Mechanical modeling of helical structures accounting for translational invariance. Part 1: Static behavior

Abstract

The purpose of this paper is to investigate the static behavior of helical structures under axial loads. Taking into account their translational invariance, the homogenization theory is applied. This approach, based on asymptotic expansion, gives the first-order approximation of the 3D elasticity problem from the solution of a 2D microscopic problem posed on the cross-section and a 1D macroscopic problem, which turns out to be a Navier-Bernoulli-Saint-Venant beam problem. By contrast with earlier references in which a reduced 3D model was built on a slice of the helical structure, the contribution of this paper is to propose a 2D microscopic model. Homogenization is first applied to helical single wire structures, i.e. helical springs. Next, axial elastic properties of a seven-wire strand are computed. The approach is validated through comparison with reference results: analytical solution for helical single wire structures and 3D detailed finite element solution for seven-wire strands

Finite element simulation of creep of spiral strands

“…The models with the linear and quadratic brick elements are computationally demanding, when the model is only approximately pitch length [30]. This would be a very small unrepresentative length for the creep analysis of strands.…”

“…Many discrete numerical models and finite element approaches have been developed to investigate global and local static, dynamic (fatigue) or metallurgical characteristics of spiral strands and ropes in the elastic and/or elastic-plastic range, and to calculate their overall mechanical properties such as axial, bending and torsional stiffness [27][28][29][30][31][32][33][34]. Some of them can predict the detailed progressive nonlinear plastic behaviour of the wire strand [33,35].…”

“…Some of them can predict the detailed progressive nonlinear plastic behaviour of the wire strand [33,35]. Some of the models are based on beam elements [22,25], but in most of them, 3D brick elements are used [27][28][29][30][31][32][33][34]. This leads to models which can be computationally demanding, for cases when the model axial length is approximately one pitch length [30].…”

“…Some of the models are based on beam elements [22,25], but in most of them, 3D brick elements are used [27][28][29][30][31][32][33][34]. This leads to models which can be computationally demanding, for cases when the model axial length is approximately one pitch length [30]. Therefore, symmetry conditions are sometimes used by the authors to reduce the model size [19] and the computational domain is restricted to a basic sector of a helical slice.…”

Finite element analysis of spiral strands with different shapes subjected to axial loads

“…Wang et al [24] presented the finite element analysis of a hoisting rope and three-layered strand to explore fretting fatigue parameters and stress distributions of the cross-section. Frikha et al [25] presented an asymptotic expansion method which has been applied to helical structures subjected to axial loads (traction and torsion) at its end sections. Stanova et al [26,27] presented parametric equations to generate arbitrary multi-layered strand ropes with circular wires and their finite element-based applications.…”