Hydrostatic Pressure Load in Pipes Modeled Using Beam Finite Elements: Theoretical Discussions and Applications

Abstract

This work presents a derivation of equivalent loads, coming from the integration of hydrostatic pressure fields on the internal and external walls of a curved pipe, which is modeled as a Euler-Bernoulli beam. To achieve that, the divergence theorem is applied to an infinitesimal-length pipe element. The Frenet coordinate system is used, leading to convenient simplifications. Finally, an expression is obtained for the equivalent distributed load along the pipe, due to pressure fields. Such load has a follower behavior and is curvature-dependent. Discussions are made, revisiting the effective tension and effective moment classical concepts, such as relating the proposed derivation with those concepts. An example of application is made in the context of analytical beam models, which is compared to a solid finite element model, experiencing a hydrostatic pressure field. Lastly, the obtained formulas are applied to an example of nonlinear buckling analysis of an initially straight pipeline, under constant internal pressurization. The postcritical configuration is obtained by using a geometric nonlinear finite element model, composed of beams, which are loaded using the expressions derived in this paper.