{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69951"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69951","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Three-Dimensional Non-Axisymmetric Anisotropic Stress Concentrations","abstract":"Unified explicit analytical solutions for the (non-axisymmetric) first and second boundary value problems of elasticity theory for a spheroidal cavity embedded in a transversely isotropic medium are presented. The analysis is based upon solutions of the homogeneous displacement equations of equilibrium in terms of three quasi-harmonic potential functions, each of which is harmonic in a space different from the physical space. Thus, three spheroidal coordinate systems with different metric scales (one for each potential) are introduced such that the three coordinate systems coincide on the surface of the spheroidal cavity. These potential functions are taken in a unique combination of the associated Legendre functions of the first and second kind.","abstract_html":"Unified explicit analytical solutions for the (non-axisymmetric) first and second boundary value problems of elasticity theory for a spheroidal cavity embedded in a transversely isotropic medium are presented. The analysis is based upon solutions of the homogeneous displacement equations of equilibrium in terms of three quasi-harmonic potential functions, each of which is harmonic in a space different from the physical space. Thus, three spheroidal coordinate systems with different metric scales (one for each potential) are introduced such that the three coordinate systems coincide on the surface of the spheroidal cavity. These potential functions are taken in a unique combination of the associated Legendre functions of the first and second kind.","abstract_has_math":false,"creators":["Zureick, Abdul Hamid"],"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":"2014-12-15T20:36:18Z","date_published":"2014-12-15T20:36:18Z","updated_at":"2026-07-22T22:26:01Z","subjects":["Engineering, Civil"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8521910"],"render_values":[{"text":"(UMI)AAI8521910","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69951","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Zureick, Abdul Hamid"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T20:36:18Z","10000-01-01","1985"]},{"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":["Engineering, Civil"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/69951","(UMI)AAI8521910"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Unified explicit analytical solutions for the (non-axisymmetric) first and second boundary value problems of elasticity theory for a spheroidal cavity embedded in a transversely isotropic medium are presented. The analysis is based upon solutions of the homogeneous displacement equations of equilibrium in terms of three quasi-harmonic potential functions, each of which is harmonic in a space different from the physical space. Thus, three spheroidal coordinate systems with different metric scales (one for each potential) are introduced such that the three coordinate systems coincide on the surface of the spheroidal cavity. These potential functions are taken in a unique combination of the associated Legendre functions of the first and second kind.","Extensive numerical data are obtained for the stress concentration factors associated with axisymmetric and non-axisymmetric problems for a variety of materials. The effect of anisotropy on the stress concentration factor is discussed in much greater detail than has been previously available in the literature.","Made available in DSpace on 2014-12-15T20:36:18Z (GMT). No. of bitstreams: 1 8521910.pdf: 2495589 bytes, checksum: 9922602a69531ae3ed005e4a4e807ed3 (MD5) Previous issue date: 1985","Embargo set by: Seth Robbins for item 70117 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","132 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985."]},{"key":"dc:title","label":"Title","values":["Three-Dimensional Non-Axisymmetric Anisotropic Stress Concentrations"]}]}],"canonical_facts":{"dc:creator":["Zureick, Abdul Hamid"],"dc:date":["2014-12-15T20:36:18Z","10000-01-01","1985"],"dc:description":["Unified explicit analytical solutions for the (non-axisymmetric) first and second boundary value problems of elasticity theory for a spheroidal cavity embedded in a transversely isotropic medium are presented. The analysis is based upon solutions of the homogeneous displacement equations of equilibrium in terms of three quasi-harmonic potential functions, each of which is harmonic in a space different from the physical space. Thus, three spheroidal coordinate systems with different metric scales (one for each potential) are introduced such that the three coordinate systems coincide on the surface of the spheroidal cavity. These potential functions are taken in a unique combination of the associated Legendre functions of the first and second kind.","Extensive numerical data are obtained for the stress concentration factors associated with axisymmetric and non-axisymmetric problems for a variety of materials. The effect of anisotropy on the stress concentration factor is discussed in much greater detail than has been previously available in the literature.","Made available in DSpace on 2014-12-15T20:36:18Z (GMT). No. of bitstreams: 1 8521910.pdf: 2495589 bytes, checksum: 9922602a69531ae3ed005e4a4e807ed3 (MD5) Previous issue date: 1985","Embargo set by: Seth Robbins for item 70117 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","132 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985."],"dc:identifier":["http://hdl.handle.net/2142/69951","(UMI)AAI8521910"],"dc:subject":["Engineering, Civil"],"dc:title":["Three-Dimensional Non-Axisymmetric Anisotropic Stress Concentrations"],"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":"2026-07-22T22:26:01Z"}