Geometrically exact mechanics of pipes conveying fluid with an axially sliding downstream end

In this study, the post-buckling patterns and stability characteristics of hanging and standing soft pipes conveying fluid, with an axially sliding downstream end, are investigated using a new nonlinear geometrically exact model. The mathematical formulation in terms of the rotation angle and lateral displacement, is derived by incorporating the lateral constraint at the downstream end into the geometrically exact model of a cantilevered pipe conveying fluid in terms of the rotation angle. Additionally, a linearized mathematical model of the system around its post-buckling path is established to assess the stability characteristics of post-buckled configurations. To determine the post-buckling patterns and their stability behavior, the shooting scheme in conjunction with the Runge-Kutta finite difference method is utilized. The analysis focuses on both hanging and standing systems, where the downstream end is simply supported and the upstream end may be either clamped or simply supported, taking into account the simultaneous influences of flow velocity and gravity. Furthermore, in the case of the standing system with both ends simply supported, the potential for snap-through buckling is examined. Ultimately, the geometrically exact patterns are compared with those obtained by the original and approximate versions of the nonlinear third-order model.