Cable Elements Research Articles

A fast and stable first-order method for simulation of flexible beams and cables

Gradient deficient beam elements (commonly known as cable elements in the literature) based on the absolute nodal coordinate formulation (ANCF) have great potential for large-scale and real-time simulation applications. In this report, a novel and stable first-order integration method for the gradient deficient ANCF element is developed in a simple linear form. The extension of the integration method to the fully parameterized cable element is also discussed. The method involves splitting the elastic potential using the quadrature points involved in the numerical integration of the continuous body and treating the forces developed by the potential at each quadrature point as though it has arisen from a relaxed constraint in the compliant constraints formalism. The integration method exhibits excellent stability properties, scales well, and can be solved efficiently, with only a single linear solve. Efficient methods for computing the required Jacobians and deformation functions and solving the resulting linear equation are discussed. The integration method is tested in three dimensions, on a cable segment formed from multiple elements and compared to other first-order integration methods in terms of the speed and accuracy. The method is demonstrated via simulating various systems, including a pendulum, a cantilever bar, and a flexible beam dropped onto cylindrical supports. Lastly, the utility and use cases of the proposed integrator are discussed.

Design method for precise-forming of air-supported structures considering weld seams

Abstract Air-supported structures have been increasingly used as formwork for constructing thin concrete shell structures. However, shape deviation from design shape of air-supported structures as airform can result in varying radius of curvature and differing stress distribution. Precise-forming is an inevitable requirement for the design of air-supported structures. This paper presents a design method of air-supported structures considering weld seams for precise-forming. Simulation method of weld seams is integrated in the full design process. Cable elements are included into computation and fill moduli of membrane elements are modified for simulating the influence of seams in warp and fill directions respectively. Force-finding for real stress distribution is utilized to deal with the influence of seams on stress distribution. Residual Pressure Method for cutting forms is adopted to avoid solving zero stress state, in which displacement restriction is imposed on the boundary in deflation analysis for actual construction. Based on a Datun air-supported structure in the shape of hemisphere and cylinder, which is designed to be 71.3 m in diameter and 39.15 m tall, three models with different considerations of weld seams are compared to reveal the influence of seams on stress distribution and cutting form. Measurement results of actual structure demonstrate excellent forming precision of the proposed design method for precise-forming.

Numerical Simulation of Tieback Excavations with Soldier Piles Using a New Unified Soil Model Considering at Rest Condition

The present research aims to understand the behavior of tieback retaining walls during the excavation. Employing the finite difference method (FDM), a 3D model was developed in this study to obtain the earth pressure diagram and horizontal movement of tieback walls during and after construction. A rigorous non-linear analysis of tieback retaining walls requires an efficient solving algorithm of the governing equations as well as a nonlinear soil constitutive law that could capture different stress paths including at rest condition during the sequences of construction. A newly proposed unified two-surface elasto–plastic model based on the critical-state soil mechanics is employed to simulate different stress paths of the matrix soil during the excavation. The model describes strain-softening and stress-dilatancy using non-associated flow rule and implements dilatancy parameter. This model is capable of adopting the proper function for the yield surface, simulating drained and undrained responses of soil under triaxial conditions as well as soil response under drained laterally confined (K0) conditions. Using the presented unified soil constitutive model, the effect of soil plasticity was incorporated into the finite difference method. In the numerical model of the tie-back retaining walls, cable structural elements are used to simulate the tendon anchors, while the shotcrete facing and soldier piles are modeled using shell and beam structural elements, respectively. Effects of different crucial factors were monitored during a comprehensive parametric study. The results gave information on the influence of the following factors on tieback walls behavior: the magnitude of anchors pre-tensioning load, the length of anchors bonded zone, the vertical position of the first anchor, and the stiffness of the soldier piles.

The Sinclair Effect: Comparing Ownership Influences on Bias in Local TV News Content

Sinclair Broadcast Group, the largest owner of U.S. local television stations, has received recent attention due to its apparent political lean and journalistic practices. This study compared the content and quality of national political news stories at Sinclair and non-Sinclair stations in three television markets. Results indicated evidence of a “Sinclair Effect,” whereby Sinclair-owned affiliate stories exhibited more cable news-style elements. Stations generally adhered to traditional journalistic principles, regardless of ownership, but Sinclair stations produced more stories with dramatic elements, commentary, and partisan sources.

Form finding and design optimization of cable network structures with flexible frames

Cable network structures consist of the cable networks and supporting frames, and the whole structures form the equilibrium states under the interactions between them. The existing methods haven’t considered the flexibility of the supporting frames and thus fail to fully capture the interactive effect between cable networks and flexible frames in the design optimization. This leads to the deviations between the design results and the real equilibrium states. Here we propose a form finding and design optimization approach for cable network structures with flexible frames. By solving the non-compatibility problem between cable and beam elements (due to rotation DOF), the cable network and supporting frame can be coupled to accurately model the real equilibrium state in the optimization model. We also derive the linear form for the determination of the free node coordinates from systematic equilibrium equations, which greatly reduces the computing cost of the optimization design and makes the multi-variable optimization more achievable. The proposed approach is effective for the form finding and design optimization of flexible supported cable networks with high surface accuracy requirements and multiple design variables. It is applied to mesh reflector antennas, and case studies are provided to verify the effectiveness of the methodology.

Nonlinear random vibrations of 3D cable-moored floating structures under seismic and wave excitations

A numerical model is constructed for carrying out the nonlinear random vibrations of 3D floating structures moored by cables under seismic and wave excitations. The floating structure is moored to the seabed by four cables that distribute symmetrically around the floating structure. The 3D nonlinear elementary stiffness matrix of cable, rather than the tangent elementary stiffness matrix of cable, is derived based on the extended Hamilton principle. The nonlinear equations of motions of the mooring cables are formulated using the 3D cable elements. The floating platform is modeled as a rigid body with six degrees of freedom. The effects of added mass and nonlinear hydrodynamic drag forces for both the floating platform and mooring cables are taken into consideration. The connection conditions which represent the relationships between the displacements of the floating platform and cables are formulated. The equations of motions of both the mooring cables and floating platform are formulated separately and then assembled as a whole system through the connection conditions. Eventually, the whole system under both horizontal seismic ground motion and wave excitation is analyzed numerically using Monte Carlo simulation method. The mean values, standard deviations and probability density functions of the responses of the floating structure and the maximum tensile force in the cables are presented and studied under various conditions.

Existing RC structures strengthened by ties under seismic sequences considering uncertainty

AbstractThe probabilistic seismic analysis of existing reinforced concrete (RC) structures, which are strengthened by cable elements (tension‐ties), is numerically investigated. Emphasis is given to uncertainties for the estimation of structural input parameters, common to old RC structures, and to accumulative effects of seismic sequences on the structure response. Monte Carlo techniques are used and the unilateral behavior of the cable elements, which can undertake tension stresses only, is strictly taken into account.

From multiscale modeling to design of synchronization mechanisms in mesh antennas

Flexible multibody simulation is supposed to be a promising method for studying the deployment dynamics of large mesh antennas and assisting the design of the related crucial mechanisms. However, fulfilling a full-scale deployment simulation of a mesh antenna is so challenging that it can be rarely found in the literature. In our opinion, the bottleneck of modeling some mesh antennas is dealing with the multiscale physics mainly sourced from the cable-pulley systems that are frequently used to transfer forces for long distance range. A traditional model of a cable-pulley is based on contact method, which involves fine cable mesh, a large amount of contact detection, and small time step for numerical integration, resulting in low calculation efficiency. To cope with this difficulty, we proposed a novel and efficient multiscale method to handle the cable-pulley systems. The basic idea is avoiding the contact detection by separating a cable into two segments: non-contact and contact segments, according to which part of the cable is in contact with the pulley. The non-contact segment is meshed with variable-length elements based on the arbitrary Lagrangian–Eulerian (ALE) formulation. The contact segment is considered an invisible segment to constrain the variable-length cable element on the pulley; its border is dynamically located by the relative configuration between the pulley and the cable. The accuracy and efficiency of the proposed method were confirmed by a numerical example. Then, it was used to evaluate, compare and design the synchronization mechanism in a kind of mesh antenna. The obtained results can directly guide the actual design of mesh antennas, and the proposed multiscale method can be applied to simulating other similar mechanical systems.

Explicit Modeling of White Matter Axonal Fiber Tracts in a Finite Element Brain Model.

Many human brain finite element (FE) models lack mesoscopic (~ 1mm) white matter structures, which may limit their capability in predicting TBI and assessing tissue-based injury metrics such as axonal strain. This study investigated an embedded method to explicitly incorporate white matter axonal fibers into an existing 50th percentile male brain model. The white matter was decomposed into myelinated axon tracts and an isotropic ground substance that had similar material properties to gray matter. The axon tract bundles were derived from a population-based tractography template explicitly modeled using 1-D cable elements. The axonal fibers and ground substance material were implemented using hyper-viscoelastic constitutive models, which were calibrated using white and gray matter brain tissue material testing data available in the literature. Finally, the new axon-based model was extensively validated for brain-skull relative deformation under various loading conditions (n = 17) and showed good biofidelity compared to other brain models. Through these analyses, we demonstrated the applicability of this method for incorporating axonal fiber tracts into an existing FE brain model. The axon-based model will be a useful tool for understanding the mechanisms of TBI, evaluating tissue-based injury metrics, and developing injury mitigation systems.

Prediction of the Pantograph/Catenary Wear Using Nonlinear Multibody System Dynamic Algorithms

In this investigation, computational multibody system (MBS) algorithms are used to develop detailed railroad vehicle models for the prediction of the wear resulting from the pantograph/catenary dynamic interaction. The wear is predicted using MBS algorithms for different motion scenarios that include constant-speed curve negotiation and acceleration and deceleration on a tangent (straight) track. The effect of the vehicle vibration in these different motion scenarios on the contact force is further used to study the wear rates of the contact wire. The wear model used in this investigation accounts for the electrical and the mechanical effects. The nonlinear finite element (FE) absolute nodal coordinate formulation (ANCF), which is suitable for implementation in MBS algorithms, is used to model the flexible catenary system, thereby eliminating the need for using incremental-rotation procedures and co-simulation techniques. In order to obtain efficient solutions, both the overhead contact line and the messenger wire are modeled using the gradient-deficient ANCF cable element. The pantograph/catenary elastic contact formulation employed in this study allows for separation between the pantograph panhead and the contact wire, and accounts for the effect of friction due to the sliding between the pantograph panhead and the catenary cable. The approach proposed in this investigation can be used to evaluate the electrical contact resistance, contribution of the arcing resulting from the panhead/catenary separation, mechanical and electrical wear contributions, and the effect of the pantograph mechanism uplift force on the wear rate. Numerical results are presented and analyzed to examine the wear rates for different motion scenarios.

Nonlinear Analysis of Spatial Cable of Long-Span Cable-Stayed Bridge considering Rigid Connection

To determine the cable sag effect and solve the rigid connection problem at cable ends of a long-span cable-stayed bridge, a two-node spatial catenary cable element with arbitrary rigid arms is developed. Using the finite rotation formula of the space vector and a differential method, the incremental relation between displacement and force at both ends of the rigid arm is given. Then, explicit expression of the tangent stiffness matrix of the element with arbitrary rigid arms is derived based on the catenary equations. Two numerical examples are provided to verify the validity of the new element. A long-span cable-stayed bridge application model is established, and the cables are simulated using three methods. The results show that the rigid end effect has influence on displacements, bending moments and rigidity and should not be ignored. The catenary cable element with arbitrary rigid arms can be used to simulate the geometric nonlinear mechanical behavior of the cables and can well solve the rigid connection problem.

Structural performance of Nissibi cable-stayed bridge during the main and aftershocks of Adıyaman-Samsat earthquake on March 2, 2017

The structural performances of long span cable-stayed bridges having different elements such as pylons, stayed cables and decks are very sensitive to earthquake ground motions due to their highly statically indeterminacy. Therefore, responses of pylon, cable and deck components of long span cable-stayed bridges should be continuously monitored to prevent structural damages. The present study aims to investigate the responses of pylons, stayed cables and deck components of Nissibi cable-stayed bridge during the main (Mw = 5.5) and aftershocks (Mw = 3.5-4.4) of Adiyaman-Samsat (Turkey) earthquake on March 2, 2017. Firstly, the properties of structural and fixed monitoring systems of Nissibi bridge are introduced, and active faults and earthquake zoning maps of Adiyaman, acceleration records and shake map of main and aftershocks of the earthquake are presented. Then, responses of the pylon, deck and cable elements during the main and aftershocks are obtained using the data taken from the fixed bridge monitoring system. The forces in cables and accelerations in the two pylons and deck are evaluated and compared with each other.

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

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.

Analysis of Cable under Dynamic Contact and Large Deformation

For simulating contact interactions and high displacement gradients between the cable and the saddle at the middle tower of triple-tower suspension bridges, a cable element is developed by combining the absolute nodal coordinate formulation and the quasi-conforming technique. New curvature strains are developed and elastic forces are explicitly formulated for the cable elements. Thereafter, it is compared to the original one to verify its locking remedies. The numerical solutions using the element are compared to analytical results and solutions by the original element. Compared to the original, the proposed element suppresses the high-frequency disturbances in the velocity and acceleration curves. Using the element, the contact and sliding behavior between the cable and the saddle is analyzed by employing parameters obtained experimentally. The saddle’s mechanical and frictional performance subjected to different friction coefficients and unbalanced cable forces is investigated. The proposed model exhibits excellent accuracy in the prediction of the sliding force and the contact status between the cable and the saddle.

Nonlinear random vibrations of moored floating structures under seismic and sea wave excitations

A numerical model is formulated for the nonlinear random vibrations of the offshore floating structures moored by cables under seismic and sea wave excitations. The upper end of each mooring cable is connected to the floating structure and the other end of each cable is fixed to the seabed. Nonlinear equations of motions of the mooring cables are formulated by using the nonlinear cable elements that are formulated based on the extended Hamilton principle. The floating platform is modeled as a rigid body with three degrees of freedom. The connection conditions which represent the relationships between the displacements of the floating platform and cables are given to derive the equations of motions of the whole system. The effects of nonlinear hydrodynamic drag forces and added-mass on both the floating platform and cables are taken into consideration. The random vibrations of the moored floating structure under both horizontal seismic ground motion and sea wave excitation are analyzed by using the Monte Carlo simulation method. The probability density functions of the displacements of the moored floating structure and the maximum tensile force in the cables are analyzed. The influences of different sag-to-span ratios, inclination angles and diameters of the mooring cables on the mean value and standard deviation of the displacements of the floating structure and the maximum tensile force in the cables are studied.

Computer implementation of piecewise cable element based on the absolute nodal coordinate formulation and its application in wire modeling

A new high-voltage electricity wire model is proposed to simulate the dynamic behavior of the wire after tension failure and the nonlinear sliding joints between the wire and the iron tower. A previously developed piecewise cable element based on the absolute nodal coordinate formulation is used with its computer implementation given in this paper. In order to describe the initial tension in the wire, a static solving approach is used to achieve equilibrium between the element elastic force and the external force including the tension. The obtained configuration of the wire is then used as the initial configuration of analysis in case of unloaded external tension force. Thereby, the dynamic behavior of the wire can be modeled. The sliding joint constraint is used to describe the motion of the wire going through the iron tower after tension failure. A new static solution approach is developed to avoid the sliding joint constraint violation in the resulting equilibrium configuration. The convergence of the piecewise cable element based on the absolute nodal coordinate formulation is tested. A set of comparative results is presented to demonstrate the feasibility of the method proposed in this investigation.

Numerical modeling of space umbrella-type mesh reflector

This paper describes numerical modeling of space umbrella-type mesh reflector. The modeling includes two stages. The first stage embraces the calculation of the shape of cable elements for reflector frontal (rear) nets by the nonlinear force density method. The second stage involves the design of the reflector finite-element model based on the calculated nets. After this, the node displacement and prestress boundary conditions are imposed to determine a node displacement field.

Spatial combined cable element for cable-supported bridges

Purpose The purpose of this paper is to analyze the cable-supported bridges more efficiently by building the finite element model with the spatial combined cable element. Design/methodology/approach The spatial combined cable element with rigid arms and elastic segments was derived. By using the analytical solution of the elastic catenary to establish the flexibility matrix at the end of the cable segment and adding it to the flexibility matrix at the ends of the two elastic segments, the flexibility matrix at the end of the cable body is obtained. Then the stiffness matrix of the cable body is established and the end force vector of cable body is given. Using the displacement transformation relationship between the two ends of the rigid arm, the stiffness matrix of the combined cable element is derived. By assigning zero to the length of the elastic segment(s) or/and the rigid arm(s), many subdivisions of the combined cable element can be obtained, even the elastic catenary element. Findings The examples in this field and specially designed examples proved the correctness of the proposed spatial combined cable element. Originality/value The combined cable element proposed in this study can be used for the design and analysis of cable-stayed bridges. Case studies show that it is able to simulate cable accurately and could also be used to simulate the suspenders in arch bridges as well in suspension bridges.

Flexible cable strength with regard to tribological interaction of its elements

This paper considers certain issues of tribological interaction between flexible cable elements. It proposes a new approach for determining frictional forces of cable elements while taking into account cable parameters. This study is the first to derive formulas of mechanical stresses in the zone of contacting elements for assessing the cable strength. The paper demonstrates how the derived formulas for cables can be used in practice for design purposes. The influence of geometric parameters of cable design on its strength has been analyzed.

Dynamic analysis of rotating satellite de-spun using <?A3B2 ACK?>flexible brush

With the continuous exploration and expansion of human beings in space, the number of satellites in space is gradually increasing. In the process of catching the failed satellites, the rolling spin of the satellite has always been the main problem which is affecting the stability of the catching system between targets and servers. The derotation mechanism, a flexible deceleration brush, is proposed, which is placed at the end of a seven-degree-of-freedom manipulator to form a racemable space robot. The momentum of the rolling target is dissipated by the contact collision between the end flexible deceleration brush and the rolling target windsurfing board. The angular velocity deceleration of the freely rolling target is carried out. Based on the rope element of the large deformation cable beam element of the absolute nodal coordinate method (ANCF), the continuum model of the flexible deceleration brush is established. According to the Hertz theory, contact collision force between the flexible deceleration brush and the rolling target windsurfing board are calculated. For the non-cooperative target of free rolling in different speeds, the effects of the length, angle and other parameters of the flexible deceleration brush on the racemization effect are analyzed by dynamics simulation, and the optimal racemization parameters are obtained in the process of the dynamics simulation. Using these parameters to verify the simulation of the racemization, the results show that the strategy, which is using flexible deceleration brush to rack non-cooperative targets, can successfully eliminate the initial spin angular velocity and it is feasible and effective.