张拉整体结构的多平衡态研究

Study on multiple equilibrium configurations of tensegrity structures

对张拉整体结构的多平衡态现象进行深入研究,首先利用解析方法分别找出平面张拉整体结构、棱柱式张拉整体结构和交叉索式张拉整体结构的多个平衡态;随后研究多个平衡态之间的能量关系,并判定这些平衡态的稳定性。分析结果表明:平面张拉整体结构有可能存在多种内力密度分布形式,且其对应的平衡都是稳定的。棱柱式张拉整体结构拥有的内力密度分布形式的数目为欧拉函数的一半,其弹性应变能随着平衡态阶次的增加而增大。交叉索式张拉整体结构也可以具有不同的内力密度分布,其最后1阶平衡态的能量最小,但未必所有交叉索式张拉整体结构都存在稳定的平衡状态。

The characteristics of multiple equilibrium configurations of tensegrity structures were studied in this work.Firstly,the multiple equilibrium states of planar tensegrity structures,prismatic tensegrity structures and star-shape tensegrity structures were identified. Next,the energy relations among the equilibrium configurations were discussed,and furthermore the stability of these structures was evaluated. The results show that the planar tensegrity structures may have several equilibrium configurations in the inner force density,and the corresponding configurations are stable. The number of inner force density patterns for prismatic configurations is one half of that of Euler function,and the elastic strain energy of structures may increase with the increase of the order of equilibrium states. In addition,the star-shape structures may also have several equilibrium configurations,and the elastic strain energy corresponding to the last order of equilibrium state is minimal. However,not all star-shape tensegrity structures may have the stable equilibrium configuration.