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 AbstractSome equations of linear elasticity are developed, including thosespecific 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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