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1.
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.  相似文献   

2.
An efficient finite element formulation is presented for geometrical nonlinear elasto-plastic analyses of tensegrity systems based on the co-rotational method. Large displacement of a space rod element is decomposed into a rigid body motion in the global coordinate system and a pure small deformation in the local coordinate system. A new form of tangent stiffness matrix, including elastic and elasto-plastic stages is derived based on the proposed approach. An incremental-iterative solution strategy in conjunction with the Newton-Raphson method is employed to obtain the geometrical nonlinear elasto-plastic behavior of tensegrities. Several numerical examples are given to illustrate the validity and efficiency of the proposed algorithm for geometrical nonlinear elasto-plastic analyses of tensegrity structures.  相似文献   

3.
A numerical method is presented for form-finding of tensegrity structures. Eigenvalue analysis and spectral decomposition are carried out iteratively to find the feasible set of force densities that satisfies the requirement on rank deficiency of the equilibrium matrix with respect to the nodal coordinates. The equilibrium matrix is shown to correspond to the geometrical stiffness matrix in the conventional finite element formulation. A unique and non-degenerate configuration of the structure can then be obtained by specifying an independent set of nodal coordinates. A simple explanation is given for the required rank deficiency of the equilibrium matrix that leads to a non-degenerate structure. Several numerical examples are presented to illustrate the robustness as well as the strong ability of searching new configurations of the proposed method.  相似文献   

4.
考察构件刚度和构件撤除对杆件系统几何稳定性的影响.从常规结构稳定理论的角度审视铰接杆件系统几何稳定性问题.基于结构稳定的能量准则和刚度矩阵的构成分析,重新考察了Maxwell准则和平衡矩阵准则的充分必要性.解释了构件零刚度和构件撤除对体系几何稳定性影响的一致性.利用自应力矩阵的特性,提出并证明了一种快速识别杆系结构中“必需杆”的方法.一种多根构件撤除后体系几何稳定性的判别准则进而被发展.该判别准则的数值效率体现在仅利用原结构平衡矩阵一次分解后的信息,杆件撤除后体系平衡矩阵的秩可通过两小规模矩阵秩之间的关系来表示.  相似文献   

5.
一阶无穷小位移机构是一类具有机构性能的特殊的新型空间结构,从工程结构的角度考虑,只有能够清除机构性而获得几何刚度的体系才是可承载的结构体系。一阶无穷小位移机构的几何刚度的获得是通过体系的相对机构位移而获得的,这与传统结构的几何刚度的概念是完全不同的。因此,研究一阶无穷小位移机构的刚化问题是非常重要的。Maxwell准则只从体系的拓扑关系来考虑体系的几何稳定性,这显然不能应用于一阶无穷小位移机构的刚化判定问题。本文基于矩阵向量空间分解的理论和一阶无穷小位移机构的概念。在体系的平衡矩阵引入了边界条件,对一阶无穷小位移机构的刚化判定问题进行了分析,运用功能原理给出了一阶无穷小位移机构刚化的等价条件和判定方法。通过几个数值算例验证了本文结论和方法是正确的、可靠的。  相似文献   

6.
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.   相似文献   

7.
We propose a Monte Carlo form-finding method that employs a stochastic procedure to determine equilibrium configurations of a tensegrity structure. This method does not involve complicated matrix operations or symmetry analysis, works for arbitrary initial configurations, and can handle large scale regular or irregular tensegrity structures with or without material/geometrical constraints.  相似文献   

8.
As a special type of novel flexible structures, tensegrity holds promise for many potential applications in such fields as materials science, biomechanics, civil and aerospace engineering. Rhombic systems are an important class of tensegrity structures, in which each bar constitutes the longest diagonal of a rhombus of four strings. In this paper, we address the design methods of rhombic structures based on the idea that many tensegrity structures can be constructed by assembling one-bar elementary cells. By analyzing the properties of rhombic cells, we first develop two novel schemes, namely, direct enumeration scheme and cell-substitution scheme. In addition, a facile and efficient method is presented to integrate several rhombic systems into a larger tensegrity structure. To illustrate the applications of these methods, some novel rhombic tensegrity structures are constructed.  相似文献   

9.
A novel analysis method is presented for form-finding of tensegrity structures. The spectral decomposition of the force density matrix and the singular value decomposition of the equilibrium matrix are performed iteratively to find the feasible sets of nodal coordinates and force densities. An algorithm of determining the sole configuration of free-form tensegrities is provided by specifying an independent set of nodal coordinates, which indicates the geometrical and mechanical properties of the structures can be at least partly controlled by the proposed method. Several illustrative examples are presented to demonstrate the efficiency and robustness in finding self-equilibrium configurations of tensegrity structures.  相似文献   

10.
This paper considers a modeling and analysis approach for the investigation of the linear and nonlinear steady-state dynamics of a base excited 3D tensegrity module carrying a top mass. The tensegrity module contains three compressive members, which may buckle and six cables (tendons). First, a dynamic model of the system is derived using Lagrange’s equation with constraints. The buckling modeling of the compressive members is based on the assumed-mode method with a single mode discretization. The tendons are modeled as piecewise linear springs, which can only take tensile forces. This research focusses on the dynamic stability of the tensegrity structure by defining the geometrical and material properties in such a way that the system is just below the static stability boundary. Static and linear dynamic analysis is performed. In the nonlinear steady-state analysis, frequency-amplitude plots, power spectral density plots, bifurcation point continuation diagrams, and Poincaré maps are presented. A tensegrity structure is designed and manufactured and an experimental set-up is realized in order to validate the model by comparing experimentally and numerically obtained responses. In the validation stage, the numerical results are based on an amplifier-shaker-tensegrity structure model. It can be concluded that the numerical results match partly quantitatively and partly qualitatively with the experimentally obtained responses.  相似文献   

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