Some Formation Problems for Linear Elastic Materials

• Main Author: Schenck, David Robert
• Other Authors: Mathematics
• Format: Others
• Published: Virginia Tech 2014
• Subjects: Formation Theory; Control Theory; Shape Control; Linear Elasticity
• Online Access: http://hdl.handle.net/10919/28608; http://scholar.lib.vt.edu/theses/available/etd-081099-174646/

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. === Ph. D.