Geometric discretization schemes and differential complexes for elasticity

In this research, we study two different geometric approaches, namely, the discrete exterior calculus and differential complexes, for developing numerical schemes for linear and nonlinear elasticity. Using some ideas from discrete exterior calculus (DEC), we present a geometric discretization scheme for incompressible linearized elasticity. After characterizing the configuration manifold of volume- preserving discrete deformations, we use Hamilton's principle on this configuration manifold. The discrete Euler-Lagrange equations are obtained without using Lagrange multipliers.

Level thesis:degree_level

Doctoral

Department dc:contributor.department

Civil and Environmental Engineering

Grantor dc:publisher

Georgia Institute of Technology

Year dc:date.issued

2013

Author dc:creator

• Angoshtari, Arzhang

Advisor dc:contributor.advisor

• Yavari, Arash

Committee members dc:contributor.committeemember

• Desroches, Reginald
• Gangbo, Wilfrid
• Garmestani, Hamid
• Thadhani, Naresh

• Geometric numerical schemes
• Elasticity complex
• Nonlinear stress functions

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/1853/49026

OAI identifier oai:identifier

oai:repository.gatech.edu:1853/49026