PSI - Issue 77

518 Tianyu Wang et al. / Procedia Structural Integrity 77 (2026) 512–520 Wang et al/ Structural Integrity Procedia 00 (2026) 000 – 000 −45°] versus [+45°/−45°/+75°/−75°] configurations revealed that the former arrangement, with high-angle plies internal, performed only 4% better under pressure-dominated loading. The physical mechanism behind this improvement involves the creation of a functionally graded structure where each ply group operates closer to its optimal loading condition. The internal 75° plies efficiently resist pressure-induced hoop stress whilst being partially shielded from torsional shear by the external 45° plies. Finally, it was concluded that under combined loading with a dominating component, the stacking sequence should use plies with appropriate orientations closer to the critical surface (e.g., internal for pressure, external for bending). However, this must be balanced against manufacturing constraints and to prevent process-induced distortions. The findings suggest that stacking sequence optimisation alone can improve load capacity by 5 – 20% without any change in material or manufacturing cost, a significant opportunity for performance enhancement in existing designs. 5. Optimal design: Maximum load diagrams Traditional design methodologies for composite structures have long been constrained by computational limitations, typically relying on ‘ point-based analysis ’— evaluating only a limited number of preselected layup configurations. Industrial practice often involves testing fewer than ten configurations, selected based on engineering intuition or previous designs, representing an infinitesimal fraction of the feasible design space. This approach, whilst being pragmatic, virtually guarantees suboptimal solutions, particularly for the cases with multiple local extremums, narrow optimal regions, or unexpected coupling effects between design parameters. To overcome these fundamental limitations, this study leverages the computational efficiency of the proposed analytical method (which improves solution speed by two orders of magnitude) whilst introducing the ‘ maximum load diagram ’ as a design optimisation approach, enabling engineers to visualise the entire performance landscape rather than sampling it sparsely. The maximum load diagram methodology systematically evaluates the ultimate load-bearing capacity across the continuous design space of winding angles. For a given stacking sequence template (e.g., [+ ₁/− ₁/+ ₂/− ₂] ), the algorithm varies ₁ and ₂ independently across their feasible ranges (typically 0° to 90° ) with fine resolution ( 1° increments). At each design point, the model computes the complete stress state under specified loads, then progressively increases the other load until a failure criterion is satisfied at any point within the structure. This limiting loading represents the ultimate capacity for that specific angle combination. The resulting 3D surface plot provides an intuitive visualisation where the and axes represent the winding angles of different ply groups, whilst the axis represents the maximum sustainable loading before failure. This visual representation transforms abstract numerical data into an intuitive ‘ topographical map ’ of the design space, where peaks represent optimal configurations, valleys indicate poor designs, and plateaus suggest robust regions insensitive to manufacturing variations. As an example, please see in Fig. 5 the maximum torque diagrams for [+ ₁/− ₁/+ ₂/− ₂] configuration under 133.5 kN axial compression, 51.7 MPa internal pressure and 10 degrees/100 ft bending. 7

Fig. 5. Torsional strength for [+ ₁/− ₁/+ ₂/− ₂] pipe