2026-09-20T16:19:47Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/109561 2023-07-11 col_2142_5131 col_2142_14787 com_2142_5130 com_2142_9630 com_2142_234

Tortorelli, Daniel A Geubelle, Philippe H Tortorelli, Daniel A Geubelle, Philippe H James, Kai Masud, Arif Alidoost, Kazem 2021-03-05T21:45:09Z 2021-03-05T21:45:09Z 2023-03-05T21:47:41Z 2020-09-15 2020-12 This thesis discusses the topological derivative and its application to fracture-based analysis and design. The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In a previous work, Silva et al. [1] developed a first-order approximation of the energy release rate field in a two-dimensional domain associated with a small edge crack at any boundary location and any orientation. In this thesis, we extend this work. We first develop higher-precision approximations of the energy release rate field using higher-order topological derivatives, which allow the analyst to accurately treat longer cracks and determine the crack lengths for which the first-order approximation is accurate. These higher-order topological derivatives are calculated using the so-called topological-shape sensitivity method [2]. We next propose an approximation of the energy release rate field in a three-dimensional domain associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. This approximation is computationally attractive because it only requires a single analysis. By contrast, current boundary element and finite element based methods require an analysis for each crack length-location-direction combination. Furthermore, this approximation is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region. We conclude by leveraging the efficiency and simplicity of the proposed approximation to develop a fracture- and gradient-based shape optimization scheme for the design of fracture-resistant linearly elastic structures. A key characteristic of the shape optimization scheme presented in this thesis is that the domain and its boundary are defined implicitly using level-set functions constructed with the aid of R-functions, which allow for the use of differentiable Boolean operations to combine the level-set functions of predefined simple geometries. This adoption of R-functions has the dual impact of (i) allowing shapes to merge and/or separate and (ii) simplifying the computation of the shape velocity fields. Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2022-12-01 The student, Kazem Alidoost, accepted the attached license on 2020-09-08 at 18:53. The student, Kazem Alidoost, submitted this Dissertation for approval on 2020-09-08 at 19:07. This Dissertation was approved for publication on 2020-09-15 at 14:16. DSpace SAF Submission Ingestion Package generated from Vireo submission #15804 on 2021-03-04 at 16:30:14 Made available in DSpace on 2021-03-05T21:45:09Z (GMT). No. of bitstreams: 3 ALIDOOST-DISSERTATION-2020.pdf: 5472760 bytes, checksum: 06c5fbb676b624a666c0254b5c4235ad (MD5) LICENSE.txt: 4211 bytes, checksum: aadcb216c788c2a0792ba81f2bc4b34b (MD5) PROQUEST_LICENSE.txt: 4557 bytes, checksum: 78d5a5574cd3c40b67d32b6d2b2c4956 (MD5) Previous issue date: 2020-09-15 Embargo set by: Seth Robbins for item 117266 Lift date: 2023-03-05T21:45:47Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 117266 Lift date: 2023-03-05T21:47:41Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system Author requested closed access (OA after 2yrs) in Vireo ETD system Limited application/pdf http://hdl.handle.net/2142/109561 en Copyright 2020 Kazem Alidoost Asymptotic Analysis Computational Mechanics Edge Cracks Energy Release Rate Surface Cracks Shape Optimization Topological Derivative The topological derivative and its applications to fracture-based analysis and design text Thesis Mechanical Sci & Engineering Theoretical & Applied Mechans University of Illinois at Urbana-Champaign Dissertation Ph.D.