서브메뉴
검색
Cellular Cosheaves, Graphic Statics, and Mechanics
Cellular Cosheaves, Graphic Statics, and Mechanics
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151330
- ISBN
- 9798382834856
- DDC
- 519
- 저자명
- Cooperband, Zoe.
- 서명/저자
- Cellular Cosheaves, Graphic Statics, and Mechanics
- 발행사항
- [Sl] : University of Pennsylvania, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 256 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Ghrist, Robert.
- 학위논문주기
- Thesis (Ph.D.)--University of Pennsylvania, 2024.
- 초록/해제
- 요약This dissertation develops cellular cosheaf theory for the analysis of physical structures. This approach generalizes well known linear matrix methods to cosheaf homology. The core contributions of this thesis are a cosheaf-theoretic development of elementary structural analysis techniques as well as a comprehensive derivation and enrichment of graphic statics: a structural duality linking loading states on a framework to its dual cellular geometry. We develop classical 2D graphic statics using homology, extending to several entirely novel relations in 3D polyhedral graphic statics using spectral sequences. We further develop the group equivariant version of graphic statics over symmetric frameworks. Cosheaf methods are broadly applicable to other structural systems. We develop a novel anchored frame system which algebraically ties together the statics and kinematics of pin-jointed trusses and moment bearing frames. For rigid origami, several kinematic models are simplified and placed within an overarching homological theory. This work provides a wealth of applications of cosheaf homology, advancing the field of applied topology.
- 일반주제명
- Applied mathematics
- 일반주제명
- Mathematics
- 일반주제명
- Systems science
- 일반주제명
- Mechanical engineering
- 키워드
- Cellular sheaves
- 키워드
- Homology
- 기타저자
- University of Pennsylvania Electrical and Systems Engineering
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008250123s2024 us c eng d■001000017161254
■00520250211151330
■006m o d
■007cr#unu||||||||
■020 ▼a9798382834856
■035 ▼a(MiAaPQ)AAI31240970
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a519
■1001 ▼aCooperband, Zoe.
■24510▼aCellular Cosheaves, Graphic Statics, and Mechanics
■260 ▼a[Sl]▼bUniversity of Pennsylvania▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a256 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Ghrist, Robert.
■5021 ▼aThesis (Ph.D.)--University of Pennsylvania, 2024.
■520 ▼aThis dissertation develops cellular cosheaf theory for the analysis of physical structures. This approach generalizes well known linear matrix methods to cosheaf homology. The core contributions of this thesis are a cosheaf-theoretic development of elementary structural analysis techniques as well as a comprehensive derivation and enrichment of graphic statics: a structural duality linking loading states on a framework to its dual cellular geometry. We develop classical 2D graphic statics using homology, extending to several entirely novel relations in 3D polyhedral graphic statics using spectral sequences. We further develop the group equivariant version of graphic statics over symmetric frameworks. Cosheaf methods are broadly applicable to other structural systems. We develop a novel anchored frame system which algebraically ties together the statics and kinematics of pin-jointed trusses and moment bearing frames. For rigid origami, several kinematic models are simplified and placed within an overarching homological theory. This work provides a wealth of applications of cosheaf homology, advancing the field of applied topology.
■590 ▼aSchool code: 0175.
■650 4▼aApplied mathematics
■650 4▼aMathematics
■650 4▼aSystems science
■650 4▼aMechanical engineering
■653 ▼aAlgebraic topology
■653 ▼aCellular sheaves
■653 ▼aHomology
■653 ▼aStructural engineering
■653 ▼aLinear matrix methods
■690 ▼a0364
■690 ▼a0405
■690 ▼a0548
■690 ▼a0790
■71020▼aUniversity of Pennsylvania▼bElectrical and Systems Engineering.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0175
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161254▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
