COMPUTER-AIDED DESIGN OF CABLE REINFORCED MEMBRANE STRUCTURES

Membrane structures present special problems to the designer. Their curved, three-dimensional forms are difficult to represent, and must be selected on the basis of both architectural and structural considerations. The static analysis of membrane structures may involve large deflections, deformation dependent loading, and slippage between the membrane material and reinforcing cables. Recent developments in the areas of surface modeling, interactive computer graphics, and finite element analysis make it possible to solve many of these problems. This thesis presents an integrated computer-aided design system, based on a combination of these technologies, which provides an effective tool for the design and analysis of membrane structures. There are three parts to the system, corresponding to the main tasks in the design and analysis of membrane structures: mathematical surface representation, solution of the initial equilibrium problem, and large deformation analysis including slip between membranes and reinforcing cables. Interactive computer graphics programs are described for each part of the design system. A common data base permits the results from any part of the system to be used directly in later stages of design.;The initial equilibrium problem involves selecting a single structural configuration, defined by a geometry, a stress distribution, and a set of loads, which is in equilibrium. After a review of existing solution methods, several new techniques for solving the initial equilibrium problem are presented. Two least squares methods are described in which equilibrium stresses are determined for fixed geometry and loads. The overdetermined method is a generalization of an existing technique for cable networks. The underdetermined method is a new technique which computes equilibrium stresses with minimal deviations from an ideal stress distribution. The existing force density method is shown to be a special case of the new assumed geometric stiffness technique in which the surface geometry and stresses are adjusted simultaneously. The iterative smoothing technique is another new method in which an equilibrium geometry is computed for a fixed stress distribution. Finally, the new slip stiffness formulations are a useful extension to the existing nonlinear displacement analysis method for solving the initial equilibrium problem.;After an initial equilibrium configuration has been determined, it is important to study the behavior of a membrane structure under a variety of design loading conditions. General techniques for the large deformation analysis of membranes and cables by the finite element method are discussed. Particular attention is devoted to the analysis of relative slip between membranes and reinforcing cables. Two new methods for modeling this behavior are presented. In the first method, specialized strain-displacement relations are developed based on the assumption of constant strain in a cable described by a series of linear segments. This method is limited to the analysis of frictionless slip in cables. The second method is a general technique for analyzing frictional slip that can be used with any element geometry including cables and membranes. A mixed Eulerian-Lagrangian displacement model is used to model slip explicitly.;Discrete transfinite mappings are shown to have significant advantages over other methods for the mathematical representation of membrane surfaces. The use of these mappings in the membrane design system is described. Data defining a surface is input graphical means and a finite element description of the surface is automatically computed and displayed in perspective images which can be viewed dynamically.