Studies On Form-finding Of Cable Membrane Structures By Femol

Cable membrane structures are flexible structures. They have to be shaped to the desired form because they have no rigidity of their own. The procedure to determine the static equilibrium forms of cable membrane structures is referred to as form finding. Form finding analysis of cable membrane structures is a highly nonlinear solution procedure and since expression of surface solutions may not be unique for numerical solutions, singularity may occur.The finite element method of lines (FEMOL) is a semi-analytical method with ordinary differential equation (ODE) solvers as supporting software. FEMOL shows great potential in form finding analysis of cable membrane structures: the solutions are in high accuracy since FEMOL is a semi-discretized method; the sought surfaces are highly continuous and smooth, which makes subsequent pattern analysis easier, nonlinear ODEs are automaticly solved by COLSYS. The main parts of the work are as follows:I. The present thesis proposed two methods to construct initial surfaces aiming to improve the convergence of subsequent form finding for membrane structures. The first method is a unified constructive method to provide an initial solution. The second is a linearized solution method for minimal surface.II. The present thesis proposed a constraint approach to make solutions of minimum surface form finding be uniquely obtained. Based on this constraint approach, a complete iteration algorithm based on nonlinear FEMOL was developed.III. Based on the virtual work principle, the governing equations of form finding for cable reinforced membrane structures were derived. The proposed constraint approach was applied successfully to overcome the singularity. Firstly form finding of sigle-directioned cable reinforced membrane structures was strudied, and then form finding of two-directioned cable reinforced membrane structures was also studied. IV. The governing equations of form finding for air-supported membrane structures and anisotropic membranes were derived. The proposed constraint approach was also applied successfully to overcome the singularity. Iteration solution based on nonlinear FEMOL was developed.This thesis shows the initial surface finding method and the proposed constraint approach are valid and versatile for overcoming singularity difficulties in numerical solution procedures, and hence can be expected to be applicable to finite element methods. In summary, FEMOL appears to be a competitive semi-analytical method for form finding analysis of cable membrane structures.