This paper presents an analytical investigation of elastic collapse of asymmetrically corroded rings under external pressure when both internal corrosion a

This paper presents an analytical investigation of elastic collapse of corroded pipes considering the corrosion asymmetry, non-uniformity and initial ovality and one novelty is that corrosion asymmetry effect is considered by introducing a misalignment parameter accounting for co-existing internal corrosion and external corrosion. Governing differential equations are derived including the effect of corrosion asymmetry, initial ovality and membrane extensibility. By perturbative techniques, the interaction between corrosion asymmetry and initial ovality is extensively discussed by explicitly calculating the critical initial ovality governing the mode shape changes during initial deformation and collapse deformation phase. One novelty is the introduction of mode shape [ ] and mode shape 8 characterized by the sign of sum of displacements of two points independent of rigid-body motion. The theoretical solution is agreeing well with the FEA results. Furthermore, for general non-uniform corrosion, unconditionally convergent power series solutions are formulated by Lyapunov artificial small parameter method. By using Holder’s inequality, an explicit estimation method of the needed truncation number is presented for good computation accuracy by a minimization process over Holder’s exponent thus enabling early truncation of the series properly in advance. An improved estimation method is proposed by coupling with Rayleigh quotient techniques and the domain interval partition approach is introduced to accelerate convergence by thoroughly discussing the special uniformly corroded case by mathematical arguments. As a novelty, this paper illustrates why this improvement might be not evident when corrosion is rather narrow theoretically. Finally by using Chebyshev polynomials and the mathematical algebraic ring structure (generated by polynomial and trigonometric functions) closed under addition, multiplication and integration operations, some calculations for rings with corrosion profile in a non-polynomial mode are presented. This paper is intending to enhance the understanding of the effect of corrosion defect on collapse of pipes under external pressure in offshore industry.

This paper presents a numerical finite element analysis of pipelines with small misalignment under internal pressure using a developed fast pipeline modelling system ABAP using Python development environment of ABAQUS. The effect of small misalignment is shown to affect at most 10% of stress levels. Extensive parametric analyses have been conducted on the pipe length, pipe thickness. Pipe length has trival effect on non-uniform stress distribution when length/diameter ratio is greater than 1. For thinner pipe, misalignment amplifies the circumferential non-uniformity more significantly than thicker pipe. This paper serves to enhance the understanding of pipes with small installation misalignment defects under pure internal pressure.

This article presents a combined analytical, experimental and numerical investigation of non-uniform shallow circular arches and manually curved initial straight beams under lateral concentrated forces, with emphasis on non-uniformity. First, the power series method by Lyapunov artificial small parameter approach is introduced for analytically determining equilibrium paths for both shallow arches and curved beams in a similar manner. A key novelty lies in the precise estimation of truncation numbers even prior to iterations achieved through asymptotic results derived from Holder’s inequality. Detailed mathematical analysis is conducted on the monotonicity properties and asymptotic behaviors of the truncation number estimation function with respect to Holder’s exponent. The extreme case of non-uniform shallow circular arch under pinned BCs featuring rigid end segments and a small weak central segment is revisited asymptotically by identifying asymptotic dependence of deformation on smallness of central segment and intuitively interpreted by proposing a two-spring model. An experimental validation is provided for the previously theoretically identified unusual snap-through behavior of shallow arch under fixed-fixed boundary conditions with stiffer ends. Next, the snap-through behavior of manually curved initially straight beam with width non-uniformity is examined focusing on the loading position and the difference between width non-uniformity and thickness non-uniformity. Both experiments and theoretical calculations reveal a snap-through transition from load-induced (separating) mode to displacement-induced (non-separating) mode as the loading position shifts from the center to the ends. Strong agreement is observed between analytical solutions and experimental results. Finally, the averaged 1 / I approach is validated for thickness-directional periodically fast-varying non-uniformity, while the least I approach proves more accurate for width-directional non-uniformity. This paper intends to advance the understanding of how non-uniformity influences on snap-through behavior of shallow arch and curved beams under a single lateral concentrated force.