PSI - Issue 77

Tianyu Wang et al. / Procedia Structural Integrity 77 (2026) 512–520 Wang et al./ Structural Integrity Procedia 00 (2026) 000 – 000

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1. Introduction Composite materials have become increasingly vital in high-performance engineering applications, particularly in the oil and gas industry, where their high strength-to-weight ratio, corrosion resistance, and manufacturing flexibility offer significant advantages over traditional material. The transition from metallic to composite pipes in subsea applications alone has resulted in weight reductions of up to 70%, enabling deeper water installations and reducing installation costs by millions of pounds per project [1]. Structures such as subsea pipelines, drill rods, and risers are routinely subjected to complex combinations of operational loads, including internal and external pressure, axial forces, torsion, and bending moments. The safe and efficient design of these components hinges on the ability to accurately predict their structural response and failure behaviour under these multifaceted loading environments [2,3]. Despite considerable research into the performance of composite pipes, a critical limitation persists in the existing literature. Most analytical [4 – 7] and numerical studies [8 – 11] tend to focus on specific, isolated load types rather than their combined effects. This reductionist approach, whilst mathematically convenient, often fails to capture the intricate stress interactions and coupling phenomena that govern the failure of thick-walled composite pipes, where three-dimensional stress states are significant. A particular gap in current understanding concerns the influence of fundamental design parameters, such as fibre winding angle and ply stacking sequence, on failure mechanisms under simultaneous axisymmetric and asymmetric loading [12, 13]. This discrepancy between academic models and the realities of engineering practice has hindered the full optimisation of composite pipe designs for demanding applications, potentially leaving significant performance gains unrealised. Furthermore, the computational burden of full 3D FEA has historically limited designers to evaluating only a handful of candidate configurations, creating a fundamental bottleneck in the optimisation process. Industrial design teams typically assess fewer than ten layup configurations during a development cycle, representing less than 1% of the feasible design space. This sparse sampling approach virtually guarantees suboptimal solutions, particularly when the performance landscape contains multiple local maxima or narrow optimal regions. This study introduces a framework for the analysis and design of composite pipes under combined loads. The work provides three primary contributions to the field. Firstly, it introduces a robust, two-level semi-analytical model rooted in 3D elasticity theory. Secondly, it provides insights into the coupling effects between different load components and their influence on failure mechanisms. Finally, it proposes a ‘ maximum load diagram ’ as a design tool. This approach moves beyond traditional point-based analysis, enabling a holistic exploration of the design space to identify optimal layup configurations that maximise load-bearing capacity whilst maintaining robustness to manufacturing variations. 2. Methodology The analytical core of this study is a novel two-level computational model [12] designed to determine the elastic stress state in multi-layered composite pipes subjected to combined loads. The foundational principle of the model is stress superposition, that remains valid for materials in an elastic state. This approach provides significant advantages in both computational efficiency and conceptual clarity by decoupling the complex, combined-load problem into two more manageable, physically distinct levels: for axisymmetric and asymmetric loads (see Fig. 1). The first level of the model addresses the stress state arising from axisymmetric loads, which include internal pressure ( ), axial force ( ), and torsion ( ). The analysis is based on the 3D theory of elasticity for an anisotropic, multi-layered cylindrical body. It is known that for a long pipe under these loading conditions, the problem possesses inherent cylindrical symmetry. Stresses and displacements are assumed to be independent of the hoop coordinate ( ), and the axial strain ( 0 ) remains constant along the pipe ’ s length, a condition enforced by the Saint-Venant principle for regions sufficiently distant from end effects. By applying these symmetry conditions to the strain-displacement and equilibrium equations, a second-order ordinary differential equation for the radial displacement is derived. Thus, a 3D problem is reduced to the 1D boundary value problem without loss of accuracy. The solution to this equation allows to determine the full strain field and, subsequently, the stresses within each layer of the pipe. The resulting stress components, radial ( ), hoop ( ), axial ( ), and shear ( ), are expressed as functions of the radial coordinate ( ) and a set of unknown constants ( , ,