When is a symmetric pin-jointed framework isostatic?

被引：49

作者：

Connelly, R. ^{[2
]}

Fowler, P. W. ^{[3
]}

Guest, S. D. ^{[1
]}

Schulze, B. ^{[4
]}

Whiteley, W. J. ^{[4
]}

机构：

[1] Univ Cambridge, Dept Engn, Cambridge CB2 1PZ, England

[2] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

[3] Univ Sheffield, Dept Chem, Sheffield S3 7HF, S Yorkshire, England

[4] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada

来源：

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES | 2009年 / 46卷 / 3-4期

基金：

英国工程与自然科学研究理事会;

关键词：

Frameworks; Isostatic; EXTENSION; RIGIDITY;

D O I：

10.1016/j.ijsolstr.2008.09.023

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

Maxwell's rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry. group representation theory is exploited to provide further necessary conditions. This paper shows how, for an isostatic framework, these conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework. (c) 2008 Elsevier Ltd. All rights reserved.

引用

页码：762 / 773

页数：12

共 27 条

[1]

Altmann SL, 1994, Point Group Theory Tables

[2]

Atkins P.W., 1970, Tables for Group Theory

[3] FULLER,BUCKMINSTER TENSEGRITY STRUCTURES AND MAXWELL,CLERK RULES FOR CONSTRUCTION OF STIFF FRAMES [J].