An infinite tube approach for the efficient modelling of collapse using the finite element method

Abstract

Tubes are employed in a wide range of engineering applications, such as production, transportation, cooling and heating of liquids and gases. For being structures often exposed to extreme operational conditions, if not properly designed, these pipes may fail, resulting not only in severe economic losses but also into human and environmental hazard depending on the application. One important failure mode of tubes is bucking, which occurs when the external pressure exceeds the internal pressure in a certain critical limit, leading to the collapse of the tube. Over the last decades, a great number of analytical and numerical studies have been conducted on the collapse of tubes, which resulted in well-stablished formulas for the critical pressure prediction for both perfect and imperfect tubes.In real engineering applications, however, the tube might be subject to other loads beyond the external pressure and the combination of these loads can substantially modify the critical collapse pressure. Despite this, there are no closed-form solutions for the collapse when multiple loads, such as tension and bending, are simultaneously or sequentially applied to the pipe. For such complex problems, the only alternatives are the numerical and experimental analyses. The most common alternative to minimize boundary condition interference is the adoption of a sample length long enough to mitigate them. For finite element models, however, this strategy might increase model size and, consequently the time and computational cost of the analysis.Therefore, aiming at more efficient finite element modelling of the collapse of tubes, this paper presents an infinite tube methodology, implemented through the coupling of certain degrees of freedom, which considerably reduces the influence of sample length and allows the adoption of lighter models while maintaining the quality of the representation of the collapse phenomenon. This methodology was implemented in a commercial finite element package, employed in collapse analyses under combined tension-bending loads and, finally, compared to classical numerical solutions from the literature.Despite the collapse of tubes being a well-stablished problem in the literature, this works still presents a major contribution to the field by presenting the detailed description of an innovative infinite tube methodology which reduces model sizes, being, therefore, of great importance for practical design applications, especially for those which require a large number of analyses, such as structural optimizations.