"Deformable Pipes with Internal Flow of Fluid and Rigid Body Degrees of Freedom"
Deformable Pipes with Internal Flow of Fluid and Rigid Body Degrees of Freedom
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The aim of the present thesis is to contribute to the field of fluid-structure interaction and the simulation of open systems with mass flow through its boundaries. Based on a novel extended version of the Lagrange equations of motion for systems containing non-material volumes, the non-linear equations of motion of elastic pipe systems conveying fluid are deduced. An alternative to existing methods utilizing Newtonian balance equations or Hamilton’s principle is thus provided. The application of the extended Lagrange equations in combination with a Ritz method directly results in a set of non-linear ordinary differential equations of motion, as opposed to the methods of derivation previously published, which result in partial differential equations of motion. The investigated pipe systems are modeled as Euler elastica, where large deflections in combination with rigid body degrees of freedom are considered without order of magnitude assumptions. The dynamics of the systems under consideration are studied in terms of a numerical stability analysis and compared to existing results. In a next step, a novel pipe finite element conveying fluid, suitable for modeling large deformations in the framework of Bernoulli Euler beam theory, is presented. The element is based on the recently introduced absolute nodal coordinate formulation of multibody dynamics. Standard numerical examples show the convergence of the deformation for increasing number of elements. The critical flow velocities for increasing number of pipe elements are compared to approaches based on Euler elastica and moving discrete masses. The results show good agreement with the reference solutions applying only a small number of pipe finite elements.