1,721,068 research outputs found
A COROTATIONAL BEAM ELEMENT TO MODEL SUSPENDED CABLES
No full textDue to their slenderness and inherent flexibility, the dynamic behavior of cables is strongly affected by
various non-linearities as geometrical, of the material behavior and stemming from the interaction
with the environment. Within this context, an interesting issue is the development of reliable and
efficient numerical methods (see the review paper: [1]). In this paper the attention is focused on the
mechanical response of the cable model.
A corotational formulation was adopted [2], [3], essentially based on the formulation proposed by
Oran in [4] and Meek and Tan in [5]. This allows to deal with stress and strain measures that
otherwise would result in non-objective formulations for large displacements and rotations. This is
particularly useful in view of the introduction of non-linear or inelastic constitutive laws (see the
companion paper [6]). The core, in the spirit of “element - independent” corotational formulations
[7], is the decomposition of the total motion of the element in a rigid component and in an
approximately pure deformation, through the introduction of a moving coordinate system attached to
the member itself (local or co-rotated frame). The procedure in [2] takes into account large nodal
displacements and rotations, but is limited to small nodal rotations increments; in this paper this limit
is critically discussed and removed
An analytical approach to model the hysteretic bending behavior of spiral strands
No full textSpiral strands are lightweight and flexible structural elements, widely employed in many different applications, moreover, they are the basic components of stranded wire ropes. Bending behavior can play an important role in modeling slack cables and in "critical" regions of flexible ropes, such as in the neighborhood of clamping devices. When a strand is bent, wires tend to slip relatively one to each other. In the present work, the critical conditions for the onset of inter-layer sliding are investigated by defining the limit domain for wire slipping (the domain of "admissible values" for the axial force of a generic wire, accounting also for the contribution due to bending of the strand). The special case of uniform bending of the strand is considered and a closed form expression of the limit domain is presented. The non-holonomic nature of the strand mechanical model developed in this work leads to a lacking of symmetry for the tangent stiffness matrix. In the paper it is proved that this condition can be de facto relaxed in practical applications and that an elastic potential function, relating the generalized stress and strain variables of the strand in bending, can be defined only under the limit kinematic hypotheses of "full stick-state" or of "full slip-state". The aforementioned results are used as the starting block from which the strand full mechanical behavior for coupled axial force and bending is derived. Knowledge in closed form of how the limit domain depends upon the strand construction parameters and current stress conditions paves the way to design optimization of the strand
KINETIC ENERGY AND INTEGRATION OF THE EQUATIONS OF MOTION OF COROTATIONAL BEAM ELEMENTS
No full textIn the last years the research group has worked to the development of a numerical procedure devoted
to investigate the dynamics of suspended cables under turbulent wind loading and subjected to large
displacements and rotations [1],[2],[3]. Within this context, starting from the formulation proposed
by Oran in [4] and by Meek and Tan in [5], a corotational shallow beam element was developed for
modeling the mechanical behavior of cable elements [2], [3].
As part of the description of the kinematics of the corotational element, when applied to modeling very
flexible structures, and in procedures for the definition and updating of the corotated reference frame,
a key point is the treatment of large three-dimensional rotations. Due to the presence of large nodal
rotations, in fact, the space of configuration of the structure is a non-linear differentiable manifold
[6]. Particular care should then be paid to the parameterization of rotations and to the interpolation
schemes adopted to numerically solve the dynamic problem. Several parameterization and update
strategies of rotations were compared in a companion paper [7], where the issue of the evaluation of
the internal forces and the static tangent stiffness matrix was discussed.
This paper concerns the description of the dynamics of the beam element. In particular, the focus is
concentrated on a new procedure for the evaluation of the inertial forces and the numerical
integration of the equations of motion
A MODEL FOR THE FRICTION CONTROLLED BENDING BEHAVIOUR OF CABLES
No full textCables can be viewed as composite structures obtained through assemblies of helical components in
hierarchical levels [1]. Their internal geometry described by means of a recursive procedure based
on the definition of a hierarchical tree and a mathematical model of the assembly process, which
defines the relationship between components pertaining to different levels of the tree. In this paper a
new procedure is proposed to evaluate their mechanical response accounting for the geometry of their
internal structure and for possible internal sliding due to biaxial bending
Un modello per la flessione biassiale ciclica di funi a trefoli
No full textIn questo lavoro si propone un modello per il calcolo della risposta meccanica delle
funi ad una generica storia di carico combinazione di estensione, torsione e flessione biassiale,
tenendo conto sia della geometria interna che dei fenomeni di scorrimento connessi alla risposta
flessionale
Mechanical modeling of metallic strands subjected to tension, torsion and bending
Get PDFAim of the present work is to build a link between a structural theory for large-scale analyses of three-dimensional cable structures undergoing, in general, large displacements and rotations, and a refined mechanical description of metallic strands, fully accounting for their composite nature and hysteretic bending behavior. A new formulation for metallic strands is presented. The strand overall mechanical behavior is modeled according to the Euler-Bernoulli beam theory. A constitutive law relating the cross sectional generalized stresses and strains of the adopted structural model is obtained by summing over the individual contributions of wires. Each wire in the strand is individually modeled as a curved thin rod. Kinematic equations are proposed to relate the wire generalized strain variables to those of the strand cross section. The equilibrium of the individual wires is analyzed under the hypothesis of radial contact between adjacent layers taking, most notably, also into account the effects due to the residual radial contact forces induced by the strand manufacturing process. Deformations of contact surfaces are neglected and friction is accounted for, through the Amontons-Coulomb law, in the study of the stick-slip conditions. The proposed sectional model accounts for some distinctive characteristic aspects of wire ropes, such as the coupling between axial force and torque and the non-linear, and non-holonomic, relation between bending moment and curvature, which is a consequence of sliding of wires. The performance of the proposed formulation is assessed with reference to well-documented physical tests and established analytical formulations. Moreover, the role of the residual contact forces due to the stranding process, on the bending behavior of a typical multi-layer strand is assessed
Dynamics of corotational beam elements in large displacements and rotations - some aspects on the kinetic energy and the integration of the equations of motions
No full textClassical structural theories able to deal with beams undergoing large displacements and rotations, with small strains, are that of 'geometrically exact' elements and the corotational approach. In this work an attempt is made to combine geometrically exact and corotational approaches, adopting the typical viewpoint of geometrically exact models in order to evaluate the inertial forces of a beam element. A new procedure for the evaluation of the inertial forces of the beam is proposed. This is based on an exact description of the kinematics of the element and on a spatial discretization which employs only nodal variables defined in the global frame of reference of the structural problem, so avoiding approximations typically introduced by the classic corotational formulations. The issue of integration of the equations of motion is addressed taking into account the non-linear character of the element configuration space, which is due to the presence of large cross-sectional rotations. It's also shown that the proposed procedure allows for a standard time stepping scheme in integrating the equations of motions, with practical advantages on the reuse of standard numerical algorithms
A corotational finite element to model bending vibrations of metallic strands
Get PDFA new formulation to model the mechanical response of metallic strands undergoing
a combination of axial load and planar bending is developed. Each wire of the strand is
modeled as an elastic curved thin rod. A kinematic model is then introduced to relate the generalized
strain variables of the strand to those of the wires. The stress-strain state of the wires
is evaluated starting from the analysis of the internal contact conditions. Friction is modeled
through the classic Amontons-Coulomb law and the elastic tangential compliance of contact
patches is accounted for. A non-holonomic material constitutive law in terms of the cross sectional
generalized stresses and strains of the Euler-Bernoulli beam theory is obtained and
implemented within a corotational beam element explicitly conceived for nonlinear static and
dynamic analyses of flexible structures. Numerical applications are presented to highlight the
role of the tangential compliance mechanism on the hysteretic bending behavior of a typical
steel strand
A corotational beam element to model the hysteretic bending behavior of metallic wire ropes
No full textIn this paper we propose a mechanical model for metallic wire ropes, starting from a description of their internal structure
as an assembly of helical curved thin rods and accounting for some characteristic aspects of their response, such as.: (a)
the coupling between axial force and torque, (b) the non-linear and non-holonomic relation between bending moment and
curvature. A numerical procedure to define a cross-sectional constitutive law in terms of generalized stress and strains of
the Euler-Bernoulli beam theory is presented together with its implementation within a 3D corotational beam element
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