{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/66903"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/66903","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Wave Propagation Problems in Certain Elastic Anisotropic Half Spaces","abstract":"The Smirnov-Sobolev method of self-similar potentials is used to solve certain wave propagation problems in anisotropic media. The solutions are expressed in terms of analytic functions which are determined from the boundary conditions in a straightforward manner. Two types of problems are considered. The first type concerns the two-dimensional case of an orthotropic material under plain-strain conditions subjected to a suddenly applied line force on the surface or in the interior of a half space. The second type treats the three-dimensional problem of a point force suddenly applied on the surface of a transversely isotropic half space. This solution is formed, in general, by a rotational superposition of the solutions for a plane strain and for an antiplane problem with appropriately defined boundary conditions. The mapping of the wave fields in the complex domain composed of a four-sheeted Riemann surface is examined in detail. Some of the techniques used in the numerical treatment of certain singularities are briefly discussed. The numerical results are given in the form of time histories for the displacements and stresses in the two-dimensional case and as time histories of only the displacements in the three-dimensional case.","abstract_html":"The Smirnov-Sobolev method of self-similar potentials is used to solve certain wave propagation problems in anisotropic media. The solutions are expressed in terms of analytic functions which are determined from the boundary conditions in a straightforward manner. Two types of problems are considered. The first type concerns the two-dimensional case of an orthotropic material under plain-strain conditions subjected to a suddenly applied line force on the surface or in the interior of a half space. The second type treats the three-dimensional problem of a point force suddenly applied on the surface of a transversely isotropic half space. This solution is formed, in general, by a rotational superposition of the solutions for a plane strain and for an antiplane problem with appropriately defined boundary conditions. The mapping of the wave fields in the complex domain composed of a four-sheeted Riemann surface is examined in detail. Some of the techniques used in the numerical treatment of certain singularities are briefly discussed. The numerical results are given in the form of time histories for the displacements and stresses in the two-dimensional case and as time histories of only the displacements in the three-dimensional case.","abstract_has_math":false,"creators":["Caracostis, C.G."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Civil Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-13T19:32:14Z","date_published":"2014-12-13T19:32:14Z","updated_at":"2026-07-22T22:25:56Z","subjects":["Applied Mechanics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8129570"],"render_values":[{"text":"(UMI)AAI8129570","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/66903","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Caracostis, C.G."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-13T19:32:14Z","10000-01-01","1981"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Civil Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied Mechanics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/66903","(UMI)AAI8129570"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The Smirnov-Sobolev method of self-similar potentials is used to solve certain wave propagation problems in anisotropic media. The solutions are expressed in terms of analytic functions which are determined from the boundary conditions in a straightforward manner. Two types of problems are considered. The first type concerns the two-dimensional case of an orthotropic material under plain-strain conditions subjected to a suddenly applied line force on the surface or in the interior of a half space. The second type treats the three-dimensional problem of a point force suddenly applied on the surface of a transversely isotropic half space. This solution is formed, in general, by a rotational superposition of the solutions for a plane strain and for an antiplane problem with appropriately defined boundary conditions. The mapping of the wave fields in the complex domain composed of a four-sheeted Riemann surface is examined in detail. Some of the techniques used in the numerical treatment of certain singularities are briefly discussed. The numerical results are given in the form of time histories for the displacements and stresses in the two-dimensional case and as time histories of only the displacements in the three-dimensional case.","Made available in DSpace on 2014-12-13T19:32:14Z (GMT). No. of bitstreams: 1 8129570.pdf: 4894141 bytes, checksum: 27043161c025d75dee077876b7445451 (MD5) Previous issue date: 1981","Embargo set by: Seth Robbins for item 67081 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","204 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981."]},{"key":"dc:title","label":"Title","values":["Wave Propagation Problems in Certain Elastic Anisotropic Half Spaces"]}]}],"canonical_facts":{"dc:creator":["Caracostis, C.G."],"dc:date":["2014-12-13T19:32:14Z","10000-01-01","1981"],"dc:description":["The Smirnov-Sobolev method of self-similar potentials is used to solve certain wave propagation problems in anisotropic media. The solutions are expressed in terms of analytic functions which are determined from the boundary conditions in a straightforward manner. Two types of problems are considered. The first type concerns the two-dimensional case of an orthotropic material under plain-strain conditions subjected to a suddenly applied line force on the surface or in the interior of a half space. The second type treats the three-dimensional problem of a point force suddenly applied on the surface of a transversely isotropic half space. This solution is formed, in general, by a rotational superposition of the solutions for a plane strain and for an antiplane problem with appropriately defined boundary conditions. The mapping of the wave fields in the complex domain composed of a four-sheeted Riemann surface is examined in detail. Some of the techniques used in the numerical treatment of certain singularities are briefly discussed. The numerical results are given in the form of time histories for the displacements and stresses in the two-dimensional case and as time histories of only the displacements in the three-dimensional case.","Made available in DSpace on 2014-12-13T19:32:14Z (GMT). No. of bitstreams: 1 8129570.pdf: 4894141 bytes, checksum: 27043161c025d75dee077876b7445451 (MD5) Previous issue date: 1981","Embargo set by: Seth Robbins for item 67081 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","204 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981."],"dc:identifier":["http://hdl.handle.net/2142/66903","(UMI)AAI8129570"],"dc:language":["eng"],"dc:subject":["Applied Mechanics"],"dc:title":["Wave Propagation Problems in Certain Elastic Anisotropic Half Spaces"],"dc:type":["text"],"thesis:degree_discipline":["Civil Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:56Z"}