A multi-layer functionally graded cylindrical shell model with imperfect interfaces and its application to subsea pipeline engineering

The widespread use of multilayer cylindrical shell structures in engineering has created a demand for theoretical models and analytical solutions that are applicable under various working conditions. In this study, the classical two-dimensional plane elasticity theory for multilayer media is extended to an axisymmetric cylindrical shell configuration, incorporating imperfect interfaces represented by distributed tangential and radial springs. The formulation incorporates layer-wise material properties and interfacial stiffness, allowing for the analysis of both homogeneous and functionally graded materials. The solution is obtained by applying boundary and interlayer continuity conditions, combined with Fourier series expansion in the circumferential and radial directions to accommodate arbitrary loading patterns. The effects of different material gradation functions and interface stiffness values on the stress distribution are investigated in detail. The model is particularly suited for analyzing infinitely long cylindrical shells, such as those used in subsea multilayer pipeline systems. Numerical results demonstrate the accuracy and applicability of the model in handling plane elasticity problems for both isotropic and graded structures. The choice of material distribution function influences not only the extrema but also the shape of the stress profiles. It is found that when the interface stiffness exceeds 2 × 10 8 MPa / m , the interface can be treated as perfectly bonded. Conversely, imperfect bonding alters the stress distribution trends and increases stress concentrations within layers. In underwater pipeline configurations, stress increases from the inner to outer layers, with radial stresses remaining continuous and circumferential stresses exhibiting discontinuities at the interfaces. Significant stress variations are observed across interlayer boundaries.