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Design curve determination for two-layered wire rope strand using p-version finite element code

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Abstract

Parametric analysis of a two-layered axially loaded strand is performed using the recently developed p-version finite element code, which describes the geometry well and takes into account all possible inter-wire motions and frictional contact between the wires. A special nonlinear contact theory was developed based on the Hertz-theory. It is assumed that the wires have homogenous, isotropic, linear elastic material properties. The developed code is a tool for designing wire rope strands that require low computer resources and short computational time. Case studies are performed to verify and demonstrate the efficiency and applicability of the method. Design curves are presented according to the strand geometry parameters such as helix angle and ratio of the wire radius in the different layers. The optimal geometry parameters for a given strand can be determined using these design curves.

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Abbreviations

a :

Vector of the displacement parameters

\( {\hat{\mathbf{a}}} \) :

Vector of the additional parameters

\( {\tilde{\mathbf{B}}}_{{\mathbf{q}}} \), \( {\tilde{\mathbf{B}}}_{{\mathbf{a}}} \) :

Approximation matrices for deformations

b :

Binormal unit vector

\( {\varvec{\Upphi}}(\varphi ) \), \( {\hat{\varvec{\Upphi }}}(\varphi ) \) :

Approximation matrices

n :

Normal unit vector

r :

Radius vector of the curved beam centreline

t :

Tangential unit vector

T 0 :

Transformation matrix

A :

Cross-sectional area

E :

Young’s modulus

F z :

Axial force

G :

Shear modulus

H :

Pitch length of the wire

I 1, I 2 :

Moment of inertia of the cross-section calculated to the axis 1 and 2

I p :

Polar moment of inertia

L :

Lame constant

M z :

Torsional moment

R 0 :

Radius of the cylinder

s :

Arc length

U strain :

Strain energy

W external :

Work of the external force

\( \bar{\varphi } \) :

Angle of the cylinder coordinate system

α:

Helix angle

κ :

Curvature

τ :

Twist per unit length

u x , u y , u z (u 1, u 2, u 3):

Displacement coordinates in the global (local) coordinate system

χ x , χ y , χ z (χ 1, χ 2, χ 3):

Angular displacement coordinates in the global (local) coordinate system

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Acknowledgments

The present research was supported by the Hungarian Academy of Sciences, by grant OTKA K67825 and by the project TÁMOP-4.2.2./B-10/1-2010-0008.

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Authors and Affiliations

  1. Institute for Logistics and Production Systems, Bay Zoltán Nonprofit Ltd., Iglói út 2, Miskolc, 3519, Hungary

    Róbert Beleznai

  2. Department of Mechanics, University of Miskolc, Egyetemváros, Miskolc, 3515, Hungary

    István Páczelt

Authors
  1. Róbert Beleznai
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  2. István Páczelt
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Correspondence to Róbert Beleznai.

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Beleznai, R., Páczelt, I. Design curve determination for two-layered wire rope strand using p-version finite element code. Engineering with Computers 29, 273–285 (2013). https://doi.org/10.1007/s00366-012-0269-7

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  • DOI: https://doi.org/10.1007/s00366-012-0269-7

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