基于群论的空间可展开结构自由度分析

为了开发构型新颖、生命力强、便于运输和储藏的空间可展开结构，使其满足所处环境的时间、空间等苛刻条件，适应特殊任务的实际需求，亟需开展空间可展开结构的自由度及折展性能分析。由于现有可展结构多具有一定的对称性，基于群论方法，从对称学角度解析结构可动的本质，提出判别对称体系可动性的充分条件。根据几何约束性质，运用矩阵理论和变分原理，推导了可展结构中典型构成单元的位移协调矩阵。利用对称子空间，推导了机构位移模态、自应力模态的对称表示，并以闭合环形可展开结构为研究对象，开展了结构自由度分析。研究工作有助于新型空间可展开结构的研发与设计，为可展结构及其衍生结构的进一步研究与应用提供了理论基础。

Mobility analysis of deployable space structures based on group theory group theory

To develop deployable structures with novel geometric configuration,strong vitality,and convenient transportation and storage,mobility and folding analysis on deployable structures is important.As the involved configurations could be effectively deployed or folded,these structures would satisfy the hard conditions of time or space,and meet the needs of some specific tasks.In fact,most existing deployable structures show certain symmetries.From the point of view of symmetry,group theory was introduced to explain the essence of kinematic mobility in-depth.Afterwards,the sufficient condition for evaluating the mobility of symmetric systems was proposed.According to the property of geometric constraints and the variational principle,the compatibility matrix of a typical member in assembling deployable structures was derived.Based on the symmetry subspaces,the symmetry representations of internal mechanisms and self-stress states were deduced.Then,symmetry-adapted mobility analysis on a few closed-loop deployable structures was presented.The study is devoted to promote the design and development of novel symmetric deployable structures,providing a basis for further studies and potential applications on novel deployable structures and kinematically indeterminate structures.