{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/25691"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/25691","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The elastic stress field produced by a point force in a cubic crystal","abstract":"Fredholm in 1900 gave a solution in principle for the dis-placements generated by a point force at the origin in an infinite elastic solid. Eshe1by in 1955 gave an approximate solution of the dilatation for the triple force at the origin wi th no moment. Eshe1by and Leibried gave expressions which converge only when [equation] The present calculation uses Fredholm's work to provide a Fourier expansion of displacement which converges for all stable cubic crystals. The convergence of the series giving the displacement due to apoint force is very slow for lithium which is on the verge of 2c:44 0 a phase change [equation] at 78. K Detailed calculations of stress fields have been made for aluminum and copper. It is noted that for Cu a contribution of additional terms besides that given by Eshe1by appears in the angular dependence of dilatation for the triple double force but for At the dilatation is in close agreement with Eshe1by's result. The elastic interaction energies of two triple double force interstitia1s and of two single double force interstitia1s with no moment are calculated. The calculated stresses are accurate to about 15 and 8 percent of their value for Cu and At, respectively. Fifteen terms for Cu and six terms for At were used in the series for stresses. Better accuracy could be obtained by including higher order terms in the expansions.","abstract_html":"Fredholm in 1900 gave a solution in principle for the dis-placements generated by a point force at the origin in an infinite elastic solid. Eshe1by in 1955 gave an approximate solution of the dilatation for the triple force at the origin wi th no moment. Eshe1by and Leibried gave expressions which converge only when [equation] The present calculation uses Fredholm's work to provide a Fourier expansion of displacement which converges for all stable cubic crystals. The convergence of the series giving the displacement due to apoint force is very slow for lithium which is on the verge of 2c:44 0 a phase change [equation] at 78. K Detailed calculations of stress fields have been made for aluminum and copper. It is noted that for Cu a contribution of additional terms besides that given by Eshe1by appears in the angular dependence of dilatation for the triple double force but for At the dilatation is in close agreement with Eshe1by's result. The elastic interaction energies of two triple double force interstitia1s and of two single double force interstitia1s with no moment are calculated. The calculated stresses are accurate to about 15 and 8 percent of their value for Cu and At, respectively. Fifteen terms for Cu and six terms for At were used in the series for stresses. Better accuracy could be obtained by including higher order terms in the expansions.","abstract_has_math":false,"creators":["Lie, Kyoon-Haeng Choh"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Koehler, James S."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-07-07T15:48:04Z","date_published":"2011-07-07T15:48:04Z","updated_at":"2026-07-22T22:25:26Z","subjects":["elastic stress field","point force","cubic crystal","infinite elastic solid"],"languages":["en"],"rights":["1967 Kyoon-Haeng Choh Lie"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["6086910"],"render_values":[{"text":"6086910","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/25691","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Koehler, James S."]},{"key":"dc:creator","label":"Author","values":["Lie, Kyoon-Haeng Choh"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-07-07T15:48:04Z","10000-01-01","1967"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["elastic stress field","point force","cubic crystal","infinite elastic solid"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1967 Kyoon-Haeng Choh Lie"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["6086910","http://hdl.handle.net/2142/25691"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Fredholm in 1900 gave a solution in principle for the dis-placements generated by a point force at the origin in an infinite elastic solid. Eshe1by in 1955 gave an approximate solution of the dilatation for the triple force at the origin wi th no moment. Eshe1by and Leibried gave expressions which converge only when [equation] The present calculation uses Fredholm's work to provide a Fourier expansion of displacement which converges for all stable cubic crystals. The convergence of the series giving the displacement due to apoint force is very slow for lithium which is on the verge of 2c:44 0 a phase change [equation] at 78. K Detailed calculations of stress fields have been made for aluminum and copper. It is noted that for Cu a contribution of additional terms besides that given by Eshe1by appears in the angular dependence of dilatation for the triple double force but for At the dilatation is in close agreement with Eshe1by's result. The elastic interaction energies of two triple double force interstitia1s and of two single double force interstitia1s with no moment are calculated. The calculated stresses are accurate to about 15 and 8 percent of their value for Cu and At, respectively. Fifteen terms for Cu and six terms for At were used in the series for stresses. Better accuracy could be obtained by including higher order terms in the expansions.","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-07-07T15:48:04Z No. of bitstreams: 1 1967_lie.pdf: 1994393 bytes, checksum: 079355c6e84863874e0d670cd2528ec6 (MD5)","Made available in DSpace on 2011-07-07T15:48:04Z (GMT). No. of bitstreams: 1 1967_lie.pdf: 1994393 bytes, checksum: 079355c6e84863874e0d670cd2528ec6 (MD5) Previous issue date: 1967","Restriction data tranferred 2014-07-01T11:32:43-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-07-07T15:48:04Z Item is restricted indefinitely.","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["The elastic stress field produced by a point force in a cubic crystal"]}]}],"canonical_facts":{"dc:contributor":["Koehler, James S."],"dc:creator":["Lie, Kyoon-Haeng Choh"],"dc:date":["2011-07-07T15:48:04Z","10000-01-01","1967"],"dc:description":["Fredholm in 1900 gave a solution in principle for the dis-placements generated by a point force at the origin in an infinite elastic solid. Eshe1by in 1955 gave an approximate solution of the dilatation for the triple force at the origin wi th no moment. Eshe1by and Leibried gave expressions which converge only when [equation] The present calculation uses Fredholm's work to provide a Fourier expansion of displacement which converges for all stable cubic crystals. The convergence of the series giving the displacement due to apoint force is very slow for lithium which is on the verge of 2c:44 0 a phase change [equation] at 78. K Detailed calculations of stress fields have been made for aluminum and copper. It is noted that for Cu a contribution of additional terms besides that given by Eshe1by appears in the angular dependence of dilatation for the triple double force but for At the dilatation is in close agreement with Eshe1by's result. The elastic interaction energies of two triple double force interstitia1s and of two single double force interstitia1s with no moment are calculated. The calculated stresses are accurate to about 15 and 8 percent of their value for Cu and At, respectively. Fifteen terms for Cu and six terms for At were used in the series for stresses. Better accuracy could be obtained by including higher order terms in the expansions.","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-07-07T15:48:04Z No. of bitstreams: 1 1967_lie.pdf: 1994393 bytes, checksum: 079355c6e84863874e0d670cd2528ec6 (MD5)","Made available in DSpace on 2011-07-07T15:48:04Z (GMT). No. of bitstreams: 1 1967_lie.pdf: 1994393 bytes, checksum: 079355c6e84863874e0d670cd2528ec6 (MD5) Previous issue date: 1967","Restriction data tranferred 2014-07-01T11:32:43-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-07-07T15:48:04Z Item is restricted indefinitely.","Thesis","U of I Only"],"dc:identifier":["6086910","http://hdl.handle.net/2142/25691"],"dc:language":["en"],"dc:rights":["1967 Kyoon-Haeng Choh Lie"],"dc:subject":["elastic stress field","point force","cubic crystal","infinite elastic solid"],"dc:title":["The elastic stress field produced by a point force in a cubic crystal"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:26Z"}