Frameworks, Tensegrities, and Symmetry

Description

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. 00.0 01.0_pp_i_iv_Frontmatter 02.0_pp_v_vi_Dedication 03.0_pp_vii_x_Contents 04.0_pp_xi_xiv_Preface 05.0_pp_1_6_Introduction 06.0_pp_7_8_The_General_Case 06.1_pp_9_16_Frameworks_and_Rigidity 06.2_pp_17_61_First-Order_Analysis_of_Frameworks 06.3_pp_62_77_Tensegrities 06.4_pp_78_109_Energy_Functions_and_the_Stress_Matrix 06.5_pp_110_134_Prestress_Stability 06.6_pp_135_154_Generic_Frameworks 06.7_pp_155_184_Finite_Mechanisms 07.0_pp_185_186_Symmetric_Structures 07.1_pp_187_204_Groups_and_Representation_Theory 07.2_pp_205_233_First-Order_Symmetry_Analysis 07.3_pp_234_268_Generating_Stable_Symmetric_Tensegrities 08.0_pp_269_270_Useful_Theorems_and_Proofs 09.0_pp_271_279_References 10.0_pp_280_284_Index