Multi-scale Analysis For Helically Wound Structure Of Marine Umbilical Cable

As the key equipment of deep-sea energy development and signal control,the design and manufacturing of marine umbilical cables have always been an international hotspot.The umbilical cable axial bearing equipment or components often have large flexural flexibility and are widely used in marine engineering.Its structures is usually made up of several sub components with large slender ratio,which are helically wound around the central component and have one dimensional periodicity in the axial direction.At the same time,the axial length of this type of structure and the geometric size of its cross sectoin are often very different,which makes a enormous workload of finite element modeling and analysis of the full structure,and reduces the computability,and even makes it impossible for this kind of optimization design.Based on the asymptotic homogenization theory,the one-dimensional periodic helical structure is equivalent to one-dimensional homogeneous beam.A new algorithm is derived for the analysis of the equivalent mechanical properties of helically wound structure,with the advantages of strict mathematical derivation and numerical finite element.It is applied to a typical one-dimensional helically wound structure using the commercial finite element software as a general tool to study the influence of the meshing division and the application of boundary conditions on the mechaical properties.The best modeling method creats a quick and effective way to obtain the structural equivalent stiffness including tensile,bending,torsion and coupling stiffness.Subsequently,the size effect on the macroscopic equivalent performance is studied to find the smallest unit cell that represents the mechanical properties of the whole,and the influence of the helix angle and the number of helical conponents on the macroscopic equivalent stiffness is discussed.It is given that a downscaling scheme for the local mirco stress of a one-dimensional periodic flexible structure microcell and that a new method for calculating the mircro stress in the uniform framework.Then,the micro stress is obtained through the downscaling algorithm based on asymtotic homogenization theory.Compared with the finite element model established accurately,the validity of the multi-scale calculation method of one-dimensional periodic helically wound structure is verified.In addition,it is analyzed that the applicable scope of solving the microcosmic stress field and the accuracy of the solution under the condition of stretching and bending.Even for complex composite load conditions,the micro stress results can meet the engineering requirements.Meanwhile,the homogenization algorithm reduces significantly in computation time compared with the finite element numerical model.The actual umbilical cable model is established to homogenize the tensile stiffness and bending stiffness compared with theoretical analytical solutions and experimental results.Compared with the traditional algorithm for calculating the stiffness of umbilical cable,the new method of homogenization can be used to calculate the tensile stiffness,bending stiffness and torsional stiffness,so as to get the complete stiffness matrix,instead of only focusing on a certain characteristic.The transformation of numerical simulation to practical engineering is completed,and the theory of homogenization is still accurate and convenient for the heterogeneous structure of this kind of complex structure.