Dynamic Analysis Of Deepwater Flexible Rods Based On The Global Coordinate Method

The riser and mooring line are important parts of Ocean Engineering,which are slender flexible structures and play an essential role for the safety guarantee of deepwater oil and gas production system.The deepwater riser and mooring line have the characteristics of small stiffness,easy to stretch and bend.It has a great influence on the mechanical properties analysis due to the geometrical nonlinearity,and the traditional linear theory of small deformation can not be used in the calculation any longer.Therefore,based on the global coordinate method and the theory of continuum mechanics,a mechanical model for the flexible slender structures of large deformation is established.It's used in the static and dynamic analysis and the results are compared with the traditional ones.On the basis of the global coordinate method,the constant symmetric mass matrix is obtained with the zero centrifugal force and zero Coriolis force.Slope coordinates are used instead of angle coordinates to avoid the coordinate system transformation and to simplify the calculation program.The stiffness matrix is varying with the coordinates updating and the elements can be regarded as isoparametric elements in the finite element discretization.Using this method,the calculation program is convenient,fast and efficient.The main work of this paper is as follows:Firstly,based on the energy variational method of the global coordinate method,slope coordinates are used instead of angle coordinates and the generalized elastic force and stiffness matrix of the element are derived by the principle of virtual work.The constant mass matrix and the external load matrix of the element are obtained by calculation,so every expression in the motion equation is derived.According to the principle of the finite element method,we get the stiffness matrix,mass matrix and external load matrix of the whole structure.Then the expressions in the equilibrium equations of the static and dynamic analysis are obtained.Secondly,the programs of the static and dynamic analysis are written with Fortran90 and simple examples are selected to test and verify the correctness and accuracy of the program.After the program can be operated correctly,the typical slender flexible body of the Ocean Engineering-mooring lines are chosen to for the static analysis.The top of the riser is hinged and the horizontal tension is applied to the bottom.Different tension parameters are selected,and the static analysis is carried on by using Newton-Raphson iteration method.Then the mooring lines' space form of static equilibrium is obtained.Compared with the analytical solution of the catenary theory,the results are prepared for the dynamic response analysis.Thirdly,the dynamic analysis of the steel catenary riser is carried on.In the dynamic analysis,the influence of flow loads is considered and the riser 's touchdown is simulated with stated seabed condition.The hinges are disposed by setting diagonals to one,and the riser is imposed by different perturbations.Newmark method is used in the dynamic analysis.The calculation results are analyzed,which may offer references for the design and optimization of deepwater risers.In conclusion,this paper is based on the energy variational method of the global coordinate method,and a mechanical model for flexible slender structures with large deformation in Ocean Engineering is established.The calculation program written by Fortran90 can be used in the static and dynamic analysis of slender structures such as deepwater risers or mooring lines and the calculation results are accurate.The energy variational method are mostly used in the dynamics of multibody systems,and the study on it in Ocean Engineering is rare.I hope this paper can provide some reference value for the application of the global coordinate method in Ocean Engineering.