자료유형  

 학위논문

Control Number  

0017161254

International Standard Book Number  

9798382834856

Dewey Decimal Classification Number  

519

Main Entry-Personal Name  

Cooperband, Zoe.

Publication, Distribution, etc. (Imprint  

[S.l.] : University of Pennsylvania., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

256 p.

General Note  

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

General Note  

Advisor: Ghrist, Robert.

Dissertation Note  

Thesis (Ph.D.)--University of Pennsylvania, 2024.

Summary, Etc.  

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. 

Subject Added Entry-Topical Term  

Applied mathematics.

Subject Added Entry-Topical Term  

Mathematics.

Subject Added Entry-Topical Term  

Systems science.

Subject Added Entry-Topical Term  

Mechanical engineering.

Index Term-Uncontrolled  

Algebraic topology

Index Term-Uncontrolled  

Cellular sheaves

Index Term-Uncontrolled  

Homology

Index Term-Uncontrolled  

Structural engineering

Index Term-Uncontrolled  

Linear matrix methods

Added Entry-Corporate Name  

University of Pennsylvania Electrical and Systems Engineering

Host Item Entry  

Dissertations Abstracts International. 85-12B.

Electronic Location and Access  

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Control Number  

joongbu:658480