Form-Finding Analysis Of Single Beam String Structure

Beam string structure (abbrev. BSS) is an inner equilibrium system whose bending resistance member and tension member is linked by brace strut. According the different disposing type in single BSS, it includes unidirectional BSS, bi-directional BSS and multidirectional BSS etc. And the behavior of single BSS determines the whole body's behavior. It is very important to understand the behavior of single BSS. BSS is widely applied in the engineering practice, but there are still many problems haven't been solved perfectly in the design and calculation of BSS. For example, there is no mature theory of the determination of stress distribution in initial equilibrium state, there is no mature theory which could be used for the determination of initial geometry in geometry zero state now, and the theory of the form optimization in loading equilibrium state is not reasonable yet. And what is more, few study on the behavior of space BSS is researched.This paper is mainly about the theory of form-finding of single BSS. On the side of the construction process of BSS, at first, the paper discusses the introduce method of the prestress in cable and some theories of form-finding of single BSS which were put forward before; secondly, based on geometry non-linear finite element theoretics, it deduces the tangent stiffness matrix of beam element and introduces the theory of answering geometric equilibrium equation, Newton-Raphson iteration, that establish the theoretical basic of form-finding of single BSS; thirdly, the paper put forward its own method of form-finding of single BSS named tangent stiffness matrix inverse iteration method; at last, according as above develops special program which achieves talking directly between people and computer, predispose and postdispose, and the paper proves the program is validate through an example.According the study work of this paper, puting forward a new method of form-finding of single BSS. This method is different from those methods that were put forward before, it is a adventruous attempt and innovation. It has a firm theoretical basic. And this method avoid some disadvantages that appeared in those old methods, provide some new routes for the researchers who will do the same research in the future. And what is more, this paper is propitious to the application of space BSS in the engineering practice.