Flexibility Analysis Of Cable And Strut Tension Structures

Cable and strut tension structure is a flexible assembly formed with the flexible member pretension. Based on the form-finding, non-linear structural analysis, nodal flexibility, kinematically and indeterminate analysis, the overall flexible performance can be evaluated accordingly for the tension structures.The force-density method is well known and applied extensively for the form-finding of cable-net structures. However, the research works are rarely for the form finding and pre-stress optimization of tensegrity because of the existence of the feasible pre-stress, various force-densities. Firstly, the force-density method is formulated in detail for the form-finding cable-net structures, and the approach is proposed emphatically for the force-density application to form-finding of tensegrity structure. On the basis of rank reduction of force-density matrix, the feasible force-density is sought, and the final equilibrium configuration can be founded through form-finding procedure. The algorithm is developed through VC++ language, and the form-finding analysis is performed for saddle-shape cable-net, a paraboloidal cable-net and double-layer tensegrity structures. The domestic literature of the application of minimum potential energy method to nonlinear static analysis of structure is very few, however it is very significant. In this paper, the application of minimum potential energy method to the nonlinear structural analysis is researched. And it is thus used in cable-net and tensegrity analysis. A VC++ program is developed, the nonlinear analysis is performed for rhombic cable-net, hexagonal cable-net and a tensegrity structure. The structural characteristic is investigated sequentially, including nonlinearity, constant pre-stress state nature.In chapter 4, the concept of nodal flexibility matrix is firstly proposed. According to the nodal flexibility matrix, the flexibility ellipsoid is formulated, and the program is developed with visual C++. Finally, the nodal flexibility nature is evaluated with flexible ellipsoid for the tension structures.In chapter 5, according to the equation of potential energy, the redundancy formula is formulated, and the elastic and geometric redundancy is deduced further. Finally, the overall flexibility and kinematically property is evaluated through redundancy for the structures.