{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/31174"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/31174","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A three dimensional generalized finite element method for thin fibers embedded in a continuum","abstract":"The realistic simulation of the behavioral mechanisms of Fiber Reinforced Composites poses a computational and implementation challenge to available Finite Element Methods (FEMs). Meshing a large number of arbitrarily distributed fibers in three dimensions and modeling damage mechanisms, while simultaneously accounting for multi-scale interactions would undermine the feasibility of available FEM for such models. This research project formulates and implements a multi-scale Generalized Finite Element Method (GFEM) using global-local enrichment functions (GFEM^{gl}) to overcome these limitations. The methodology is verified by comparing the solution to specific linear elastic problems obtained by using GFEM^{gl} against solutions from the traditional FEM approach. In addition, these examples accentuate the limitations of the usage of FEM to solve them. The GFEM^{gl} is finally applied to a key concept in the design of advanced composite materials, namely Crack-Bridging, to demonstrate its versatility.","abstract_html":"The realistic simulation of the behavioral mechanisms of Fiber Reinforced Composites poses a computational and implementation challenge to available Finite Element Methods (FEMs). Meshing a large number of arbitrarily distributed fibers in three dimensions and modeling damage mechanisms, while simultaneously accounting for multi-scale interactions would undermine the feasibility of available FEM for such models. This research project formulates and implements a multi-scale Generalized Finite Element Method (GFEM) using global-local enrichment functions (GFEM^{gl}) to overcome these limitations. The methodology is verified by comparing the solution to specific linear elastic problems obtained by using GFEM^{gl} against solutions from the traditional FEM approach. In addition, these examples accentuate the limitations of the usage of FEM to solve them. The GFEM^{gl} is finally applied to a key concept in the design of advanced composite materials, namely Crack-Bridging, to demonstrate its versatility.","abstract_has_math":false,"creators":["Krishnan, Aditya"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Civil Engineering","degree_department":null,"school":null,"contributors":["Duarte, C. Armando"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-22T00:33:31Z","date_published":"2012-05-22T00:33:31Z","updated_at":"2026-07-22T22:25:30Z","subjects":["Generalized Finite Element Method (GFEM)","Global-local analysis","Multi-scale problem","Fiber Reinforced Composites"],"languages":["en"],"rights":["Copyright 2012 by Aditya Krishnan. All rights reserved"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/31174","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Duarte, C. 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The methodology is verified by comparing the solution to specific linear elastic problems obtained by using GFEM^{gl} against solutions from the traditional FEM approach. In addition, these examples accentuate the limitations of the usage of FEM to solve them. The GFEM^{gl} is finally applied to a key concept in the design of advanced composite materials, namely Crack-Bridging, to demonstrate its versatility.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-04-27T19:27:33Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Krishnan_Aditya.pdf: 3678060 bytes, checksum: b97b58e6aaa27f462632aeba9ff429d2 (MD5)","Made available in DSpace on 2012-05-22T00:33:31Z (GMT). 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This research project formulates and implements a multi-scale Generalized Finite Element Method (GFEM) using global-local enrichment functions (GFEM^{gl}) to overcome these limitations. The methodology is verified by comparing the solution to specific linear elastic problems obtained by using GFEM^{gl} against solutions from the traditional FEM approach. In addition, these examples accentuate the limitations of the usage of FEM to solve them. The GFEM^{gl} is finally applied to a key concept in the design of advanced composite materials, namely Crack-Bridging, to demonstrate its versatility.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-04-27T19:27:33Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Krishnan_Aditya.pdf: 3678060 bytes, checksum: b97b58e6aaa27f462632aeba9ff429d2 (MD5)","Made available in DSpace on 2012-05-22T00:33:31Z (GMT). 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