Title page for ETD etd-081099-174646


Type of Document Dissertation
Author Schenck, David Robert
Author's Email Address schenck@math.vt.edu
URN etd-081099-174646
Title Some Formation Problems for Linear Elastic Materials
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Russell, David L. Committee Chair
Kim, Jong Uhn Committee Member
Lin, Tao Committee Member
Rogers, Robert C. Committee Member
Wheeler, Robert L. Committee Member
Keywords
  • Formation Theory
  • Control Theory
  • Shape Control
  • Linear Elasticity
Date of Defense 1999-07-26
Availability unrestricted
Abstract
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 $L^2$ 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.

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