Some Formation Problems for Linear Elastic Materials

by Schenck, David Robert

Abstract (Summary)
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.
Bibliographical Information:

Advisor:David L. Russell; Jong Kim; Tao Lin; Robert Rogers; Robert Wheeler

School:Virginia Polytechnic Institute and State University

School Location:USA - Virginia

Source Type:Master's Thesis



Date of Publication:08/14/1999

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