Robert Connelly

Frameworks, Tensegrities, and Symmetry (eBook, PDF)

• Format: PDF

Produktbeschreibung

This introduction to the theory of rigid structures explains how to analyze the performance of built and natural structures under loads, paying special attention to the role of geometry. The book unifies the engineering and mathematical literatures by exploring different notions of rigidity - local, global, and universal - and how they are interrelated. Important results are stated formally, but also clarified with a wide range of revealing examples. An important generalization is to tensegrities, where fixed distances are replaced with 'cables' not allowed to increase in length and 'struts' not allowed to decrease in length. A special feature is the analysis of symmetric tensegrities, where the symmetry of the structure is used to simplify matters and allows the theory of group representations to be applied. Written for researchers and graduate students in structural engineering and mathematics, this work is also of interest to computer scientists and physicists.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 27. Januar 2022
• Englisch
• ISBN-13: 9781009234221
• Artikelnr.: 66177519

Autorenporträt

Robert Connelly is professor of mathematics at Cornell University and a pioneer in the study of tensegrities. His research focuses on discrete geometry, computational geometry, and the rigidity of discrete structures and its relations to flexible surfaces, asteroid shapes, opening rulers, granular materials, and tensegrities. In 2012 he was elected a fellow of the American Mathematical Society.

Inhaltsangabe

1. Introduction
Part I. The General Case: 2. Frameworks and Rigidity
3. First-Order Analysis of Frameworks
4. Tensegrities
5. Energy Functions and the Stress Matrix
6. Prestress Stability
7. Generic Frameworks
8. Finite Mechanisms
Part II. Symmetric Structures: 9. Groups and Representation Theory
10. First-Order Symmetry Analysis
11. Generating Stable Symmetric Tensegrities
A. Useful Theorems and Proofs.