Research On Multi-scale Analysis For Helically Wound Structures With Considertion Of Shear Effects

Helically wound structures are widely applied in the industrial field,such as offshore flexible composite risers(flexible pipes and umbilical cables)in the subsea production system.Helically wound structures can not only resist the tensile load but have the excellent flexibility,which guarantees that offshore composite risers are able to adapt the complex condition.Due to the complex configuration of helically wound structures,it is hard to calculate the stiffness and stress property through the analytical theory.The analysis of mechanical property of helically wound structures is usually based on the numerical method.Besides,because helically wound structures are thin and long and there is a large difference between the axial length and the size of the cross section,the numerical simulation based on the real structures model need heavy computation,and it is hard to carry out the efficient structural analysis and optimization design.Therefore,3D heterogeneous helically wound structures were equivalent to 1D homogeneous structures to conduct the multiscale analysis in this study.The effective stiffness property was calculated in the upscale analysis,and the effective stress property was obtained in the downscale analysis.Firstly,due to the one-dimensional periodicity of helically wound structures,asymptotic homogenization theory was introduced to construct the multiscale effective analysis method for helically wound structures,where helically wound structures are equivalent to a Timoshenko beam model with consideration of shear effects.Further,the numerical method based on the unit-cell model was given,which extremely improves the analysis efficiency of the mechanical property of helically wound structures.Besides,the optimal method to create the finite element model of helically wound structures was determined in the upscale analysis,and the effective tensile,bending,torsional and shear stiffness were calculated.Further,according to the effective analysis method developed in this study,the change trend of the shear coefficient of helically wound structures with the slenderness ratio was analyzed,and it is found that the shear effect have a large influence on short beams,especially when the slenderness ratio is less than 5:1.Then,through the analysis of the effective stiffness of non-equal-scale helically wound structures,it is found that the effective bending and shear stiffness see a nonlinear growth as the number of wound subcomponents increases.In the downscale analysis,with consideration of shear effects on the effective stress,the first-order approximation of the effective stress of helically wound structures was derived,and the corresponding finite element method was given.The exact finite element model was taken as the reference,and the error analysis of the effective stress of helically wound structures was conducted when the structures are under tension,bending,tension and bending coupled conditions.Comparing the effective stress errors from the effective analysis method with and without consideration shear effects,it is found that the effective stress analysis method with consideration shear effects is better for the analysis when structures are under bending,bending and tension coupled conditions,and two effective analysis method have a similar accuracy when structures are under the tension condition.This research is supported by the innovative talents support plan for colleges and universities in Liaoning province,‘the multiscale optimization design of deep-water flexible pipes and cables’(LR2017001).In this study,the effective analysis of mechanical properties of helically wound structures with equal and non-equal scale subcomponents was conducted,and the multi-scale effective analysis method developed can guide the structural analysis and design of helically wound structures.