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| Mobility of highly symmetric structures based on group theory |
| Received:June 05, 2011 Revised:December 22, 2011 |
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| DOI：10.7511/jslx20125005 |
| KeyWord:revolving joint criteria for mobility symmetric structure equilibrium matrix group theory |
| Author | Institution |
| 陈耀 |
东南大学 混凝土及预应力混凝土结构教育部重点实验室, 南京 ;东南大学 国家预应力工程技术研究中心, 南京 |
| 冯健 |
东南大学 混凝土及预应力混凝土结构教育部重点实验室, 南京 ;东南大学 国家预应力工程技术研究中心, 南京 |
| 夏仕洋 |
东南大学 混凝土及预应力混凝土结构教育部重点实验室, 南京 ;东南大学 国家预应力工程技术研究中心, 南京 |
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| Abstract: |
| Based on the group theory,a novel method for determining the mobility of highly symmetric over-constrained assemblies is proposed.Different from the pin-jointed assemblies,these structures consist of revolving joints and rigid links,and have many modes of self-stresses.Thus,it is difficult to investigate their geometric stabilities using the conventional criteria for the mobility.By the equilibrium equation about the internal forces and external loads of each element,this study gives the equilibrium matrix and the compatibility matrix for these structures.The modes of mechanism displacement and self-stresses are obtained from the null-spaces of the matrices.Using the subspaces of irreducible representations and the characters from a symmetry group,the symmetry adapted modes of mechanisms and self-stresses could be accordingly expressed,and they will reveal the mobility.Some typical examples based on the geometries of polyhedra are discussed.It could be concluded that the proposed technique is convenient and feasible,and each of the illustrative structures has a single degree of freedom and is validated to be foldable. |
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