Variationally consistent methods for Lagrangian dynamics in continuum mechanics

Rapid dynamics are commonly encountered in industrial applications such as forging, crash tests and many others. These problems are typically non-linear due to large deformations and/or non-linear constitutive relations. Such problems are typically modelled from a Lagrangian viewpoint, where the mesh is attached to the body; hence, large deformations lead to large distortions in the mesh. Explicit numerical methods are considered to be efficient in these cases where large meshes and small time-steps are employed for spatial and temporal resolution. However, incompressible and nearly incompressible materials pose a problem as the timestep stability restriction in explicit methods becomes increasingly severe. Most of the numerical methods employed for such simulations, are developed from discretization of the equations of motion. Recently, Variational Integrators have been developed where the numerical time integration scheme is developed from a variational principle based on Hamilton's principle of stationary action. Such methods ensure conservation of linear and angular momentum, which lead to more physically consistent simulations.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Lahiri, Sudeep Kumar

Advisor dc:contributor.advisor

• Jamie Peraire.

• Aeronautics and Astronautics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/39597

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/39597