A finite element formulation for cables suitable for dynamic modelling (original) (raw)
Dynamics of cable structures – Modeling and applications
2013
v The objective of the present work is to re-examine and appropriately modify the geometrically exact beam theory, originally developed by Simo, and develop a nonlinear finite-element formulation to describe the static and dynamic behavior of flexible electrical equipment cables. The work is motivated by the need to better understand and predict the highly nonlinear response of flexible electrical conductors to earthquake excitations. Dynamic interaction between flexible cables and interconnected substation equipment is in fact believed to explain some of the severe damage sustained by such equipment in recent earthquakes. In the first part of this report, the nonlinear equations of motion of a beam undergoing large displacements and rotations are derived from the 3D theory of continuum mechanics by use of the virtual power equation. A linear viscoelastic constitutive equation and an additional mass proportional damping mechanism are used to account for energy dissipation. The weak ...
Nonlinear static and dynamic analysis of mixed cable elements
2017
This paper presents a family of finite elements for the nonlinear static and dynamic analysis of cables based on a mixed variational formulation in curvilinear coordinates and finite deformations. This formulation identifies stress measures, in the form of axial forces, and conjugate deformation measures for the nonlinear catenary problem. The continuity requirements lead to two distinct implementations: one with a continuous axial force distribution and one with a discontinuous. Two examples from the literature on nonlinear cable analysis are used to validate the proposed formulation for St VenantKirchhoff elastic materials. These studies show that displacements and axial forces are captured with high accuracy for both the static and the dynamic case.
Cable Dynamic Modeling and Applications in Three-Dimensional Space
Lecture Notes in Mechanical Engineering, 2018
Dynamic modeling of cables in three-dimensional space is a problem with great difficulty and complexity. This article discusses a new dynamic modeling formalism, including applications in the underwater environment. It is assumed that the cable is formed by rigid links connected by elastic fictitious joints, allowing elevation, azimuth and torsion movements. Algorithms have been developed to automatically generate the dynamic model for any number of links selected for the discrete approximation of the flexible structure. Three practical situations are tested: cable out of the water with free terminal load; underwater considering dynamics with or without ocean current; with terminal load fixed to the seabed. Constraint forces obtained through proportional and derivative control were applied to the terminal load to fix it to the seabed. The algorithms were determined from the Euler-Lagrange formalism, and in all situations the simulations showed physically consistent results.
Dynamics of traveling, inextensible cables
2004
The closed-form solution for rigid-body motions of two-dimensional traveling, sagged cables with a nonlinear geometrical constraint is developed. This closed-form solution shows that the rigid-body motions are always stable even if the translation speed is over the critical speed. With increasing translation speed, the translation motion effects on the cable increase accordingly. When the translation speed is much greater than the critical speed, the vibration effects compared to the translation motion effects can be ignored. Therefore, for an infinite translation speed, the initial and dynamic configurations for the inextensible cable are identical. The dynamic configuration of the inextensible cables is obtained in this paper, which provides a basis to get the dynamic responses of sagged, elastic cables.
Numerical Analysis of Cable Structures
Civil-Comp Proceedings
The paper presents a comparison of computational methods used in the static analysis of cable structures. Two different methods are used, the method of dynamic relaxation and the force density method. The dynamic relaxation method is presented in more detail. The sample design will be compared for accuracy, computational time and the conditions and speed of convergence of the methods used.
Advanced Control Strategies in Cable Dynamics
Computational Science, Engineering & Technology Series, 2007
Cables have undergone great change. In the past they served merely as structural members with high strength characteristics; now cables have become advanced components with multiple features such as controlled dynamics, enhanced environmental durability and sensing ability. These enhancements are the result of a variety of different technologies based on a growing understanding of cable dynamics. The present article summarizes the basics of cable dynamics and control systems modeling particularly with reference to suspended cables, stays and stayed-structures. The control strategies are discussed in terms of both the continuous cable model and its reduced representation in an appropriate discrete basis. The fundamental concepts within the field of cable engineering of passive, semi-active and active control are discussed, as well as different types of control strategies evidencing the peculiar interaction between inherent cable nonlinear dynamics and the control design process.
Dynamic modeling of cables with external forces applied to the terminal load
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2020
Cables are flexible structures often used in underwater applications, mainly related to oil extraction industry. This paper proposes a new dynamic modeling of cables that includes the action of external forces applied to its terminal load in two situations: free terminal load and fixed to the seabed. The continuous cable flexibility is approximated by rigid links connected by fictitious elastic joints that allow elevation, azimuth and torsion movements. External forces applied to the terminal load are considered in two situations: written in the inertial framework and written in the body framework. Generic algorithms are proposed for the automatic generation of models considering any number of links in the discrete approximation of continuous cable's flexibility. The simulation results were very close to the experimental ones, thus validating the proposed modeling formalism. A software was developed to animate the cable with three-dimensional spatial configuration for viewing the simulation results. These animations showed physically the expected results, as well as a great sense of physical reality.
Nonlinear elasto-plastic analysis of slack and taut cable structures
Engineering with Computers, 2016
Cable elements are important structural components in a wide variety of tension structures such as cable-supported bridges, marine and offshore structures, guy lines for towers, power supply lines, and salvage structures due to their structural advantages as well as the esthetic appearance. Since the highly nonlinear behavior exhibits in this element, the effects of flexibility and large displacements in a cable should be considered in establishing the equilibrium equations. There are two types of cable elements, i.e., the cable-stayed element with a shallow sag and the catenary element with a deep sag. A shallow cable is defined as one with a sag to span ratio of less than 1:8 according to Refs. . Although the actual profile of cable is the catenary configuration, the geometry of a shallow cable element can be treated as a parabolic profile. In general, two major approaches can be used to formulate the cable element: (1) the analytical approach based on exact analytical expressions of catenary element and (2) the finite element approach based on the interpolation polynomial functions. In the first method, the exact expressions for the deformed geometry of elastic catenary are used to describe the realistic behavior of cables. The curved cable segment is modeled by a single two-node catenary element without internal joints and the nodes are located at cable intersections and external points only. This element can be used to model cables with larger sag as well as smaller one. The concept of this method was proposed by O'Brien and Francis [3] and later developed by Jayaraman and Knudson [4], Yang and Tsay [5], Such et al. [6], Andreu et al. [7], Thai and Kim [8], and Impollonia et al. [9]. As a second approach, the finite element method based on the interpolation polynomial functions has been widely used because of its versatility and accordingly a large Abstract This paper presents the geometrically nonlinear analysis of the slack and taut cable structures considering the material inelasticity subjected to self-weight, pretension, and external loads. The finite element procedure is briefly summarized using the Lagrangian formulation associated with isoparametric interpolation polynomials and the Newton-Raphson iterative scheme with incremental load. The simple and efficient method to determine the initial equilibrium state of the slack cable systems under selfweight as well as support motions is presented using the penalty method. The numerical algorithm to evaluate the tangent modulus of elasticity of cable is presented based on the iterative scheme. The accuracy and reliability of the present study are verified by comparing the predictions with those generated by well-reported slack and taut cable structure problems. The effect of the yielding of cable segments on displacements and stresses of cable structures is investigated. Keywords Cable structures • Nonlinear analysis • Elasto-plastic analysis • Finite element method * Jaehong Lee
Nonlinear Dynamic Analysis of Cables Under Accelerated Moving Masses
The paper deals with the nonlinear dynamic analysis of accelerated moving masses applied on cable structures. This mechanical system is often used in systems for transport buckets of commodities, for transport of passenger, such as cable cars and high-speed rail, and also enables the use of autonomous systems used for inspection and maintenance of cable structures. The structural systems are modeled numerically with the aid of a formulation based on the finite element method considering the absolute coordinates concept. There are several recent papers that perform analyses of moving masses travelling under constant velocities, using different methods of solution, considering a high level of complexity for the transient problem and for the implementation of the algorithms. Thus, it becomes necessary the development of more accuracy numerical methods, but also simple, for the dynamic nonlinear formulation. The main objective of this paper is to present a numerical approach of the system mass-cable using the concept of positional geometrical nonlinearity. This concept allows the use of a single global system of coordinates for each finite element. Therefore, the formulation unifies the dynamic force terms, i.e. inertial, Coriolis and centrifugal. Using this methodology, the analysis will be presented to cables subjected to moving masses traveling with variable velocities. The analyses will be developed for horizontal sagged cables (with same level of supports), for inclined sagged cables (with supports at different levels) and for straight cables (with cable deflection negligible). For these problems, sets of results will be presented for the mechanical behavior analyses of the cable, as the midspan vibration during the course of the mass along the cable (forced vibrations) and after the mass finishing their entire course (free vibrations). The distribution and the variation of normal forces in some finite elements also will be presented. Preliminary results point to the increase of stiffness of the system mass-cable during the course of the mass, with the increase of mass velocity, and to the variations of a) email: flaviomo@dees.ufmg.br b) email: vecci@dees.ufmg.br c) email: mgreco@dees.ufmg.br normal forces in the finite elements. Furthermore, above certain speeds the equilibrium state of the system mass-cable shows qualitative variations.