Research And Application Of Rigid Component’s Redudancy

Generally, rigid structure includes the truss structure, the framed structure and the composite structure which contains both trusses and frames. The spatial latticed structure is a typical kind of rigid structure, and it has many advantages such as reasonable stress, simple in calculation, high stiffness with less material, convenient construction and so on. Because of those advantages, it has been widely used in engineering. This paper consummated the theory of the rigid structure redundancy, and applied it to evaluate the behavior of the spatial latticed structure under common loading and accidental loading.First, a method to calculate the truss structure was presented. The redundancy of the truss structure was based on the potential energy. Through the differential equations solution of the potential energy, we can get the equilibrium equation, physical equation and geometric coordinate equation, and then the redundancy formula can be mathematically formulated by the three equations.Based on the theory of truss structure redundancy, the plane framed structure’s redundancy formula can be formulated by considering the potential energy of bending. And by considering the potential energy of torsion, the way to calculate the spacial framed structure’s redundancy was also found. Then by the way of split the total potential energy into some basic potential energies, the redundancy formula of composite structure was solved out and established a relatively complete theoretical system of rigid structure’s redundancy.On the foundation of theoretical analysis, the program composition with MATLAB was used to calculate some typical examples. The properties of rigid structure’s redundancy was drawn by these examples, and the influence of the structure’s geometric construction, cross section parameter, constraining conditions and the external loads was also found. Considering most current researches on the importance coefficients were based on some particular loads, which cannot reflect the basic properties of structure, this paper used the redundancy as a quantitative index to evaluate the importance coefficients of the components, so that the robustness of structure would be evaluated. The examples proved that we can evaluate different optimum designs and enhance designs by comparing the value and distribution of redundancy, which confirmed the effectiveness of the redundancy on the importance coefficients.