数字状张拉整体结构的构型设计与力学性能模拟

针对大型张拉整体结构的设计问题,选取四棱柱状张拉整体结构和截角正八面体状张拉整体结构作为基本胞元,采用节点连接节点的方式建立球柱组合式数字状张拉整体结构,并使用基于结构刚度矩阵的大变形非线性数值求解方法对其进行力学性能分析.在两类胞元满足各自的自平衡条件和稳定性条件的前提下,组合得到的数字状张拉整体结构亦处于自平衡稳定状态,搭建了实物模型进行验证.以数字8状张拉整体结构为例,模拟研究了结构承受自重等分布载荷和单轴拉压等端部载荷时的静力学响应,以及结构无阻尼振动时的固有频率和模态等动力学性能.结果表明,结构在自重作用下的变形行为受初始预应力、压杆密度和拉索刚度的影响较大,对其进行合理配置方可确保结构具有足够刚度抵抗自重;结构在单轴拉压作用下呈现非线性的载荷-位移曲线,拉伸刚度随变形量的增大而增大,压缩刚度随变形量的增大而减小;结构的固有频率随初始预应力的增大而增大,而模态振型基本不变.研究结果丰富了大型张拉整体结构的外形种类,有望推动此类结构在土木建筑、结构材料等领域的应用. 

NUMBER-SHAPED TENSEGRITY STRUCTURES: CONFIGURATION DESIGN AND MECHANICAL PROPERTIES ANALYSIS

Due to the novel mechanical properties, tensegrity structures have found various applications in science and engineering, and the design of large-scale tensegrities becomes a vital issue. In this paper, a series of number-shaped tensegrity structures are proposed by assembling the cylindrical and spherical tensegrity elementary cells. Specifically, the quadruplex prismatic tensegrities and the truncated regular octahedral tensegrities are selected as the elementary cells and then connected by using the node-on-node assembly scheme. Furthermore, structural stiffness matrix-based numerical method is employed to simulate the mechanical responses of the assembled tensegrities. Our results show that the obtained number-shaped tensegrities are self-equilibrated and stable when the elementary cells satisfy their self-equilibrium and stability conditions, respectively. A physical sculpture is also constructed using the aluminium alloy bars and nylon strings. Taking the eight-shaped tensegrity structure as an example, the static mechanical responses of the structure subjected to self-weight loading and uniaxial tension/compression are simulated, as well as the structural natural frequencies and modes of its free vibration. The simulations show that the tensegrity could have enough rigidity to bear the self-weight when the structural pre-stress level, the mass density of the compressed bars, and the stiffness of the tensioned strings match well. The load-displacement curves of the tensegrity under uniaxial loading are nonlinear, that is, the tensile stiffness increases with the tensile deformation, while the compressive stiffness decreases with the compressive deformation. The structural natural frequencies are dependent on the pre-stress level, while the vibration modes change little. The present work enriches the shapes of large-scale tensegrities and would promote their applications in civil and material engineering.