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.
- The first self-contained treatment of the rigidity theory of discrete structures, written by leading experts in the field
- Provides a focused 'mini-course' on symmetry and group representations that equips reader to use them efficiently
- Supported by software for constructing symmetric tensegrities in three-space: https://robertconnelly.github.io/symmetric-tensegrity/
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Reviews & endorsements
'Rigidity theory mathematicians and structural engineers are like two branches of a tribe that separated long ago. In the intervening time, the language and knowledge of each group has evolved to where concepts no longer align and common terms no longer have common meanings. As a result, when they interact today, confusion reigns. Frameworks, Tensegrities and Symmetry is a guide that both groups can use to understand the other.' William F. Baker, Skidmore, Owings & Merrill
'The authors promise 'an attempt to build a bridge between two cultures' and they have done a remarkable job of this unenviable task. Requiring only a minimum of mathematical and engineering prerequisites the book develops intuitively, and rigorously, the rigidity theory of both bar frameworks and tensegrity frameworks and applies this theory to analyse built structures. Two masters of the field have carefully designed the book to move seamlessly between the analysis and synthesis of specific structures and providing the general, generic and symmetric theories.' Anthony Nixon, Lancaster University
'This excellent book unifies the engineering and mathematical literature by exploring different notions of rigidity - local, global and universal - and how they are interrelated. A lot of revealing examples accompany the mathematically precise description, hence the book can be recommended to researchers and students of mathematics, structural engineering, physics and computer science alike.' Andras Recski, Mathematical Reviews
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Product details
- Date Published: January 2022
- format: Hardback
- isbn: 9780521879101
- length: 350 pages
- dimensions: 250 x 174 x 19 mm
- weight: 0.69kg
- availability: In stock
Table of Contents
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.
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Authors
Robert Connelly, Cornell University, New York
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.
Simon D. Guest, University of Cambridge
Simon D. Guest is Professor of Structural Mechanics in the Structures Group of the Department of Engineering at the University of Cambridge, and Head of the Civil Engineering Division. His research straddles the border between traditional structural mechanics and the study of mechanisms, and includes work on 'morphing' and 'deployable' structures.