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On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra

Y.T. Feng, Yuanqiang Tan, Yuntian Feng Orcid Logo

Engineering Computations, Volume: ahead-of-print, Issue: ahead-of-print

Swansea University Author: Yuntian Feng Orcid Logo

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DOI (Published version): 10.1108/EC-03-2019-0124

Abstract

PurposeContact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called ent...

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Published in: Engineering Computations
ISSN: 0264-4401
Published: 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa50478
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first_indexed 2019-05-22T15:49:10Z
last_indexed 2019-09-10T15:27:31Z
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fullrecord <?xml version="1.0"?><rfc1807><datestamp>2019-09-10T13:31:42.8473819</datestamp><bib-version>v2</bib-version><id>50478</id><entry>2019-05-22</entry><title>On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra</title><swanseaauthors><author><sid>d66794f9c1357969a5badf654f960275</sid><ORCID>0000-0002-6396-8698</ORCID><firstname>Yuntian</firstname><surname>Feng</surname><name>Yuntian Feng</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2019-05-22</date><deptcode>CIVL</deptcode><abstract>PurposeContact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called entrance block of two polyhedra and reduces the contact to evaluate the distance between the reference point to the corresponding entrance block, but effective implementation is still lacking.Design/methodology/approachIn this paper, the equivalence of the entrance block and the Minkowski difference of two polyhedra is emphasised and two well-known Minkowski difference-based contact detection and overlap computation algorithms, GJK and expanding polytope algorithm (EPA), are chosen as the possible numerical approaches to the 3D contact theory for DDA, and also as alternatives for computing polyhedral contact features in DEM. The key algorithmic issues are outlined and their important features are highlighted.FindingsNumerical examples indicate that the average number of updates required in GJK for polyhedral contact is around 6, and only 1 or 2 iterations are needed in EPA to find the overlap and all the relevant contact features when the overlap between polyhedra is small.Originality/valueThe equivalence of the entrance block in DDA and the Minkowski difference of two polyhedra is emphasised; GJK- and EPA-based contact algorithms are applied to convex polyhedra in DEM; energy conservation is guaranteed for the contact theory used; and numerical results demonstrate the effectiveness of the proposed methodologies.</abstract><type>Journal Article</type><journal>Engineering Computations</journal><volume>ahead-of-print</volume><journalNumber>ahead-of-print</journalNumber><publisher/><issnPrint>0264-4401</issnPrint><keywords/><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2019</publishedYear><publishedDate>2019-12-31</publishedDate><doi>10.1108/EC-03-2019-0124</doi><url/><notes/><college>COLLEGE NANME</college><department>Civil Engineering</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>CIVL</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2019-09-10T13:31:42.8473819</lastEdited><Created>2019-05-22T09:21:53.5660973</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering</level></path><authors><author><firstname>Y.T.</firstname><surname>Feng</surname><order>1</order></author><author><firstname>Yuanqiang</firstname><surname>Tan</surname><order>2</order></author><author><firstname>Yuntian</firstname><surname>Feng</surname><orcid>0000-0002-6396-8698</orcid><order>3</order></author></authors><documents><document><filename>0050478-22052019093746.pdf</filename><originalFilename>feng2019.pdf</originalFilename><uploaded>2019-05-22T09:37:46.4070000</uploaded><type>Output</type><contentLength>6738214</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2019-05-22T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807>
spelling 2019-09-10T13:31:42.8473819 v2 50478 2019-05-22 On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra d66794f9c1357969a5badf654f960275 0000-0002-6396-8698 Yuntian Feng Yuntian Feng true false 2019-05-22 CIVL PurposeContact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called entrance block of two polyhedra and reduces the contact to evaluate the distance between the reference point to the corresponding entrance block, but effective implementation is still lacking.Design/methodology/approachIn this paper, the equivalence of the entrance block and the Minkowski difference of two polyhedra is emphasised and two well-known Minkowski difference-based contact detection and overlap computation algorithms, GJK and expanding polytope algorithm (EPA), are chosen as the possible numerical approaches to the 3D contact theory for DDA, and also as alternatives for computing polyhedral contact features in DEM. The key algorithmic issues are outlined and their important features are highlighted.FindingsNumerical examples indicate that the average number of updates required in GJK for polyhedral contact is around 6, and only 1 or 2 iterations are needed in EPA to find the overlap and all the relevant contact features when the overlap between polyhedra is small.Originality/valueThe equivalence of the entrance block in DDA and the Minkowski difference of two polyhedra is emphasised; GJK- and EPA-based contact algorithms are applied to convex polyhedra in DEM; energy conservation is guaranteed for the contact theory used; and numerical results demonstrate the effectiveness of the proposed methodologies. Journal Article Engineering Computations ahead-of-print ahead-of-print 0264-4401 31 12 2019 2019-12-31 10.1108/EC-03-2019-0124 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2019-09-10T13:31:42.8473819 2019-05-22T09:21:53.5660973 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Y.T. Feng 1 Yuanqiang Tan 2 Yuntian Feng 0000-0002-6396-8698 3 0050478-22052019093746.pdf feng2019.pdf 2019-05-22T09:37:46.4070000 Output 6738214 application/pdf Accepted Manuscript true 2019-05-22T00:00:00.0000000 true eng
title On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra
spellingShingle On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra
Yuntian Feng
title_short On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra
title_full On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra
title_fullStr On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra
title_full_unstemmed On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra
title_sort On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra
author_id_str_mv d66794f9c1357969a5badf654f960275
author_id_fullname_str_mv d66794f9c1357969a5badf654f960275_***_Yuntian Feng
author Yuntian Feng
author2 Y.T. Feng
Yuanqiang Tan
Yuntian Feng
format Journal article
container_title Engineering Computations
container_volume ahead-of-print
container_issue ahead-of-print
publishDate 2019
institution Swansea University
issn 0264-4401
doi_str_mv 10.1108/EC-03-2019-0124
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
active_str 0
description PurposeContact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called entrance block of two polyhedra and reduces the contact to evaluate the distance between the reference point to the corresponding entrance block, but effective implementation is still lacking.Design/methodology/approachIn this paper, the equivalence of the entrance block and the Minkowski difference of two polyhedra is emphasised and two well-known Minkowski difference-based contact detection and overlap computation algorithms, GJK and expanding polytope algorithm (EPA), are chosen as the possible numerical approaches to the 3D contact theory for DDA, and also as alternatives for computing polyhedral contact features in DEM. The key algorithmic issues are outlined and their important features are highlighted.FindingsNumerical examples indicate that the average number of updates required in GJK for polyhedral contact is around 6, and only 1 or 2 iterations are needed in EPA to find the overlap and all the relevant contact features when the overlap between polyhedra is small.Originality/valueThe equivalence of the entrance block in DDA and the Minkowski difference of two polyhedra is emphasised; GJK- and EPA-based contact algorithms are applied to convex polyhedra in DEM; energy conservation is guaranteed for the contact theory used; and numerical results demonstrate the effectiveness of the proposed methodologies.
published_date 2019-12-31T04:01:57Z
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score 11.035655

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