Stability conditions for tensegrity structures
Stability conditions for tensegrity structures
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DOI：
10.1016/j.ijsolstr.2006.10.027
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发表时间：
2007-06
影响因子：
3.6
通讯作者：
Jingyao Zhang;M. Ohsaki
中科院分区：
文献类型：
--
作者：
Jingyao Zhang;M. Ohsaki
基于线性刚度矩阵与几何刚度矩阵之和的切线刚度矩阵的正定性，推导了张拉整体结构的稳定性条件。通过考虑几何刚度矩阵零空间中的仿射运动，给出了系统稳定性的必要条件。证明了该条件与数学刚性理论导出的条件是等价的，从而解决了工程领域稳定性理论与数学领域稳定性理论之间的矛盾。进一步证明了当结构满足必要的稳定性条件，几何刚度矩阵为半正定且非退化秩亏最小时，保证结构稳定.
Stability conditions for tensegrity structures are derived based on positive definiteness of the tangent stiffness matrix, which is the sum of the linear and geometrical stiffness matrices. A necessary stability condition is presented by considering the affine motions that lie in the null-space of the geometrical stiffness matrix. The condition is demonstrated to be equivalent to that derived from the mathematical rigidity theory so as to resolve the discrepancy between the stability theories in the fields of engineering and mathematics. Furthermore, it is shown that the structure is guaranteed to be stable, if the structure satisfies the necessary stability condition and the geometrical stiffness matrix is positive semidefinite with the minimum rank deficiency for non-degeneracy.