The current work elaborates a methodology for the simulation and characterization of the mechanical response of helical structures to radial and thermal loads. The model is extensively validated using both analytical, closed-form expressions and commercial finite element models over a wide range of geometric configurations. Thereupon, the influence of the helix geometry on the construction's radial and thermal loading mechanical properties is analyzed, while a case study comparison of the helix radial and thermal, with the helix axial and torsional loading mechanical properties is made. The results indicate that depending on the helix geometry, the forces and moments created by radial or thermal loads can be considerably higher than the ones induced by axial or torsional loads, rendering their incorporation an indispensable part of the analysis.
SaidA., AbderrazekD., FakhreddineD., MohamedT. and MohamedH., Finite element method for the stress analysis of isotropic cylindrical helical spring, Journal of Mechanics24 (2005), 1068-1078.
2.
ShahsavariH. and Ostoja-StarzewskiM., Spectral finite element of a helix, Mechanics Research Communications32(2) (2005), 147-152.
3.
FraternaliF., ThevamaranR. and DaraioC., Multiscale mass-spring model for high-rate compression of vertically aligned carbon nanotube foams, Journal of Applied Mechanics81(12) (2014), 121006.
4.
LepidiM. and GattulliV., Static and dynamic response of elastic suspended cables with thermal effects, International Journal of Solids and Structures49(9) (2012), 1103-1116.
5.
PipesR.B. and HubertP., Helical carbon nanotube arrays: Thermal expansion, Composites Science and Technology63(11) (2003), 1571-1579.
6.
ReeseS.P., MaasS. and WeissJ., Micromechanical models of helical superstructures in ligament and tendon fibers predict large Poisson's ratios, Journal of Biomechanics43(7) (2010), 1394-400.
7.
HruskaF.H., Tangential forces in wire ropes, Wire and Wire Products28(5) (1953), 455-460.
8.
MachidaS. and DurelliA.J., Response of a strand to axial and torsional displacements, Journal of Mechanical Engineering Science15 (1973), 241-251.
9.
CostelloG.A., Theory of Wire Rope, Springer, New York, 1997.
10.
RaoofM. and KraincanicI., Prediction of coupled axial/torsional stiffness coefficients of locked-coil ropes, Computers and Structures69 (1998).
11.
SathikhS., MoorthyM.B.K. and KrishnanM., A symmetric linear elastic model for helical wire strands under axisymmetric loads, The Journal of Strain Analysis for Engineering Design31(5) (1996), 389-399.
12.
KarathanasopoulosN. and KressG., Mechanical response of a helical body to axial, torsional and radial strain, International Journal of Mechanical Sciences94-95 (2015), 260-265.
13.
JiangW.G., YaoM.S. and WaltonJ.M., A concise finite element model for simple straight wire rope strand, International Journal of Mechanical Sciences41 (1999), 143-161.
14.
StanovaE., FedorkoG., FabianM. and KmetS., Computer modelling of wire strands and ropes part II: Finite element-based applications, Advances in Engineering Software42(6) (2011), 322-331.
15.
KarathanasopoulosN. and AngelikopoulosP., Optimal structural arrangements of multilayer helical assemblies, International Journal of Solids and Structures78-79 (2016), 1-8.
16.
NawrockiA. and LabrosseM., A finite element model for simple straight wire rope strands, Computers and Structures77 (2000), 345-359.
17.
JiangW.G., WarbyM.K. and HenshallJ.L., Statically indeterminate contacts in axially loaded wire strand, European Journal of Mechanics, A/Solids27(1) (2008), 69-78.
18.
LaurentC.P., LatilP., DurvilleD., RahouadjR., GeindreauC., OrgéasL. and GanghofferJ.-F., Mechanical behaviour of a fibrous scaffold for ligament tissue engineering: Finite elements analysis vs. x-ray tomography imaging, Journal of the Mechanical Behavior of Biomedical Materials40 (2014), 222-233.
19.
ZhangG. and ZhaoY., Mechanical characteristics of nanoscale springs, Journal of Applied Physics95(1) (2004), 267.
20.
WangR. and Ravi-ChandarK., Mechanical response of a metallic aortic stent-part I: Pressure-diameter relationship, Journal of Applied Mechanics71(5) (2004), 697.
21.
IsayamaH., NakaiY., ToyokawaY., TogawaO., GonC., ItoY., YashimaY., YagiokaH., KogureH., SasakiT., ArizumiT., MatsubaraS., YamamotoN., SasahiraN., HiranoK., TsujinoT., TodaN., TadaM., KawabeT. and OmataM., Measurement of radial and axial forces of biliary self-expandable metallic stents, Gastrointestinal Endoscopy70(1) (2009), 37-44.
22.
LiS.-L., KimW.-Y., ChengT.-H. and OhI.-K., A helical ionic polymer-metal composite actuator for radius control of biomedical active stents, Smart Materials and Structures20 (2011), 035008.
23.
XuZ.-D. and WuZ., Simulation of the effect of temperature variation on damage detection in a long-span cable-stayed bridge, Structural Health Monitoring6(3) (2007), 177-189.
24.
GentryT.R. and HusainM., Thermal compatibility of concrete and composite reinforcements, 1999.
25.
KarathanasopoulosN. and KressG., Two dimensional modeling of helical structures, an application to simple strands, Computers and Structures174 (1 October 2016), 79-84. doi: 10.1016/j.compstruc.2015.08.016.
26.
ItskovM., Tensor Algebra and Tensor Analysis for Engineers, Springer, 2007.
27.
WempnerG., Mechanincs of solids with Applications to Thin Bodies, Springer Science and Business Media, 1981.
28.
ChapelleD. and BatheK.J., The Finite Element Analysis of Shells: Fundamentals, Springer, 2011.
