{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/115941"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/115941","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Convolution method in elastodynamics","abstract":"Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-08-01","abstract_html":"Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-08-01","abstract_has_math":false,"creators":["Amiri Hezaveh, Amirhossein"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Theoretical & Applied Mechans","degree_department":null,"school":null,"contributors":["Ostoja-Starzewski, Martin","Masud, Arif","Sehitoglu, Huseyin","West, Mathew"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-08","date_published":"2022-08","updated_at":"2026-07-22T22:24:55Z","subjects":["Elastodynamics","Finite Element Method","Nonlinear Mechanics"],"languages":["en","eng"],"rights":["Copyright 2022 Amirhossein Amiri Hezaveh"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/115941","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ostoja-Starzewski, Martin","Masud, Arif","Sehitoglu, Huseyin","West, Mathew"]},{"key":"dc:creator","label":"Author","values":["Amiri Hezaveh, Amirhossein"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-08","2022-07-15"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Theoretical & Applied Mechans"]},{"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":["Elastodynamics","Finite Element Method","Nonlinear Mechanics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Amirhossein Amiri Hezaveh"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/115941"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-08-01","The student, Amirhossein Amiri Hezaveh, accepted the attached license on 2022-07-14 at 19:12.","The student, Amirhossein Amiri Hezaveh, submitted this Dissertation for approval on 2022-07-14 at 19:57.","This Dissertation was approved for publication on 2022-07-15 at 15:37.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18324 on 2022-11-16 at 10:56:15","Theoretical solid mechanics is mainly based on the equations of motion in terms of displacement fields. Using the constitutive and kinematic equations, the equations of motion that initially involve the stress fields are written in terms of spatial and time derivatives of the displacement field. These equations are at the center of analytical and computational attempts in solid mechanics. However, this approach contains seemingly unresolvable challenges. As an example, in nonlinear elastodynamics, it is well-understood that the Newmark average acceleration method (the trapezoidal rule) fails to conserve the balance of energy and the balance of angular momentum. While several algorithms in the literature attempted to address this challenge, all of them are based on a rather intricate formulation that still falls short in some practical problems. In this dissertation, by contrast, wave phenomena in elastic materials are investigated through the so-called alternative field equations where the convolution product appears in the place of time derivative. In the first step of the study, the stress equations of motion for electromagneto-elastic materials are derived. As the name suggests, in the new framework, the equations of motion are written in terms of the stress field. These equations provide a new foundation to establish numerical methods in terms of stress rather than displacement, which is an appropriate strategy for addressing problems with Neumann boundary conditions. In the next step, based on the alternative field equations, convolutional variational principles for electromagneto-elastic materials are established. Upon convolutional variational principles, a new time-domain finite element method, namely, Convolution Finite Element Method (CFEM), is then introduced for linear elastodynamics problems. It is shown that this new dynamic finite element approach inherits surprising characteristics that cannot be found in the classical methods. Finally, by using the CFEM, a new solution procedure for nonlinear elastodynamics is established. The new algorithm, which is based on the CFEM and Newton-Raphson method, leads to a simple solution procedure while conserving energy and angular momentum."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Convolution method in elastodynamics"]}]}],"canonical_facts":{"dc:contributor":["Ostoja-Starzewski, Martin","Masud, Arif","Sehitoglu, Huseyin","West, Mathew"],"dc:creator":["Amiri Hezaveh, Amirhossein"],"dc:date":["2022-08","2022-07-15"],"dc:description":["Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-08-01","The student, Amirhossein Amiri Hezaveh, accepted the attached license on 2022-07-14 at 19:12.","The student, Amirhossein Amiri Hezaveh, submitted this Dissertation for approval on 2022-07-14 at 19:57.","This Dissertation was approved for publication on 2022-07-15 at 15:37.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18324 on 2022-11-16 at 10:56:15","Theoretical solid mechanics is mainly based on the equations of motion in terms of displacement fields. Using the constitutive and kinematic equations, the equations of motion that initially involve the stress fields are written in terms of spatial and time derivatives of the displacement field. These equations are at the center of analytical and computational attempts in solid mechanics. However, this approach contains seemingly unresolvable challenges. As an example, in nonlinear elastodynamics, it is well-understood that the Newmark average acceleration method (the trapezoidal rule) fails to conserve the balance of energy and the balance of angular momentum. While several algorithms in the literature attempted to address this challenge, all of them are based on a rather intricate formulation that still falls short in some practical problems. In this dissertation, by contrast, wave phenomena in elastic materials are investigated through the so-called alternative field equations where the convolution product appears in the place of time derivative. In the first step of the study, the stress equations of motion for electromagneto-elastic materials are derived. As the name suggests, in the new framework, the equations of motion are written in terms of the stress field. These equations provide a new foundation to establish numerical methods in terms of stress rather than displacement, which is an appropriate strategy for addressing problems with Neumann boundary conditions. In the next step, based on the alternative field equations, convolutional variational principles for electromagneto-elastic materials are established. Upon convolutional variational principles, a new time-domain finite element method, namely, Convolution Finite Element Method (CFEM), is then introduced for linear elastodynamics problems. It is shown that this new dynamic finite element approach inherits surprising characteristics that cannot be found in the classical methods. Finally, by using the CFEM, a new solution procedure for nonlinear elastodynamics is established. The new algorithm, which is based on the CFEM and Newton-Raphson method, leads to a simple solution procedure while conserving energy and angular momentum."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/115941"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Amirhossein Amiri Hezaveh"],"dc:subject":["Elastodynamics","Finite Element Method","Nonlinear Mechanics"],"dc:title":["Convolution method in elastodynamics"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Theoretical & Applied Mechans"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:55Z"}