{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71667"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71667","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The Boundary Integral Equation Method for Torsion of an Inhomogeneous Variable Diameter Shaft","abstract":"A Boundary Integral Equation (BIE) formulation is developed which is capable of analyzing the torsion of a variable diameter shaft with an axisymmetric shear modulus in a particular form. The governing differential equation for this problem is the equation of the Generalized Bi-axially Symmetric Potential Theory (GBSPT), and its fundamental solution can be obtained by considering the "ring of potential". Piecewise-quadratic shape functions are used for the approximations of the functions and the boundary. Gaussian quadrature with four Gaussian points are used for the numerical integration.","abstract_html":"A Boundary Integral Equation (BIE) formulation is developed which is capable of analyzing the torsion of a variable diameter shaft with an axisymmetric shear modulus in a particular form. The governing differential equation for this problem is the equation of the Generalized Bi-axially Symmetric Potential Theory (GBSPT), and its fundamental solution can be obtained by considering the "ring of potential". Piecewise-quadratic shape functions are used for the approximations of the functions and the boundary. Gaussian quadrature with four Gaussian points are used for the numerical integration.","abstract_has_math":false,"creators":["Wu, Yensen"],"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":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T19:12:27Z","date_published":"2014-12-16T19:12:27Z","updated_at":"2026-07-22T22:26:05Z","subjects":["Applied Mechanics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8203643"],"render_values":[{"text":"(UMI)AAI8203643","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71667","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Wu, Yensen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T19:12:27Z","10000-01-01","1981"]},{"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"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71667","(UMI)AAI8203643"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Boundary Integral Equation (BIE) formulation is developed which is capable of analyzing the torsion of a variable diameter shaft with an axisymmetric shear modulus in a particular form. The governing differential equation for this problem is the equation of the Generalized Bi-axially Symmetric Potential Theory (GBSPT), and its fundamental solution can be obtained by considering the "ring of potential". Piecewise-quadratic shape functions are used for the approximations of the functions and the boundary. Gaussian quadrature with four Gaussian points are used for the numerical integration.","Stress concentration problems for the homogeneous U-grooved shaft, fillet shoulder shaft and the inhomogeneous U-grooved shaft with an axial hole are examined. Possible future studies are suggested.","Made available in DSpace on 2014-12-16T19:12:27Z (GMT). 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The governing differential equation for this problem is the equation of the Generalized Bi-axially Symmetric Potential Theory (GBSPT), and its fundamental solution can be obtained by considering the "ring of potential". Piecewise-quadratic shape functions are used for the approximations of the functions and the boundary. Gaussian quadrature with four Gaussian points are used for the numerical integration.","Stress concentration problems for the homogeneous U-grooved shaft, fillet shoulder shaft and the inhomogeneous U-grooved shaft with an axial hole are examined. Possible future studies are suggested.","Made available in DSpace on 2014-12-16T19:12:27Z (GMT). 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