An analytical investigation of the collapse of asymmetrically corroded pipes under external pressure

This paper presents an analytical investigation of elastic collapse of asymmetrically corroded rings under external pressure when both internal corrosion and external corrosion exist. Governing equations are derived for membrane inextensible and membrane extensible cases; a full continuity condition is rigorously derived by the Euler-Bernoulli beam assumption. Comparison with finite element analysis (FEA) shows good agreement for load-displacement curves but membrane extensibility should be included to accurately predict the initial deformation phase, although the discrepancy for both the inextensible and extensible models vanishes for larger deformation phases. By the perturbation technique, the initial load-displacement slope is calculated, and extensive parametric analysis shows complicated dependency of this slope on the misalignment parameter and the angular extent of corrosion. We also present an infallible semi-analytical perturbation solution for both homogeneous and inhomogeneous cases by the Lyapunov arbitrary small-parameter method and show that the resulting power series always converges; then a mathematical argument of analyticity has been presented to illustrate that the so-called homotopy analysis method in the literature converges when the convergence controlling parameter is lying in (-2, 0). This paper serves to enhance the understanding of asymmetrically corroded rings and it is mainly relevant to offshore engineering.