Eventos Anais de eventos
DINAME 2017
XVII International Symposium on Dynamic Problems of Mechanics
Novel modular modeling methodology applied to the problem of a pipe conveying fluid
Submission Author:
Renato Maia Matarazzo Orsino , SP , Brazil
Co-Authors:
Renato Maia Matarazzo Orsino, CELSO Pupo Pesce
Presenter: Renato Maia Matarazzo Orsino
doi://10.26678/ABCM.DINAME2017.DIN17-0064
Abstract
This paper proposes an extension of a novel modular modeling approach, originally developed for lumped parameter systems, to the derivation of FEM-discretized equations of motion of one-dimensional distributed parameter systems. The novel methodology is characterized by the use of a recursive algorithm based on projection operators that allows any constraint condition to be considered a posteriori. This leads to a modular approach in which a system can be conceived as the top member of a hierarchy in which the increase of complexity from one level to the parent one is associated to the enforcement of some constraints. For lumped parameter systems this allows the implementation of modeling procedures starting from already known mathematical models of subsystems. In the case of distributed parameter systems, such a novel methodology not only allows to explore subsystem-based modeling strategies, but also makes it possible to propose formulations in which compatibility and boundary conditions are treated as constraints. The benchmark chosen to explore these further possibilities is the extensively studied problem of a cantilevered pipe conveying fluid. Supposing a solid pipe that respects the hypotheses of the Linear Theory of Elasticity, but is subject to geometric nonlinearities, and assuming an axial plug-flow, a Hamiltonian derivation of the discretized equations of motion is performed without an a priori enforcement of neither compatibility nor boundary conditions. After that, proposing a formulation that reconciles the use of the Finite Element Method along with the modular modeling algorithm for one-dimensional distributed parameter systems, some numerical simulations are performed in order to address qualitatively this novel methodology.
Keywords
Analytical Mechanics, mathematical modeling, Finite Element Method, Modular Modeling, Pipe Conveying Fluid
