Abstract 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.

中文翻译：

---

轴对称载荷作用下无粘结柔性立管接触算法研究

摘要 无粘结柔性立管的结构非常复杂。提出一种高效的力学模型是非常必要的。应用最小总势能原理，提出轴对称载荷作用下的理论模型。相邻层之间的几何关系通过两种方法（罚函数法和拉格朗日乘子法）引入模型中。在本文中，可以通过附加函数导出两个可以直接添加到原始刚度矩阵的附加矩阵。以2.5英寸8层典型柔性立管试验为基础，结合有限元方法，讨论了惩罚函数法中惩罚参数的取值，验证了两种模型的准确性。结果表明：在轴对称载荷作用下，惩罚函数的取值可以保持一致；拉格朗日乘子法会增加变量个数，使刚度矩阵奇异，但计算结果更准确，对相邻层与内压的关系更敏感；惩罚函数法没有添加额外的变量，因此计算更方便，但结果的准确性不如拉格朗日乘子法。