Some Formation Problems for Linear Elastic Materials

Some equations of linear elasticity are developed, including those specific to certain actuator structures considered in formation theory. The invariance of the strain-energy under the transformation from rectangular to spherical coordinates is then established for use in two specific formation problems. The first problem, involving an elastic structure with a cylindrical equilibrium configuration, is formulated in two dimensions using polar coordinates. It is shown that L² controls suffice to obtain boundary displacements in H^1/2. The second problem has a spherical equilibrium configuration and utilizes the elastic equations in spherical coordinates. Results similar to those obtained in the two dimensional case are indicated for the three dimensional problem.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1999

Author dc:creator

• Schenck, David Robert

Chair dc:contributor.committeechair

• Russell, David L.

Committee members dc:contributor.committeemember

• Kim, Jong Uhn
• Lin, Tao
• Rogers, Robert C.
• Wheeler, Robert L.

• Formation Theory
• Control Theory
• Shape Control
• Linear Elasticity

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-081099-174646

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28608