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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 the irreducible representation of its matrix, a criterion for determining symmetric uncertain systems is proposed. Firstly, according to the irreducible representation of the correlation matrix and the Shure orthogonal relation, a symmetrical coordinate system is constructed to describe the symmetry property of the structure, and the structural equilibrium matrix is transformed into a diagonalized partition matrix. Then, based on the zero space and the left zero space of the independent subblock matrix, and the symmetrical properties associated with each matrix, the symmetric representation of the displacement mode and the self-stress mode of the structure mechanism is obtained. Based on the order structure of the two symmetry properties Movable performance. The movability of the classic uncertain rod system satisfying “Maxwell criterion ” is determined, including symmetric rod system with no displacement, symmetrical ring system and diagonal square pyramid plate grid. The analysis results show that the judgment criterion described in this paper is reasonable and effective, which effectively makes up for the defects of the Guest method, such as leaky misjudgment and misjudgment. The conclusion of the judgment is consistent with that of the existing literature. The rod systems all have the symmetry of internal mechanism displacement mode, which belongs to the movable structure.