Nonlinear Dynamic Response Analysis Of Slender Rods In Deepwater

Mooring line and riser are important slender rods used in the ocean engineering.The main characteristics described for them are the large slenderness ratio.For the analysis of the polyester mooring line,it is easy to be deformed with bending stiffness due to its small tensile stiffness.An improvement is made to the classical rod theory to simulate the geometrical nonlinearity such as large displacement,large rotation,large stretch,and large bending deformation.The new model relaxs the limitations of the current models like lumped mass method,slender rod theory and nonlinear beam model.Meanwhile,the Kim's linear viscoelastic model and the nonlinear soil stiffness model are introduced and assembled into the slender rod model which then has the ability to solve the material nonlinear problem and the boundary nonlinear problem.And then an asynchronous coupling method is proposed with the help of the new slender rod model and the indirect method.Firstly,the large stretched rod model is developed and the FEM numerical method is provided.Under the large stretch configuration,the length of the rod is changed obviously,then there is a big difference between the current configuration and the reference configuration which can't be solved by the classical rod model.So this paper is to find the elemental definitions and methods to describe the geometrical nonlinear relationship with the strain,stress,curvature and so on.Then the large stretch rod model is generated with the assumption of the mapping of the points between the current configuration and the reference configuration.The weak form equivalent equation is made with the FEM,and the static case is solved with the Newton method.The dynamic case is solved with the explicit Moulton method.And both of the static and dynamic cases are verified with the analytical problems.Good comparisons show the new rod model has the ability to solve the large deformations.Secondly,a unified material model is generated based on the linear material,the viscoelastic material,the internal structural damping and the possion affection,and assembled into the slender rod model.The polyester mooring line is different from the chain and the steel with the viscoelastic characteristics like creep,relaxation and hysteresis which can't be solved with the classical rod theory.The geometrical nonlinearity and the material nonlinearity make it hard to solve the dynamic response of the polyester mooring line.Kim developed a new viscoelastic model based on the linear solid model,and get a good performance under the tests.This paper will use Kim's viscoelastic model to find a solution to the polyester with new rod models.The basic constitutive equations are converted to the tension-strain format.Then the FEM is carried out to solve it and compared with the analytic case which is designed for the specific problem.The results show a good performance of the internal coupled method for the nonlinearities.Thirdly,a nonlinear soil stiffness model is developed in the slender rod theory.The sea floor is the necessary boundary condition for the catenary mooring line and the steel catenary riser(SCR),but only spring model is used in the classical slender rod theory.The stiffness of the sea floor plays an important role on the dynamic response and the stress distribution.The JIP(Joint Industry Project)make research on the influence of the sea floor for the structures with the real scale model test.And many soil models are developed to try to simulate the actual sea floor.The P-y curve model is chosen to simulate the nonlinearity of the soil stiffness.Three models are provided to simulate the small displacement motion,large displacement motion and motion reversion.Finally,the FEM is utilized to make the numerical solution to simulate the dynamic response in the TDZ(Touch Down Zone).Finally,an asynchronous coupling method is proposed together with the slender rod theory.There are softwares to solve the coupling problem in the time domain,but some problems still need to be solved like the coupling method and how to make it fast.In this paper,the coupling between the floating structure and the slender rods is constructed with the indirect method of time domain in which the motion of the floating structure is solved in the frequency domain,and then converted into the time domain which is coupled with the slender rod model.The asynchronous method is offered to fix the time step difference between the floating structure and the slender rods.And this method shows a good result when compared with the commercial code AQWA.