基于力密度矩阵和平衡矩阵的张拉整体结构找形方法

Form-finding Method of Tensegrity Structures Grounded on Force Density Matrix and Equilibrium Matrix

提出了一种基于力密度矩阵和平衡矩阵的张拉整体结构找形新方法,结构的几何拓扑关系和单元类型是本找形方法所需的唯一条件.为了找到合适的节点坐标和力密度,将结构体系的力密度矩阵和平衡矩阵分别采用谱分解和奇异值分解进行循环迭代,直至满足对应矩阵最小秩缺失的必要条件.通过几个典型算例证明了利用本方法寻找张拉整体结构自平衡状态的效率和鲁棒性,可为寻找新型、非对称并且复杂的张拉整体结构提供借鉴.

A novel method is presented for form-finding of tensegrity structures based on the force density ma-trix and equilibrium matrix. The topology and the types of members are the only information required in thisform-finding process. To find the feasible sets of nodal coordinates and force densities, the spectral decom-position of force density matrix and the singular value decomposition of the equilibrium matrix were iterativelyperformed until the necessary minimum rank deficiency conditions satisfied. Several illustrative examples arepresented to demonstrate the efficiency and robustness in finding self-equilibrium configurations of tensegritystructures, and a theoretical guide is provided to find new, asymmetric and complex tensegrity structures.