Form Finding Analysis And Program Design Of Tensioned Membrane Structures

Tensioned membrane structures is made of soft fabric and clenched by flexible cables or rigid supports to produce stiffness and cover a large space. Different from traditional structures , tensioned membrane structures is a flexible system and their stiffness is provided by geometrical cured surface and prestresses. Tensioned membrane structures must be prestressed for stiffness so that an initial equilibrium shape meeting architectural service requirements can be established. So form finding is the first and important process in design of membrane structures .The main contents in this paper are as follows.1 Force density method is applied to initial equilibrium shape finding of tensioned membrane structures. The advantage of this method is that with the constrained point coordinate ,the coordinate of every node can be known by solving a linear equation group, and the problem of initial coordinate and nonlinear convergence are avoided. On the basis of force density matrix of cable element ,a force density matrix of triangle membrane element is introduced. By assembling force density matrix of every element, the whole equilibrium equation of the structure can be obtained, which can also be obtained by the finite element method by assembling the element stiffness matrix similarly. This process is clearly and simple in concept and easy to program.2 The nonlinear element method is a efficient method for the form-finding of tensioned membrane structures, which can obtain satisfactory precision and the universal software for finite element analysis can be adopted. In this paper, a method using the shape derived by the force density method as the tentative shape for form-finding by the nonlinear element method is adopted, which convergence rapidly. A object-oriented program is completed for this method .3 The design of membrane structure contain the membrane structure itself and the supporting structure. At present , the design of membrane and its supporting structure is separated, which bring some errors in calculation due to the displacement of the membrane and the supporting structures can not be harmonized exactly. In this paper, the effect of separated calculation for form-finding of the membrane structure with different supporting structures is discussed. A new stiffness matrix of spatial beam element is introduced for geometric nonlinear analysis of spatial frame structures...