{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/35451"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/35451","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Solution of St.-Venant's and Almansi-Michell's Problems","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","abstract_html":"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","abstract_has_math":false,"creators":["Placidi, Luca"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Science and Mechanics","degree_department":"Engineering Science and Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Bates, Robert C."],"committee_members":["Morris, Don H.","Henneke, Edmund G. II"],"year":2002,"date_issued":"2002-05-02","date_published":"2002-05-02","updated_at":"2026-07-22T22:19:47Z","subjects":["Polynomial hypothesis","Saint-Venant's Problem","Linear Elasticity","Non Linear Elasticity","Stressed Reference Configuration","Clebsch hypothesis"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-10212002-043618"],"render_values":[{"text":"etd-10212002-043618","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/35451","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Bates, Robert C."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Morris, Don H.","Henneke, Edmund G. 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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"]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Solution of St.-Venant's and Almansi-Michell's Problems"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Bates, Robert C."],"dc:contributor.committeemember":["Morris, Don H.","Henneke, Edmund G. II"],"dc:contributor.department":["Engineering Science and Mechanics"],"dc:creator":["Placidi, Luca"],"dc:date.accessioned":["2014-03-14T20:46:53Z"],"dc:date.available":["2014-03-14T20:46:53Z","2003-10-24"],"dc:date.issued":["2002-05-02"],"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"],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-10212002-043618"],"dc:identifier.uri":["http://hdl.handle.net/10919/35451"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Polynomial hypothesis","Saint-Venant's Problem","Linear Elasticity","Non Linear Elasticity","Stressed Reference Configuration","Clebsch hypothesis"],"dc:title":["Solution of St.-Venant's and Almansi-Michell's Problems"],"dc:type":["Thesis"],"thesis:degree_discipline":["Engineering Science and Mechanics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:47Z"}