对称型动不定杆系结构的可动性判定准则

发布时间：2018-08-04 07:51

【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。
[Abstract]:Based on the symmetry theory and its matrix irreducible representation, a criterion for a symmetric dynamic indeterminate system is proposed. Firstly, according to the irreducible representation of the association matrix and the orthogonal relation of Shure, a symmetric coordinate system is established to describe the symmetric properties of the structure, and the structure equilibrium matrix is converted to a diagonalization block matrix. The zero space and the left zero space of the matrix, as well as the symmetric properties associated with each matrix, get the displacement mode of the structure and the symmetric expression of the self stress mode, and determine the dynamic performance of the structure according to the order of the two symmetric attributes. The motion of the classical dynamic indefinite bar system which satisfies the "Maxwell criterion" is determined, including the non displacement agreement. The analysis results show that the criterion is reasonable and effective, and it can make up for the defects such as leakage and misjudgement in the Guest method, and the conclusion is in agreement with the results obtained from the existing literature. The symmetrical internal mechanism displacement mode is a movable structure.
【作者单位】：东南大学混凝土及预应力混凝土结构教育部重点实验室;东南大学国家预应力工程技术研究中心;
【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)
【分类号】：TU399

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