双V形三维构件张拉结构的矩阵分析与预应力优化研究

张拉结构是由不连续的受压构件和连续的受拉绳索组成的特殊结构体系,含有三维受压构件的张拉结构利用三维受压构件代替一维杆,增加了结构的稳定性与可控制性,是张拉结构发展的新趋势.利用取自正四面体四条斜边组成的双V形受压构件,以及纵向和环向绳索制得张拉整体结构模型,并用矩阵平衡法进行分析.建立矩阵时将传统杆索结构中只考虑杆轴向压力的平衡矩阵扩展到考虑三维构件弯曲的空间铰接体系复合平衡矩阵;再根据平衡矩阵理论以及奇异值分解理论得到该模型的自应力模态.在优化过程中,绳索受拉条件与力的均匀性作为优化目标,运用人工鱼群算法对构件预应力进行优化.结果证明结构的稳定性良好,绳索与受压构件拉压合理,以及对不同类别预应力分别进行均匀性优化的结果更好更具有针对性.

Matrix equilibrium analysis and prestress optimization of tensegrity structure with double V shape compression members

Tensegrity structure is a special structural system composed of discontinuous compression members and continuous tensile cables. Tensegrity structure with three dimensional components using 3D compression members instead of linear bars, increasing the system stability and controllability, is a new tendency in investigation. In this paper, the compression member is geometrically a double V shape selected from the four sides of a regular tetrahedron. The system is analyzed by an equilibrium matrix method. Traditional equilibrium matrix theory in a cable-bar system is expanded to a 3D components and cable system, considering both axis stress and bending stress in the components. Self-stress mode of the system is calculated from the matrix. The artificial fish swarm algorithm is adopted in the pre-stress optimization process; the objective is the system stability, cable tensioning ability, and prestress uniformity. The results show the stability of the structure is good, the cable tensioning and the stress in compression members are reasonable. In the condition the loadings are divided in different types respectively, the prestress uniformity optimization has a better and targeted result.