Some Formation Problems for Linear Elastic Materials

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dc.contributor.authorSchenck, David Roberten
dc.contributor.committeechairRussell, David L.en
dc.contributor.committeememberKim, Jong Uhnen
dc.contributor.committeememberLin, Taoen
dc.contributor.committeememberRogers, Robert C.en
dc.contributor.committeememberWheeler, Robert L.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:15:02Zen
dc.date.adate1999-08-14en
dc.date.available2014-03-14T20:15:02Zen
dc.date.issued1999-07-26en
dc.date.rdate2000-08-14en
dc.date.sdate1999-08-10en
dc.description.abstractSome 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<sup>1/2</sup>. 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.en
dc.description.degreePh. D.en
dc.identifier.otheretd-081099-174646en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-081099-174646/en
dc.identifier.urihttp://hdl.handle.net/10919/28608en
dc.publisherVirginia Techen
dc.relation.haspartmaster.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectFormation Theoryen
dc.subjectControl Theoryen
dc.subjectShape Controlen
dc.subjectLinear Elasticityen
dc.titleSome Formation Problems for Linear Elastic Materialsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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