{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/8037"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/8037","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Investigation of efficient geometric shape algorithms for numerical simulation of discrete particle systems","abstract":"The efficiency of a discrete particle simulation implementation relies on several factors, including the geometric representation, contact resolution, and neighbor-sorting algorithm used. The focus here is on the first two of this list: the geometric representation and the corresponding contact resolution. An argument is developed to advocate the use of geometric representations with inconstant radius based on results of a numerical study of angles of repose for deposited grains. The equivalent spheres method is then developed as a potential cure for the problems arising from constant radius geometric representations. A coherent approach to utilizing this geometry in discrete element modeling is developed. This includes the proposal of an accurate, robust contact resolution algorithm and explicit functions to describe moments of inertia. Considerations for numerical modeling are also addressed, including numerical integration, formulation of rotation transformations, and resolution of forces and motions in the context of rigid body motions. The details of a generalized computational implementation of the representation are also given, and empirical convergence properties are compared with a different method for detecting contact between ellipsoidal approximations.","abstract_html":"The efficiency of a discrete particle simulation implementation relies on several factors, including the geometric representation, contact resolution, and neighbor-sorting algorithm used. The focus here is on the first two of this list: the geometric representation and the corresponding contact resolution. An argument is developed to advocate the use of geometric representations with inconstant radius based on results of a numerical study of angles of repose for deposited grains. The equivalent spheres method is then developed as a potential cure for the problems arising from constant radius geometric representations. A coherent approach to utilizing this geometry in discrete element modeling is developed. This includes the proposal of an accurate, robust contact resolution algorithm and explicit functions to describe moments of inertia. Considerations for numerical modeling are also addressed, including numerical integration, formulation of rotation transformations, and resolution of forces and motions in the context of rigid body motions. The details of a generalized computational implementation of the representation are also given, and empirical convergence properties are compared with a different method for detecting contact between ellipsoidal approximations.","abstract_has_math":false,"creators":["Johnson, Scott M. (Scott Matthew), 1978-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering.","school":null,"contributors":[],"advisors":["John R. Williams."],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003","date_published":"2003","updated_at":"2026-07-22T22:22:21Z","subjects":["Civil and Environmental Engineering."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/8037","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["John R. Williams."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering."]},{"key":"dc:creator","label":"Author","values":["Johnson, Scott M. (Scott Matthew), 1978-"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2005-08-24T22:15:41Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2005-08-24T22:15:41Z"]},{"key":"dc:date.issued","label":"Date","values":["2003"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Civil and Environmental Engineering."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/8037"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2003.","Includes bibliographical references (leaves 46-49)."]},{"key":"dc:description.abstract","label":"Abstract","values":["The efficiency of a discrete particle simulation implementation relies on several factors, including the geometric representation, contact resolution, and neighbor-sorting algorithm used. The focus here is on the first two of this list: the geometric representation and the corresponding contact resolution. An argument is developed to advocate the use of geometric representations with inconstant radius based on results of a numerical study of angles of repose for deposited grains. The equivalent spheres method is then developed as a potential cure for the problems arising from constant radius geometric representations. A coherent approach to utilizing this geometry in discrete element modeling is developed. This includes the proposal of an accurate, robust contact resolution algorithm and explicit functions to describe moments of inertia. Considerations for numerical modeling are also addressed, including numerical integration, formulation of rotation transformations, and resolution of forces and motions in the context of rigid body motions. The details of a generalized computational implementation of the representation are also given, and empirical convergence properties are compared with a different method for detecting contact between ellipsoidal approximations."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Investigation of efficient geometric shape algorithms for numerical simulation of discrete particle systems"]}]}],"canonical_facts":{"dc:contributor.advisor":["John R. Williams."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering."],"dc:creator":["Johnson, Scott M. (Scott Matthew), 1978-"],"dc:date.accessioned":["2005-08-24T22:15:41Z"],"dc:date.available":["2005-08-24T22:15:41Z"],"dc:date.issued":["2003"],"dc:description":["Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2003.","Includes bibliographical references (leaves 46-49)."],"dc:description.abstract":["The efficiency of a discrete particle simulation implementation relies on several factors, including the geometric representation, contact resolution, and neighbor-sorting algorithm used. The focus here is on the first two of this list: the geometric representation and the corresponding contact resolution. An argument is developed to advocate the use of geometric representations with inconstant radius based on results of a numerical study of angles of repose for deposited grains. The equivalent spheres method is then developed as a potential cure for the problems arising from constant radius geometric representations. A coherent approach to utilizing this geometry in discrete element modeling is developed. This includes the proposal of an accurate, robust contact resolution algorithm and explicit functions to describe moments of inertia. Considerations for numerical modeling are also addressed, including numerical integration, formulation of rotation transformations, and resolution of forces and motions in the context of rigid body motions. The details of a generalized computational implementation of the representation are also given, and empirical convergence properties are compared with a different method for detecting contact between ellipsoidal approximations."],"dc:description.degree":["S.M."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/1721.1/8037"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Civil and Environmental Engineering."],"dc:title":["Investigation of efficient geometric shape algorithms for numerical simulation of discrete particle systems"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:22:21Z"}