{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/21031"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/21031","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Design sensitivity analysis for nonlinear dynamic thermoelastic systems","abstract":"Two adjoint formulations are developed for the design sensitivity analysis of linear and nonlinear dynamic thermoelastic systems. The variation of a general design functional is expressed in explicit form with respect to variations of the design quantities, i.e. material properties, applied loads, prescribed boundary conditions, initial conditions, and shape. The design functional is expressed in terms of these explicit quantities and the implicit response variables: displacement, temperature, stress, strain, heat flux vector, temperature gradient, reaction forces, and reaction surface flux. The convolution is employed, in lieu of the time mappings used in other approaches to account for transient response. The design sensitivities for dynamic thermoelastic, nonlinear uncoupled dynamic thermoelastic problems are presented here for the first time. The use of the convolution for sensitivity analysis is also presented here for the first time. By formulating these sensitivities, numerical optimization algorithms currently used for elastostatic structure redesign, can be applied to nonlinear dynamic thermoelastic systems.","abstract_html":"Two adjoint formulations are developed for the design sensitivity analysis of linear and nonlinear dynamic thermoelastic systems. The variation of a general design functional is expressed in explicit form with respect to variations of the design quantities, i.e. material properties, applied loads, prescribed boundary conditions, initial conditions, and shape. The design functional is expressed in terms of these explicit quantities and the implicit response variables: displacement, temperature, stress, strain, heat flux vector, temperature gradient, reaction forces, and reaction surface flux. The convolution is employed, in lieu of the time mappings used in other approaches to account for transient response. The design sensitivities for dynamic thermoelastic, nonlinear uncoupled dynamic thermoelastic problems are presented here for the first time. The use of the convolution for sensitivity analysis is also presented here for the first time. By formulating these sensitivities, numerical optimization algorithms currently used for elastostatic structure redesign, can be applied to nonlinear dynamic thermoelastic systems.","abstract_has_math":false,"creators":["Tortorelli, Daniel A."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Science and Engineering","degree_department":null,"school":null,"contributors":["Lu, Stephen C-Y"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:56:20Z","date_published":"2011-05-07T12:56:20Z","updated_at":"2026-07-22T22:25:17Z","subjects":["Engineering, Mechanical"],"languages":["eng"],"rights":["Copyright 1989 Tortorelli, Daniel Anthony"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8916316","(UMI)AAI8916316"],"render_values":[{"text":"AAI8916316","href":null,"code":true},{"text":"(UMI)AAI8916316","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/21031","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Lu, Stephen C-Y"]},{"key":"dc:creator","label":"Author","values":["Tortorelli, Daniel A."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:56:20Z","10000-01-01","1989"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Science and 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, Mechanical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1989 Tortorelli, Daniel Anthony"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8916316","(UMI)AAI8916316","http://hdl.handle.net/2142/21031"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Two adjoint formulations are developed for the design sensitivity analysis of linear and nonlinear dynamic thermoelastic systems. The variation of a general design functional is expressed in explicit form with respect to variations of the design quantities, i.e. material properties, applied loads, prescribed boundary conditions, initial conditions, and shape. The design functional is expressed in terms of these explicit quantities and the implicit response variables: displacement, temperature, stress, strain, heat flux vector, temperature gradient, reaction forces, and reaction surface flux. The convolution is employed, in lieu of the time mappings used in other approaches to account for transient response. The design sensitivities for dynamic thermoelastic, nonlinear uncoupled dynamic thermoelastic problems are presented here for the first time. The use of the convolution for sensitivity analysis is also presented here for the first time. By formulating these sensitivities, numerical optimization algorithms currently used for elastostatic structure redesign, can be applied to nonlinear dynamic thermoelastic systems.","Sensitivities for linear elastodynamic and dynamic thermoelastic problems are derived by incorporating the reciprocal theorem between a variation of the real design and an adjoint system. The Lagrange multiplier method is utilized to formulate sensitivities for nonlinear uncoupled dynamic thermoelastic problems. These formulations may also be specialized for linear and nonlinear transient conduction problems.","The finite element method is used to demonstrate the numerical implementation of the formulations. Shape sensitivities are evaluated and compared with finite difference calculations to validate the results. A numerical optimization algorithm is combined with the sensitivity analyses to redesign the geometry of a mold in a casting problem and the shape of structure whose response is governed by a nonlinear quasi-static thermoelastic system.","Made available in DSpace on 2011-05-07T12:56:20Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8916316.pdf: 4532913 bytes, checksum: b12fea3742bb268ff7605d792b032c4a (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:48:01Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:21:43-05:00 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"]},{"key":"dc:title","label":"Title","values":["Design sensitivity analysis for nonlinear dynamic thermoelastic systems"]}]}],"canonical_facts":{"dc:contributor":["Lu, Stephen C-Y"],"dc:creator":["Tortorelli, Daniel A."],"dc:date":["2011-05-07T12:56:20Z","10000-01-01","1989"],"dc:description":["Two adjoint formulations are developed for the design sensitivity analysis of linear and nonlinear dynamic thermoelastic systems. The variation of a general design functional is expressed in explicit form with respect to variations of the design quantities, i.e. material properties, applied loads, prescribed boundary conditions, initial conditions, and shape. The design functional is expressed in terms of these explicit quantities and the implicit response variables: displacement, temperature, stress, strain, heat flux vector, temperature gradient, reaction forces, and reaction surface flux. The convolution is employed, in lieu of the time mappings used in other approaches to account for transient response. The design sensitivities for dynamic thermoelastic, nonlinear uncoupled dynamic thermoelastic problems are presented here for the first time. The use of the convolution for sensitivity analysis is also presented here for the first time. By formulating these sensitivities, numerical optimization algorithms currently used for elastostatic structure redesign, can be applied to nonlinear dynamic thermoelastic systems.","Sensitivities for linear elastodynamic and dynamic thermoelastic problems are derived by incorporating the reciprocal theorem between a variation of the real design and an adjoint system. The Lagrange multiplier method is utilized to formulate sensitivities for nonlinear uncoupled dynamic thermoelastic problems. These formulations may also be specialized for linear and nonlinear transient conduction problems.","The finite element method is used to demonstrate the numerical implementation of the formulations. Shape sensitivities are evaluated and compared with finite difference calculations to validate the results. A numerical optimization algorithm is combined with the sensitivity analyses to redesign the geometry of a mold in a casting problem and the shape of structure whose response is governed by a nonlinear quasi-static thermoelastic system.","Made available in DSpace on 2011-05-07T12:56:20Z (GMT). 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