{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/97524"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/97524","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Transient wave propagation on random fields with fractal and Hurst effects","abstract":"Due to its significance in natural sciences and engineering fields, wave propagation through random heterogeneous media is a significant area of fundamental and applied research. Recently two models have been developed, Cauchy and Dagum models, that can simulate random fields with fractal and Hurst characteristics. Not only can fractal and Hurst characteristics be captured with these models, but they are decoupled. We evaluate the impact of these random fields on linear and nonlinear wave propagation using cellular automata, a local computational method, and propagation of acceleration waves. In this study, we evaluate cellular automata's response to a normal, impulse line load on a half-space. We first evaluate the surface response for homogeneous material properties by comparing cellular automata to the theoretical, analytical solution from classical elasticity and experimental results. We also include the response of peridynamics, a non-local continuum mechanics theory which is based on an integro-differential governing equation. We then introduce disorder to the mass-density. We first evaluate the surface response of cellular automata to uncorrelated mass-density fields, known as white noise. The random fields vary in coarseness as compared to cellular automata's node density. Then, we evaluate the response of cellular automata to Dagum and Cauchy random fields using the Monte Carlo method. For the propagation of acceleration waves, we apply Dagum and Cauchy random fields to dissipation and elastic non-linearity. We study how the fractal and Hurst characteristics alter the probability of shock formation as well as the distance to form a shock. Lastly, in our studies of peridynamics, we found that peridynamic problems are typically solved via numerical simulations. Some analytical solutions exist for one-dimensional systems. Here, we propose an alternative method to find analytical solutions by assuming a form for displacement and determine the loading function required to achieve that deformation. Our analytical peridynamic solutions are presented.","abstract_html":"Due to its significance in natural sciences and engineering fields, wave propagation through random heterogeneous media is a significant area of fundamental and applied research. Recently two models have been developed, Cauchy and Dagum models, that can simulate random fields with fractal and Hurst characteristics. Not only can fractal and Hurst characteristics be captured with these models, but they are decoupled. We evaluate the impact of these random fields on linear and nonlinear wave propagation using cellular automata, a local computational method, and propagation of acceleration waves. In this study, we evaluate cellular automata's response to a normal, impulse line load on a half-space. We first evaluate the surface response for homogeneous material properties by comparing cellular automata to the theoretical, analytical solution from classical elasticity and experimental results. We also include the response of peridynamics, a non-local continuum mechanics theory which is based on an integro-differential governing equation. We then introduce disorder to the mass-density. We first evaluate the surface response of cellular automata to uncorrelated mass-density fields, known as white noise. The random fields vary in coarseness as compared to cellular automata's node density. Then, we evaluate the response of cellular automata to Dagum and Cauchy random fields using the Monte Carlo method. For the propagation of acceleration waves, we apply Dagum and Cauchy random fields to dissipation and elastic non-linearity. We study how the fractal and Hurst characteristics alter the probability of shock formation as well as the distance to form a shock. Lastly, in our studies of peridynamics, we found that peridynamic problems are typically solved via numerical simulations. Some analytical solutions exist for one-dimensional systems. Here, we propose an alternative method to find analytical solutions by assuming a form for displacement and determine the loading function required to achieve that deformation. Our analytical peridynamic solutions are presented.","abstract_has_math":false,"creators":["Nishawala, Vinesh Vijay"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Ostoja-Starzewski, Martin","Elbanna, Ahmed","Hilton, Harry","Sinha, Sanjiv"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-08-10T19:51:31Z","date_published":"2017-08-10T19:51:31Z","updated_at":"2026-07-22T22:24:34Z","subjects":["Peridynamics","Cellular automata","Wave motion","Computational mechanics","Fractals","Hurst coefficient"],"languages":["en"],"rights":["Copyright 2016 Vinesh Nishawala"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/97524","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ostoja-Starzewski, Martin","Elbanna, Ahmed","Hilton, Harry","Sinha, Sanjiv"]},{"key":"dc:creator","label":"Author","values":["Nishawala, Vinesh Vijay"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-08-10T19:51:31Z","2019-08-11T09:15:21Z","2016-12-20","2017-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical 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":["Peridynamics","Cellular automata","Wave motion","Computational mechanics","Fractals","Hurst coefficient"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Vinesh Nishawala"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/97524"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Due to its significance in natural sciences and engineering fields, wave propagation through random heterogeneous media is a significant area of fundamental and applied research. Recently two models have been developed, Cauchy and Dagum models, that can simulate random fields with fractal and Hurst characteristics. Not only can fractal and Hurst characteristics be captured with these models, but they are decoupled. We evaluate the impact of these random fields on linear and nonlinear wave propagation using cellular automata, a local computational method, and propagation of acceleration waves. In this study, we evaluate cellular automata's response to a normal, impulse line load on a half-space. We first evaluate the surface response for homogeneous material properties by comparing cellular automata to the theoretical, analytical solution from classical elasticity and experimental results. We also include the response of peridynamics, a non-local continuum mechanics theory which is based on an integro-differential governing equation. We then introduce disorder to the mass-density. We first evaluate the surface response of cellular automata to uncorrelated mass-density fields, known as white noise. The random fields vary in coarseness as compared to cellular automata's node density. Then, we evaluate the response of cellular automata to Dagum and Cauchy random fields using the Monte Carlo method. For the propagation of acceleration waves, we apply Dagum and Cauchy random fields to dissipation and elastic non-linearity. We study how the fractal and Hurst characteristics alter the probability of shock formation as well as the distance to form a shock. Lastly, in our studies of peridynamics, we found that peridynamic problems are typically solved via numerical simulations. Some analytical solutions exist for one-dimensional systems. Here, we propose an alternative method to find analytical solutions by assuming a form for displacement and determine the loading function required to achieve that deformation. Our analytical peridynamic solutions are presented.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-05-01","The student, Vinesh Nishawala, accepted the attached license on 2016-12-16 at 15:06.","The student, Vinesh Nishawala, submitted this Dissertation for approval on 2016-12-16 at 15:14.","This Dissertation was approved for publication on 2016-12-20 at 09:32.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10517 on 2017-08-10 at 14:29:00","Made available in DSpace on 2017-08-10T19:51:31Z (GMT). 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Recently two models have been developed, Cauchy and Dagum models, that can simulate random fields with fractal and Hurst characteristics. Not only can fractal and Hurst characteristics be captured with these models, but they are decoupled. We evaluate the impact of these random fields on linear and nonlinear wave propagation using cellular automata, a local computational method, and propagation of acceleration waves. In this study, we evaluate cellular automata's response to a normal, impulse line load on a half-space. We first evaluate the surface response for homogeneous material properties by comparing cellular automata to the theoretical, analytical solution from classical elasticity and experimental results. We also include the response of peridynamics, a non-local continuum mechanics theory which is based on an integro-differential governing equation. We then introduce disorder to the mass-density. We first evaluate the surface response of cellular automata to uncorrelated mass-density fields, known as white noise. The random fields vary in coarseness as compared to cellular automata's node density. Then, we evaluate the response of cellular automata to Dagum and Cauchy random fields using the Monte Carlo method. For the propagation of acceleration waves, we apply Dagum and Cauchy random fields to dissipation and elastic non-linearity. We study how the fractal and Hurst characteristics alter the probability of shock formation as well as the distance to form a shock. Lastly, in our studies of peridynamics, we found that peridynamic problems are typically solved via numerical simulations. Some analytical solutions exist for one-dimensional systems. Here, we propose an alternative method to find analytical solutions by assuming a form for displacement and determine the loading function required to achieve that deformation. Our analytical peridynamic solutions are presented.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-05-01","The student, Vinesh Nishawala, accepted the attached license on 2016-12-16 at 15:06.","The student, Vinesh Nishawala, submitted this Dissertation for approval on 2016-12-16 at 15:14.","This Dissertation was approved for publication on 2016-12-20 at 09:32.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10517 on 2017-08-10 at 14:29:00","Made available in DSpace on 2017-08-10T19:51:31Z (GMT). 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