Absolute Nodal Coordinate Formulation Research Articles

Effects of vertical and lateral riser-soil interactions on vortex-induced vibration of a steel catenary riser

A numerical model for computing the vortex-induced vibration (VIV) and fatigue damage of steel catenary risers (SCRs) was developed. The structural dynamics were accurately simulated using an absolute nodal coordinate formulation (ANCF). The Van der Pol wake oscillator is applied to generate the fluctuating lift, which is further transformed into the cross-flow direction by considering the structural deformation. The Randolph-Quiggin (RQ) model and the Coulomb friction ‘bilinear’ model are employed to simulate the vertical and lateral riser-soil interactions, respectively. After case validations, the effects of riser-soil interaction on the VIV amplitude, frequency, mode, and fatigue of the SCR at different current angles are investigated, and a sensitivity study of different seabed model parameters is discussed. The bands of significant VIV frequencies were broadened by riser-soil interactions, accompanied by more frequency components of disturbance and more abundant vibration modes. Severe fatigue damage cannot be captured by the truncated model, and seabed models that require improvement are ignored. It is suggested that vertical and lateral riser-soil interactions should be considered in the evaluation of VIV fatigue damage for SCRs.

Dynamic modeling of flexible multibody systems with complex geometry via finite cell method of absolute nodal coordinate formulation

Dynamic modeling of flexible multibody systems with complex geometry via finite cell method of absolute nodal coordinate formulation

Deployment Simulation of Foldable Membranes Using Absolute Nodal Coordinate Formulation and Validation

It has become a trend to use foldable membranes to construct large spacecraft structures such as solar sails, antennas, and drag sails with the advantages of being lightweight and having high packing efficiency. To enhance the existing numerical simulation of membrane deployment, the nonlinear behavior of the crease is finely described based on experiments and integrated into the numerical model via the principle of virtual work. Specifically, a foldable membrane is modeled as a multibody system (MBS) based on the absolute nodal coordinate formulation (ANCF), where the flexible facet is meshed with both ANCF triangular and quadrilateral thin shell elements and the crease is treated as a virtual torsional spring with special constraints along the fold line. The MBS modeling method is validated via the deployment experiment of a Z-folding membrane. The deployment of a four-unit Miura-ori membrane is further analyzed to show the capability of the approach in modeling foldable membranes with complicated configurations. Good agreement is obtained on the membrane-deformed configurations between the simulation and experiment. Additionally, the driving force at the corners is obtained. This research is expected to provide a more accurate simulation to facilitate the design and optimization of the space deployable membrane structure.

High-fidelity flexible multibody model considering torsional deformation for nonequatorial space elevator

Space elevators are a promising technology for future space transportation. The primary component of a space elevator is a tether deployed from a geostationary orbit towards the Earth and into deep space. Payloads can be transported using a climber moving along the tether. However, obtaining a deeper comprehension of the precise dynamics of a space elevator is challenging. The tether could have various deformations such as elongation, bending, and torsion owing to its flexible nature and the low level of vibration damping in space. Therefore, understanding those effects on the tether is essential for the design concept of a space elevator. Reproducing the behavior of space tether systems on the ground is challenging, which is primarily due to the scale of the system and the difficulty of accurately replicating a space environment. Thus, high-fidelity numerical analysis methods are required to analyze the dynamic response of space elevators precisely. Previously proposed analysis models of space tether systems with climbers have focused on elongation, bending, and rigid body motion of the tether, and the effect of torsional deformation has been neglected. However, a tether can be twisted easily owing to its low torsional stiffness. This study established high-fidelity numerical simulation models for space elevators considering large deformations including the torsion of a tether. This study developed a flexible multibody model with a moving climber using the absolute nodal coordinate formulation with 14 degrees of freedom. Further, the gravitational perturbation caused by the non-sphericity of the Earth was considered. Using the constructed model, the motion and deformation of nonequatorial space elevators caused by the climber motion and the disturbance in the space environment were investigated. The obtained results indicate that gravitational perturbation can induce torsional deformation, particularly at higher anchor latitudes.

Research on cable dynamic response of a catenary anchor leg mooring system based on ANCF

This paper presents a dynamic analysis model for a catenary anchor leg mooring (CALM) system based on the absolute nodal coordinate formulation (ANCF) method, combined with continuum mechanics and finite element theory. This model uses absolute slope coordinates instead of traditional angle coordinates to better describe the large deformation and large displacement of the cables. The paper derives the element mass matrix, generalized stiffness matrix, and the element external load matrix, including the Morison force transformed into the ANCF framework, based on the virtual work principle. The accuracy and reliability of the ANCF program are validated using static and dynamic beam models, as well as submerged tether models. Furthermore, a comparative analysis of the ANCF mooring cable model with OpenFAST and MoorDyn accentuates the program's practical value in real engineering applications. Finally, we systematically analyzed the dynamic characteristics of a CALM single-point mooring system, revealing that the mooring forces in the cables significantly influence the high-frequency motion of the buoy. Additionally, the reduction in the length of the mooring cables, to an appropriate extent, enhances the stability of the system, which further attests to the effectiveness and practicality of the ANCF model that has been developed.

Deployment dynamics and experiments of a tendon-actuated flexible manipulator

The quantity of space debris on Earth orbit has escalated tremendously in recent years, presenting a significant hazard to human space operations. It is urgent to develop effective measures to capture and remove various space debris. For this purpose, this paper presents a tendon-actuated flexible deployable manipulator. The flexible manipulator consists of several deployable units connected by Cardan joints and actuated by tendons. Compared with the present technologies for capturing space debris such as rigid robotic arm or flying net, this flexible manipulator is deployable, reusable, lightweight and applicable to the capture of large space debris. In order to investigate its deployment dynamics, an accurate dynamic model of the flexible manipulator is established based on the natural coordinate formulation (NCF) and the absolute nodal coordinate formulation (ANCF). Subsequently, numerical simulations are carried out to study the effects of system parameters and the base satellite on its deployment dynamics. Finally, ground experiments for both deployment and bending of the flexible manipulator are conducted to verify its effectiveness and feasibility.

Dynamic modeling of a soft robotic fish driven by dielectric elastomer based on the ANCF and IB-LBM

Dielectric elastomer (DE) is an intelligent and pliable material that exhibits significant deformation when subjected to an electric field. It possesses attributes such as remarkable strain, exceptional energy density, rapid responsiveness, and minimal weight, making it uniquely advantageous in the propulsion of bionic fish. Due to the nonlinearity and large deformation characteristics of DEs, it is challenging to accurately describe their complex deformations. The absolute nodal coordinate formulation (ANCF) possesses notable advantages in precisely depicting phenomena entailing substantial deformation and displacement. This paper focuses on the study of a bionic robotic fish driven by dielectric elastomer actuators (DEAs) based on body/caudal fin (BCF) propulsion, wherein the fish body is delineated as a laminated beam structure. By combining the ANCF higher-order beam element with the DE constitutive model and the neo-Hookean hyperelastic constitutive model, the dynamic equations of the laminated beam are derived. The interaction between the bionic fish and the fluid is effectively handled through the implementation of the immersed boundary - lattice Boltzmann method (IB-LBM), and by combining ANCF with IB-LBM, the dynamic responses of the fish under voltage excitation and fluid resistance are simulated and analyzed. This study would contribute to the exploration of the intricate mechanism behind the substantial amplitude motion of bionic robotic fish driven by DEAs, yielding valuable insights for further research endeavors.

Theoretical modeling and dynamics analysis of a rotating piezoelectric laminated beam with different setting angles

Dynamics modeling and analysis of a rotating piezoelectric laminated beam (RPLB) considering the effect of the setting angle is presented in this paper. The rotating piezoelectric energy harvester can be simplified as a RPLB which is fixed at a rotating hub. It is easy to know that a steady transversal deformation would be produced due to the transversal component of centrifugal force when the beam is not along the radial direction (the setting angle is not equal to 0° or 180°). However, the variation of steady transversal deformation and its effect were rarely considered by existing theoretical models about the rotating harvesters. To this end, a novel nonlinear dynamics model of the RPLB is developed by the combination of floating frame reference (FFR) and absolute nodal coordinate formulation. In the model, the position coordinates and gradients on the FFR are used as the nodal coordinates to describe deformation field. The enthalpy, elastic and kinetic energies of the RPLB are derived with consideration of the piezoelectric constitutive equation and the rotation of the FFR. Thus, the dynamics equations of the RPLB can be developed by using the Lagrange's equations of second kind. The results obtained from the model show agreement with those obtained from the previous literatures, which verifies the correctness of the model. Several examples are presented to analyze the effects of rotating speed, setting angle and tip mass on steady transversal deformation, output voltage and modal characteristics.

Multi-body dynamical modeling and prediction of flexible origami/kirigami structures by affine transformation

A generalized multi-body dynamical modeling method of Origami/Kirigami structures considering the elastic–flexible coupling of surfaces and nonlinear creases is proposed. For different structures with complex spatial configuration and constraints, an Affine Transformation (AT) technique based on Absolute Nodal Coordinate Formulation (ANCF) is proposed to make the modeling more convenient and efficient. The surfaces are discretized by triangle reduced elements, and the constitutive relations of creases are described by nonlinear state-dependent torque constraints. The proof of the topological invariance of configurations is also given. The simulation of the folding capacity and dynamic behaviors on two Origami structures, Origami solar array mechanism, and enclosed Yoshimura Origami, are given, which verifies the effectiveness of the modeling method. Additionally, the quantitative dynamic behaviors contributes to the design principle of a Kirigami structure for multi-stability. Comparisons between theoretical results from modeling and experiments demonstrate the effectiveness of the modeling method and crease design. The AT-ANCF lays a theoretical foundation for dynamic prediction and design for large deformation Origami/ Kirigami structures, which has significant potential applications in dynamic properties design in the fields of aerospace, robotic etc.

Adaptive ANCF method described by arbitrary Lagrange-Euler formulation with application in variable-length underwater tethered systems moving in limited spaces

The nonlinear effect of the variable-length cable may dominate the design of Remotely Operated Vehicles (ROVs) due to the interaction between the flexible cable and surroundings, especially when moving in limited spaces. This paper develops a novel adaptive Absolute Nodal Coordinate Formulation (ANCF) described by Arbitrary Lagrange-Euler (ALE) formulation to investigate the nonlinear dynamics of variable-length underwater tethered systems going across obstacles. The adaptive element techniques are adopted to efficiently simulate the moving contact. Fine meshes are generated autonomously to capture the detailed contact behaviors in contact areas while coarse meshes emerge in non-contact areas, thus significantly reducing DOFs and contact pairs. Additionally, the precontact searching algorithm based on the axis-aligned bounding box (AABB) is employed for the acceleration of the contact detection, which is crucial when element number increases as the mass flow. Combined with the experimental records and analytical solutions in two numerical examples, the accuracy and efficiency of the proposed methodology are further assessed by a comprehensive comparison among the fine, coarse, and adaptive mesh results. The numerical algorithm provides an efficient means for developing a feed-forward controller to compensate the nonlinear cable effects on ROVs when moving in limited space.

Modeling and vibration control of a rotating flexible plate actuated by MFC

The macro fiber composite (MFC) is a novel piezoelectric intelligent material, which is widely used in the field of vibration control due to its flexibility and larger actuation forces than PZT. In this paper, a laminated plate model considering the anisotropy of MFC is developed and applied to the vibration control of a rotating plate. The laminated plate is defined as a layerwise model, which deformation is described by the Absolute Nodal Coordinate Formulation (ANCF). The MFC laminated plate element contains 48 degrees of freedom (DOFs) where the effect of MFC element can be internally incorporated without increasing the DOFs of system. Simultaneously, a neural network PD control is adopted to control the vibration of the rotating plate. Eventually, static, dynamic, and modal analyses are performed to investigate the effects of different parameters. Several vibration simulations are carried out to illustrate the ability of MFC patches on vibration control. The findings in this article would be applied to mechanical prediction and control for rotor blades of helicopters, solar panels, etc.

Absolute Nodal Coordinate Formulation-Based Shape-Sensing Approach for Large Deformation: Three-Dimensional Beam

In recent years, fiber-optic shape sensing, which means reconstructing the deformation state of structures from strain information measured by fiber-optic sensors, has attracted interest from many fields. Most of the existing shape-sensing research for flexible three-dimensional (3D) slender structures is based on simple strain-curvature transformation, relying on standardized substrates with a circular cross section and particular forms of fiber layouts. To develop a more general shape-sensing method that can be applied to a wider range of practical engineering conditions, in this paper, the strain–displacement relationship of 3D slender structures under the effect of multiple deformation modes coupling is described by introducing absolute nodal coordinate formulation element, and the deformation reconstruction problem is reorganized into a nonlinear optimization problem that can be applied to large deformation and accommodates different cross-sectional shapes and optical fiber layouts. Due to the rapid increase in the calculation difficulties of nonlinear optimization problems with the number of variables, an element-by-element solving strategy is adopted, and nodal degrees of freedom that have less influence on the overall shape of the structure are merged. In addition, in order to address the issue of local strain anomalies caused by unmodeled factors such as section warping, the pointwise matching between the theoretical strains and measured strains is relaxed to an average matching in subregions to capture the overall deformation, improving the robustness and computational efficiency of the solution process. The accuracy and computational performance of the proposed method are verified through numerical simulation and experiment.

Deep CNN-Based Static Modeling of Soft Robots Utilizing Absolute Nodal Coordinate Formulation.

Soft continuum robots, inspired by the adaptability and agility of natural soft-bodied organisms like octopuses and elephant trunks, present a frontier in robotics research. However, exploiting their full potential necessitates precise modeling and control for specific motion and manipulation tasks. This study introduces an innovative approach using Deep Convolutional Neural Networks (CNN) for the inverse quasi-static modeling of these robots within the Absolute Nodal Coordinate Formulation (ANCF) framework. The ANCF effectively represents the complex non-linear behavior of soft continuum robots, while the CNN-based models are optimized for computational efficiency and precision. This combination is crucial for addressing the complex inverse statics problems associated with ANCF-modeled robots. Extensive numerical experiments were conducted to assess the performance of these Deep CNN-based models, demonstrating their suitability for real-time simulation and control in statics modeling. Additionally, this study includes a detailed cross-validation experiment to identify the most effective model architecture, taking into account factors such as the number of layers, activation functions, and unit configurations. The results highlight the significant benefits of integrating Deep CNN with ANCF models, paving the way for advanced statics modeling in soft continuum robotics.

Development of inverse static model of continuum robots based on absolute nodal coordinates formulation for large deformation applications

AbstractContinuum robotics has emerged as a prominent trend within the robotics field for about two decades. Nevertheless, motion analysis of continuum robots based on dynamic modelling remains severely limited. In the realm of continuum robots, it is obvious that simplified theoretical models or first-order approximations utilizing springs and dampers are insufficient for capturing the dynamics of soft-bodied structures. This inadequacy is especially apparent in applications involving significant deformations in 3D space, continuous actuation, and interface effects. In this regard, the development of precise theoretical models is crucial. Within this particular framework, the paper presents the absolute nodal coordinates formulation (ANCF) to construct the kinematic models of continuum robots. The transformation between the structural, body, and element coordinate systems, as well as the derivation of the generalized external forces and moments using the principle of virtual work and the velocity gradient tensor, are demonstrated. Additionally, it proceeds to develop the strain measures required for the computation of the elastic forces of elements with circular cross sections, ultimately enabling the construction of the Forward Static Model (FSM) of continuum robots. A procedure based on B-spline surface geometry is proposed to figure out the robot shapes in space and generate the necessary nodal coordinates and gradients of ANCF elements. Finally, the inverse static model (ISM) of the ANCF-B-spline generated structure is presented using an iterative solution approach. The effectiveness of the proposed model is evaluated by the analysis of numerical examples. According to the numerical results, it can be inferred that the ANCF method well captures the modelling aspects of continuum robots. The results obtained from the FSM demonstrate a high level of accuracy, moreover, the driving forces based on the ISM provide, from a practical standpoint, satisfactory results.

Dynamics analysis of a rigid-flexible-liquid coupled satellite antenna system via absolute nodal coordinate formulation curvature continuity constraints

Typically, Euler and Lagrangian approaches are primarily used in fluid dynamics and multibody system (MBS) dynamics models, respectively. Absolute nodal coordinate formulation (ANCF), as a Lagrangian nonlinear finite element method (FEM), can effectively handle large deformation problems and incorporate the arbitrary Lagrange-Eulerian (ALE) method for fluids turbulence and breaking. Therefore, we have established a rigid-flexible-liquid coupled satellite antenna system dynamics model via ANCF. Navier-Stokes equations and virtual work principle are applied to formulate the fluid-structure interaction (FSI) dynamics equations. A penalty function is used to describe liquid incompressibility. Bi-directional FSI effects are solved simultaneously and brick fluid element elastic force is validated with reference experiments. Moreover, we introduce curvature continuity constraints to make the liquid free surface continuous. Results indicate that curvature continuity constraints can smoother liquid free surface and eliminate the protrusions and depressions caused by assembling brick fluid elements. Furthermore, we achieve simulation results consistent with reference experiments by using fewer elements with curvature continuity constraints. In addition, due to bi-directional FSI effects, liquid sloshing will magnify satellite antenna vibrations and simultaneously oscillate the advancing tank.

Three-dimensional dynamics of supported pipe conveying fluid with arbitrary initial spatial shape

In order to meet different requirements of engineering applications, pipes conveying fluid usually have the geometric characteristic of a spatial initial shape. In this paper, a three-dimensional theoretical model based on absolute node coordinate formulation (ANCF) is proposed to analyze the dynamical behavior of spatial pipes conveying fluid with arbitrary initial shape. By introducing the spatial Frenet frame as the local coordinate, the global coordinate of each point on the pipe centerline is intuitively represented first. Considering the tensile, torsional and bending deformations of the pipe, the governing equations of spatial pipes conveying fluid are derived by means of the generalized Lagrange equation. Then the process of solving nonlinear static deformation, natural frequencies and nonlinear dynamic responses of the pipe is given. Further, by comparing the results calculated by the ANCF method with those of previous studies on straight and curved pipes, the effectiveness of the proposed three-dimensional ANCF model is verified. Finally, the nonlinear responses and natural frequencies of spatial pipes with three different initial shapes are calculated and some of them are compared with the results obtained using finite element simulations. The results show that the three-dimensional ANCF model proposed in this study has good feasibility and wide application prospect in nonlinear dynamics analysis of fluid-conveying pipes with complex initial shapes.

Structure Dynamic Analysis of C-9 Parachute Using Absolute Nodal Coordinate Formulation Thin Shell Element

In parachute fluid structure interaction (FSI) simulation, traditional parachute structure discrete methods including classic finite element method and mass-spring-damp method suffers from its large computational cost and deficiency in describing material property. This paper develops a generic shell element based on absolute nodal coordinate formulation (ANCF) to model parachute canopy to reduce computation resources and retain membrane strain/stress analyzing capability. We conduct multiple validation cases of ANCF plate and shell element and compare with current literature, in which large deformation configuration and stress distribution have been verified. A 1/4 C-9 parachute canopy inflation process by uniform pressure is simulated by discretizing into 7 ANCF shell and 84 shell element, for which the number of element discretization reduces to 1/10 than classic FEM and computational cost is considerably reduced using band sparse matrix solving technique.

Mechanically induced temperature oscillations in the coupled thermo-elasticity analysis of articulated dynamical systems

This article discusses a new approach for predicting and quantifying mechanically induced temperature oscillations in the coupled thermo-elasticity analysis of articulated mechanical systems (AMS). In this approach, the constrained equations of motion are solved simultaneously with discrete temperature equations obtained by converting heat partial-differential equation to a set of first-order ordinary differential equations. Dependence of the temperature gradients and their spatial derivatives on the position gradients, spinning motion, and curvatures is discussed. The approach captures dependence of the temperature-oscillation frequencies on the mechanical-displacement frequencies. The temperature field can be selected to ensure continuity of the temperature gradients at the nodal points. To generalize the AMS coupled thermo-elasticity formulation and capture the effect of the boundary and motion constraints (BMC) on the thermal expansion, the proposed method is based on integrating thermodynamics and Lagrange-D’Alembert principles. The absolute nodal coordinate formulation (ANCF) is used to describe continuum displacement and obtain accurate description of the reference-configuration geometry and change of this geometry due to deformations. A thermal-analysis large-displacement formulation is used to allow converting heat energy to kinetic energy, ensuring stress-free thermal expansion in case of unconstrained uniform thermal expansion. Cholesky heat coordinates are used to define an identity coefficient matrix for the efficient solution of the discretized heat equations. The approach presented is applicable to the two different forms of the heat equation used in the literature; one form is explicit function of the stresses while the other form does not depend explicitly on the stresses. Because of the need for using ANCF finite elements to achieve a higher degree of continuity in the coupled thermomechanical approach introduced in this article, the concept of the ANCF mesh topology is discussed.

Dynamic modeling and simulation for pneumatic landing airbag system with frictional contact

The landing airbag system, a mechanism composed of thin-walled structures, is designed to ensure the safe landing of a lander. To investigate the dynamic behavior of the landing airbag with large deformations, a novel modeling approach incorporating gas exchange and frictional contact is proposed. The Absolute Nodal Coordinate Formulation (ANCF) is introduced to model the flexible airbag. Subsequently, the gas parameters inside the airbag are calculated by integrating the Control Volume (CV) Method and the energy conservation equation. Additionally, based on master–slave techniques, a frictional contact formulation for the thin-walled structure and the rigid plane is presented, in which the normal contact force is estimated using the penalty method, and the velocity-based friction model accounting for the stick–slip transition characterizes the tangential friction. Furthermore, the bounding box technology is adopted to improve contact detection efficiency. A series of numerical examples are performed, which demonstrates the proposed model’s advantages in terms of precision and versatility. Finally, the landing dynamic characteristics of the airbag landing system for the small lunar lander are successfully revealed, and the parameter analysis for the airbag system is expected to aid the design optimization of the airbag cushioning system.

Improvement on the axial force accuracy of the ANCF Euler-Bernoulli beam element with the second-order approximate function of the centerline and precise constraint equations

The conventional Euler-Bernoulli beam element of the absolute nodal coordinate formulation (ANCF) yields incorrect axial force due to the existence of the first-order approximate function of the centerline and over-constraint equations. This work aims to improve the axial force accuracy of the element by using the second-order centerline approximate function and precise constraint equations. The second-order function includes the quintic Hermite shape function and the vector of nodal coordinates containing zeroth to second-order derivatives of position. The elastic force vector of the element and its tangent stiffness were then formulated based on the decoupled elastic line method. The exact kinematic requirements of three types of constraint points were fully clarified. On this basis, the corresponding concise constraint equations, constraint Jacobian and Hessian matrices were rigorously derived in the context of ANCF, where G2 continuity was demonstrated to be satisfied at the node acted by an inclined concentrated force, the relative rotation constraint of the rigid joint was described using the dot product of the gradients on both sides of the joint, and the fixing gradient direction at the partially-clamped end was expressed by using the zero cross product of the end gradients in the initial and deformed configurations. Large deformation problems of typical beams under fixed and follower loads were solved using five types of elements, where the results of the ABAQUS B22 elements were taken as a reference for validation. It is found that when using the first- and second-order beam elements having over-constraint equations of the three types of constraint points, obvious axial force error occurs near the corresponding constraint points. In comparison, a few second-order elements containing the derived constraint equations output correct axial force consistent with ABAQUS. However, a large number of the first-order elements containing the correct constraint equations still yield inaccurate axial force in certain beam regions.