Fluid-conveying pipes in the floating frame of reference formulation

This work presents a new formulation for flexible fluid-conveying pipe elements based on the widely used floating frame of reference formulation. The elements can be used as a tool for the analysis of flexible multibody systems that contain fluid-conveying pipes, as it is well known that the movement of the fluid can influence the behavior and stability of such systems. The pipe defines a control volume through which the fluid, which is considered to be a moving mass, axially flows. The velocity of a material point of the fluid is therefore a material derivative of its position, representing the large rigid movement and small elastic deformation of the pipe along with the velocity of the fluid with respect to the pipe. The equations of motion are derived through the principle of virtual work, spatial discretization by finite element interpolation functions, and model reduction. A simplification of the consistent equations of motion is proposed, which avoids the use of inertia shape integrals and reduces the effort required to implement the developed fluid-conveying pipe elements in existing multibody software. The developed elements are validated by simulation of a straight cantilevered pipe and a curved pipe constrained on one end by a hinge. A simulation of a concrete printing system illustrates the straightforward incorporation of the elements in larger multibody systems.