A Computationally Efficient p-Refinement Finite Element Method Approach for the Fracture Analysis of Axially Cracked Pipes with Composite Patch Reinforcement

Cylindrical shells are widely used in pipelines, pressure vessels, and aircraft fuselages due to their efficient internal pressure distribution. However, axial cracks caused by fatigue, environmental effects, or mechanical loading compromise structural integrity, requiring effective reinforcement. This study presents a finite element modeling approach integrating p-refinement techniques for the efficient analysis of axially cracked pipes reinforced with composite patches. The proposed method unifies equivalent single-layer and layer-wise theories into a single finite element type, improving computational efficiency and eliminating the need for multiple element types in transition elements. Benchmark studies show that the proposed model accurately predicts mechanical behavior, with maximum displacement and stress intensity factors (SIFs) deviating by less than 5% from reference solutions. Fracture analysis using the virtual crack closure technique confirms the accuracy of the SIF calculations. In patched cracked pipes, the proposed model achieves a 67% reduction in degrees of freedom compared to conventional p-refinement layer-wise models, while maintaining computational accuracy. Additionally, boron–epoxy composite patches reduce SIFs by up to 40%, demonstrating effective crack reinforcement. These findings support computationally efficient damage-tolerant design strategies for pressurized cylindrical structures in aerospace, marine, and mechanical engineering.