Deformation will occur for the flexible structures undergoing large rigid-body motion such as the opening of an umbrella, which poses a problem falling into the category of dynamics of deformable bodies, an intersected area between structural dynamics and rigid-body dynamics. Based on the Euler-Bernoulli beam theory, an FE model is developed to simulate the process of deployment of an umbrella under a zero gravity circumstance in which the structural FEA is adopted to define the displacement field of beam elements. The position of an arbitrary point on a body is located by a set of generalized coordinates of the system, including rigid and elastic sets characterizing rigid-body motion and deformation for the components, respectively. After formulating the kinetic energy, potential energy and generalized forces of the system, the governing equations of motion with different holonomic constraint conditions corresponding to the stages of the deployment are then derived by invoking Lagrange's equations with multipliers. As for the validation of this model, a rigid FE model and a continuum rigid-body model are also derived. The numeric process reveals that significant periodic vibration is induced on the leaf at full deployment if an initial velocity is applied on the sleeve of the modeled umbrella and the deformation of the members causes the retard of the deployment. Comparison of the results shows good agreement between 3-element and 6-element models, and the deformable models are validated by the rigid-body ones. Although the formulation is based on the holonomic 2-body model, it is also applicable to a more complicated nonholonomic system.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.98969 |
| Date | January 2006 |
| Creators | Hu, Jun An, 1968- |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Engineering (Department of Civil Engineering and Applied Mechanics.) |
| Rights | © Jun An Hu, 2006 |
| Relation | alephsysno: 002490990, proquestno: AAIMR24966, Theses scanned by UMI/ProQuest. |
Page generated in 0.0605 seconds