对称型动不定杆系结构的可动性判定准则  

A unified criterion for movability of kinematically indeterminate frameworks with symmetry

作　　者：陈耀[1,2] 冯健[1,2] 马瑞君[1] 

机构地区：[1]东南大学混凝土及预应力混凝土结构教育部重点实验室,江苏南京210096 [2]东南大学国家预应力工程技术研究中心,江苏南京210096

出　　处：《建筑结构学报》2015年第6期101-107,116,共8页Journal of Building Structures

基　　金：国家自然科学基金项目(51278116);东南大学优秀博士学位论文培育对象项目(YBPY1201)

摘　　要：基于对称学理论及其矩阵不可约表示,提出了对称型动不定体系的判定准则。首先,根据关联矩阵的不可约表示及舒尔正交关系,建立了用于描述结构对称属性的对称坐标系,将结构平衡矩阵转化为对角化分块矩阵。随后,根据独立分块矩阵的零空间与左零空间,以及各矩阵所关联的对称属性,得到结构机构位移模态、自应力模态的对称表示,并根据二者对称属性的阶次判定结构的可动性能。对满足"Maxwell准则"的经典动不定杆系结构进行了可动性判定,包括无位移约束对称杆系、环向对称型杆系及斜放四角锥平板网架等。分析结果表明:文中所述判定准则是合理有效的,有效弥补了Guest方法中存在的漏解、误判等缺陷,判定结论与已有文献所得分析结果一致;算例中所讨论的对称动不定杆系皆具有全对称的内部机构位移模态,属于可动结构。Based on the theory of symmetry and its matrix representation,a unified method is proposed for evaluating the movability of symmetric pin-jointed assemblies. Using the irreducible representations from associated matrices and the Great Orthogonality Theorem,symmetry-adapted coordinate system is built to describe the symmetry of a structure,and to transform the original equilibrium matrix into a series of independent matrices in a block-diagonalized form.Then the symmetries of mechanism modes and self-stress states through the null space and left null space of the subblocks and the symmetry associated with each sub-block can be obtained. Subsequently,the comparison between the symmetry order of mechanism modes and self-stress states can reveal the movability of a symmetric structure. Some classical examples which satisfy the well-known ‘Maxwell rule 'are discussed,including free-standing pin-jointed assemblies,a type of symmetric ring structures,and diagonal square pyramid space grids. Numerical results show that the proposed method is reasonable and convenient,as the method solves the shortage of the existing symmetry method proposed by Guest,such as missing a solution,and the misjudgment. The results are in good accordance with the corresponding ones of some published articles. Moreover,all the illustrative structures have fully symmetric internal mechanisms,and thus are verified to be transformable.

关 键 词：对称结构 可动性 机构位移模态 预应力 铰接杆系 

分 类 号：TU399[建筑科学—结构工程]