Research on contact algorithm of unbonded flexible riser under axisymmetric load

The structure of unbonded flexible riser is very complex. It is very necessary to propose an efficient mechanical model. Applying the principle of minimum total potential energy, the theoretical model under axially symmetrical load is proposed in this paper. The geometric relationship between adjacent layers is introduced into the model by two methods (penalty function method and Lagrange multiplier method). In this paper, two additional matrices which can be directly added to the original stiffness matrix are derived by additional functions. Based on the experiment of the 2.5-inch 8-layer typical flexible riser, and combined with the finite element method, the value of penalty parameter in penalty function method is discussed and the accuracy of the two models is verified. The results show that: the value of penalty function can be consistent under the action of axisymmetric load; the Lagrange multiplier method will increase the number of variables and make the stiffness matrix singular, but the calculation results are more accurate and more sensitive to the relationship between adjacent layers and internal pressure; the penalty function method does not add extra variables, so it is more convenient to calculate, but the accuracy of the result is not as good as Lagrange multiplier method.