{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/21553"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/21553","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Development and applications of hypersingular boundary integral equations for three-dimensional acoustics and elastodynamics","abstract":"The boundary integral equation/boundary element method (BIE/BEM) has emerged as a powerful alternative tool to other numerical methods for many problems in engineering. The hypersingular BIE's, which are derivatives of conventional BIE's, are indispensable for the analyses of many problems in mechanics by BIE/BEM, such as wave scattering, crack problems, plate bending, thin body and thin inclusion problems, for which the conventional BIE's are insufficient or fail. However, the application of hypersingular BIE's had been very limited because of the difficulty in dealing with the hypersingular integrals involved. In this thesis, the hypersingular BIE's for 3-D acoustic and elastic wave problems are presented in weakly-singular forms. For this purpose, three integral identities for the fundamental solutions of both potential and elastostatic problems are established and employed. These weakly-singular forms of the hypersingular BIE's can be handled easily and no special quadratures are needed in the numerical computation. The composite BIE formulations, which use a linear combination of the conventional and hypersingular BIE's, are applied to overcome the fictitious eigenfrequency difficulty (nonunique solutions) existing in the conventional BIE formulations of exterior acoustic and elastic wave problems. Overhauser $C\\sp1$ continuous boundary elements, which satisfy the smoothness requirement of the hypersingular BIE's, are implemented for these composite BIE formulations and compared with the traditional $C\\sp0$ conforming quadratic and non-conforming quadratic elements. Numerical examples of scattering in both acoustic and elastic media clearly demonstrate the effectiveness and efficiency of the developed formulations.","abstract_html":"The boundary integral equation/boundary element method (BIE/BEM) has emerged as a powerful alternative tool to other numerical methods for many problems in engineering. The hypersingular BIE's, which are derivatives of conventional BIE's, are indispensable for the analyses of many problems in mechanics by BIE/BEM, such as wave scattering, crack problems, plate bending, thin body and thin inclusion problems, for which the conventional BIE's are insufficient or fail. However, the application of hypersingular BIE's had been very limited because of the difficulty in dealing with the hypersingular integrals involved. In this thesis, the hypersingular BIE's for 3-D acoustic and elastic wave problems are presented in weakly-singular forms. For this purpose, three integral identities for the fundamental solutions of both potential and elastostatic problems are established and employed. These weakly-singular forms of the hypersingular BIE's can be handled easily and no special quadratures are needed in the numerical computation. The composite BIE formulations, which use a linear combination of the conventional and hypersingular BIE's, are applied to overcome the fictitious eigenfrequency difficulty (nonunique solutions) existing in the conventional BIE formulations of exterior acoustic and elastic wave problems. Overhauser $C\\sp1$ continuous boundary elements, which satisfy the smoothness requirement of the hypersingular BIE's, are implemented for these composite BIE formulations and compared with the traditional $C\\sp0$ conforming quadratic and non-conforming quadratic elements. Numerical examples of scattering in both acoustic and elastic media clearly demonstrate the effectiveness and efficiency of the developed formulations.","abstract_has_math":true,"creators":["Liu, Yijun"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Theoretical and Applied Mechanics","degree_department":null,"school":null,"contributors":["Rizzo, Frank J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:12:02Z","date_published":"2011-05-07T13:12:02Z","updated_at":"2026-07-22T22:25:18Z","subjects":["Applied Mechanics","Mathematics","Physics, Acoustics"],"languages":["eng"],"rights":["Copyright 1992 Liu, Yijun"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9215851","(UMI)AAI9215851"],"render_values":[{"text":"AAI9215851","href":null,"code":true},{"text":"(UMI)AAI9215851","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/21553","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rizzo, Frank J."]},{"key":"dc:creator","label":"Author","values":["Liu, Yijun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:12:02Z","10000-01-01","1992"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Theoretical and Applied Mechanics"]},{"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","Mathematics","Physics, Acoustics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1992 Liu, Yijun"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9215851","(UMI)AAI9215851","http://hdl.handle.net/2142/21553"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The boundary integral equation/boundary element method (BIE/BEM) has emerged as a powerful alternative tool to other numerical methods for many problems in engineering. The hypersingular BIE's, which are derivatives of conventional BIE's, are indispensable for the analyses of many problems in mechanics by BIE/BEM, such as wave scattering, crack problems, plate bending, thin body and thin inclusion problems, for which the conventional BIE's are insufficient or fail. However, the application of hypersingular BIE's had been very limited because of the difficulty in dealing with the hypersingular integrals involved. In this thesis, the hypersingular BIE's for 3-D acoustic and elastic wave problems are presented in weakly-singular forms. For this purpose, three integral identities for the fundamental solutions of both potential and elastostatic problems are established and employed. These weakly-singular forms of the hypersingular BIE's can be handled easily and no special quadratures are needed in the numerical computation. The composite BIE formulations, which use a linear combination of the conventional and hypersingular BIE's, are applied to overcome the fictitious eigenfrequency difficulty (nonunique solutions) existing in the conventional BIE formulations of exterior acoustic and elastic wave problems. Overhauser $C\\sp1$ continuous boundary elements, which satisfy the smoothness requirement of the hypersingular BIE's, are implemented for these composite BIE formulations and compared with the traditional $C\\sp0$ conforming quadratic and non-conforming quadratic elements. Numerical examples of scattering in both acoustic and elastic media clearly demonstrate the effectiveness and efficiency of the developed formulations.","Made available in DSpace on 2011-05-07T13:12:02Z (GMT). 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The hypersingular BIE's, which are derivatives of conventional BIE's, are indispensable for the analyses of many problems in mechanics by BIE/BEM, such as wave scattering, crack problems, plate bending, thin body and thin inclusion problems, for which the conventional BIE's are insufficient or fail. However, the application of hypersingular BIE's had been very limited because of the difficulty in dealing with the hypersingular integrals involved. In this thesis, the hypersingular BIE's for 3-D acoustic and elastic wave problems are presented in weakly-singular forms. For this purpose, three integral identities for the fundamental solutions of both potential and elastostatic problems are established and employed. These weakly-singular forms of the hypersingular BIE's can be handled easily and no special quadratures are needed in the numerical computation. The composite BIE formulations, which use a linear combination of the conventional and hypersingular BIE's, are applied to overcome the fictitious eigenfrequency difficulty (nonunique solutions) existing in the conventional BIE formulations of exterior acoustic and elastic wave problems. Overhauser $C\\sp1$ continuous boundary elements, which satisfy the smoothness requirement of the hypersingular BIE's, are implemented for these composite BIE formulations and compared with the traditional $C\\sp0$ conforming quadratic and non-conforming quadratic elements. Numerical examples of scattering in both acoustic and elastic media clearly demonstrate the effectiveness and efficiency of the developed formulations.","Made available in DSpace on 2011-05-07T13:12:02Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9215851.pdf: 4024177 bytes, checksum: 97804e2f5c1a297a235714960ced5a71 (MD5) Previous issue date: 1992","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:51:34Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:23:41-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9215851","(UMI)AAI9215851","http://hdl.handle.net/2142/21553"],"dc:language":["eng"],"dc:rights":["Copyright 1992 Liu, Yijun"],"dc:subject":["Applied Mechanics","Mathematics","Physics, Acoustics"],"dc:title":["Development and applications of hypersingular boundary integral equations for three-dimensional acoustics and elastodynamics"],"dc:type":["text"],"thesis:degree_discipline":["Theoretical and Applied Mechanics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:18Z"}