Frameworks, Tensegrities, and Symmetry

Why don't things fall down? Engineering meets mathematics in this introduction to the geometry of rigid and flexible structures.

Robert Connelly (Author), Simon D. Guest (Author)

9780521879101, Cambridge University Press

Hardback, published 27 January 2022

350 pages
25 x 17.4 x 1.9 cm, 0.69 kg

'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

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.

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.

Subject Areas: Structural engineering [TNC], Robotics [TJFM1], Combinatorics & graph theory [PBV], Geometry [PBM], Discrete mathematics [PBD]