Advanced Flexibility Analysis and Nozzle Load Optimization for Critical Pipelines Connected to Compressors, Pumps, and Pressure Vessels

Critical piping attached to compressors, pumps and pressure vessels occupies a narrow design space in which flexibility must be sufficient to protect equipment nozzles, but stiffness must remain adequate for vibration control, alignment, maintainability and pressure containment. Recent literature has expanded the analytical basis for this problem through refined finite-element modelling, updated piping and machinery standards, digital monitoring and optimisation-based support design. This review synthesises scholarship and authoritative engineering sources published between 2020 and 2025 to clarify how advanced flexibility analysis and nozzle-load optimisation are being reframed for safety-critical industrial piping. The review used a transparent source-search and thematic synthesis process covering scholarly databases, standards repositories and specialist engineering literature. The synthesis identifies four dominant themes: load-path modelling at equipment interfaces, stress classification and local shell behaviour, support and routing optimisation, and the emergence of data-informed integrity management. The evidence shows strong convergence around the need to treat nozzle loads as coupled structural, thermal, hydraulic and operational phenomena rather than as isolated compliance checks. However, the literature remains fragmented across piping stress analysis, pressure-vessel design, rotating-equipment installation and digital integrity research. Persistent gaps include limited validation under transient thermal and dynamic loads, sparse treatment of multi-equipment systems, inconsistent representation of support friction and poor integration between design-stage optimisation and operational monitoring. The review proposes future work on benchmarked digital twins, uncertainty-aware optimisation, life-cycle nozzle-load governance and machine-readable acceptance criteria. Its contribution is an integrated conceptual basis for more resilient, verifiable and adaptable piping systems connected to critical equipment.