demonstrated. Large deformation problems of cantilever microbeams are solved and the influences of material length scale on beam deformation are studied. When the beam thickness becomes smaller, the deflection of the microbeam calculated by the current model is smaller, and the size effect becomes more significant. The size effect only has influence on the bending vibration of the microbeam. The variations of the angular speed as well as the scale parameter can trigger frequency veering phenomena. The present work could be used in dynamic or vibration predictions for microelectromechanical systems (MEMS) with both large displacements and large deformations.

Adaptive ANCF method and its application in planar flexible cables

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.

Analyses of the overhead-line cable stringing and sagging on hilly terrain with an absolute nodal coordinate formulation

The method of absolute nodal coordinate formulation (ANCF) is used to solve the problem of determining the cable sags and the forces during the cable stringing and sagging process for overhead lines. The problem of calculating the sagging tables due to the temporary supporting cable sheave deflection during the construction phase is emphasized on hilly terrain. Two different models for the contact point between the cable and the sheave are analyzed. The most important advantage of this newly proposed approach is that it opens up the possibilities for analyzing more complex overhead-line structures that are a consequence of the line compaction, e.g., using unconventional insulating applications. The paper describes the basic steps of an ANCF algorithm to solve the presented problem. It also provides numerical examples in order to verify the ANCF method by comparing it with the results of other known approaches based on catenary equations.

Modeling and Analysis of Wire Rope in the Drilling Device Using ANCF Method

The wire rope of drilling device is modeled by using absolute nodal coordinate formulation (ANCF) which is presented for the analysis of three dimensional flexible cable in this paper. This formulation is suited for the analysis of large rotation and deformation problem. Only axial and bending deformations are taken into account in this paper, which increases the computational efficiency without affecting the precision. Vibrations of the drilling mechanism and the wire rope under different preloads are simulated. It can be seen from the emulational results that resonance will occur when the preload increases to a certain value and the amplitude is the largest in this case.

Behavior of thin rectangular ANCF shell elements in various mesh configurations

The absolute nodal coordinate formulation (ANCF) is characterized by being developed specifically for dynamic analysis of large deformation problems. The objective of the study is to investigate how the shape of the initial mesh configuration influences the obtained numerical solution. After a thorough review of three available formulations, they are used in three different convergence studies. Initially a reference study is conducted to determine how the ANCF performs in an uniform and rectangular mesh. Subsequently, the ANCF methods sensitivity to irregular mesh is investigated and finally, the ability of the ANCF method to describe curved structures is evaluated. This study concludes that thin ANCF shell elements are sensitive to both the initial shape and their loading condition. Furthermore, both the initial configuration and the loading condition affect how the ANCF-based models converge. It is suggested that models containing thin ANCF shell elements are subjected to extensive validation studies, before they are used in a design process.

A thin plate element based on the combined arbitrary Lagrange–Euler and absolute nodal coordinate formulations

The goal of this study is to expand the combination of the arbitrary Lagrange–Euler (ALE) and absolute nodal coordinate formulation (ANCF) to plate elements. In the ALE–ANCF method, nodal coordinates are not associated with any specific material points. This means that nodal positions in a finite element mesh can be varied during simulations forward in time. This article contains a description of the kinematics and equation of motion of a thin ALE–ANCF plate element. The element kinematics is described using C1 continuous shape functions and elastic forces are evaluated using a combined membrane and curvature approach. The presented plate element formulation is validated by comparison with a conventional ANCF plate element.

Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods

This paper employs a new finite element formulation for dynamics analysis of a viscoelastic flexible multibody system. The viscoelastic constitutive equation used to describe the behavior of the system is a three-parameter fractional derivative model. Based on continuum mechanics, the three-parameter fractional derivative model is modified and the proposed new fractional derivative model can reduce to the widely used elastic constitutive model, which meets the continuum mechanics law strictly for pure elastic materials. The system equations of motion are derived based on the absolute nodal coordinate formulation (ANCF) and the principle of virtual work, which can relax the small deformation assumption in the traditional finite element implementation. In order to implement the viscoelastic model into the absolute nodal coordinate, the Grunwald definition of the fractional derivative is employed. Based on a comparison of the HHT-I3 method and the Newmark method, the HHT-I3 method is used to solve the equations of motion. Another particularity of the proposed method based on the ANCF method lies in the storage of displacement history only during the integration process, reducing the numerical computation considerably. Numerical examples are presented in order to analyze the effects of the truncation number of the Grunwald series (fading memory phenomena) and the value of several fractional model parameters and solution convergence aspects.