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Virginia Tech

Solution of St.-Venant's and Almansi-Michell's Problems

Abstract

dc:description.abstract

We use the semi-inverse method to solve a St. Venant and an Almansi-Michell problem for a prismatic body made of a homogeneous and isotropic elastic material that is stress free in the reference configuration. In the St. Venant problem, only the end faces of the prismatic body are loaded by a set of self-equilibrated forces. In the Almansi-Michell problem self equilibrated surface tractions are also applied on the mantle of the body. The St. Venant problem is also analyzed for the following two cases: (i) the reference configuration is subjected to a hydrostatic pressure, and (ii) stress-strain relations contain terms that are quadratic in displacement gradients. The Signorini method is also used to analyze the St. Venant problem. Both for the St. Venant and the Almansi-Michell problems, the solution of the three dimensional problem is reduced to that of solving a sequence of two dimensional problems. For the St. Venant problem involving a second-order elastic material, the first order deformation is assumed to be an infinitesimal twist. In the solution of the Almansi-Michell problem, surface tractions on the mantle of the cylindrical body are expressed as a polynomial in the axial coordinate. When solving the problem by the semi-inverse method, displacements are also expressed as a polynomial in the axial coordinate. An explicit solution is obtained for a hollow circular cylindrical body with surface tractions on the mantle given by an affine function of the axial coordinate

Degree

thesis:*
Name thesis:degree_name
Master of Science
Level thesis:degree_level
masters
Discipline thesis:degree_discipline
Engineering Science and Mechanics
Department dc:contributor.department
Engineering Science and Mechanics
Grantor dc:publisher
Virginia Tech
Year dc:date.issued
2002

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Placidi, Luca
Chair dc:contributor.committeechair
  • Bates, Robert C.
Committee members dc:contributor.committeemember
  • Morris, Don H.
  • Henneke, Edmund G. II

Subjects

dc:subject × 6

Rights

dc:rights
Statement dc:rights
  • In Copyright

Identifiers

dc:identifier.*
Dc Identifier Other
etd-10212002-043618
OAI identifier oai:identifier
oai:vtechworks.lib.vt.edu:10919/35451

Chain of custody

source
Harvested from
Virginia Tech
Base URL
vtechworks.lib.vt.edu/oai/request
Last updated
2026-07-22
Source record
OAI-PMH GetRecord
citation

Placidi, Luca. Solution of St.-Venant's and Almansi-Michell's Problems. masters thesis, Virginia Tech, 2002. http://hdl.handle.net/10919/35451