Cutting Pattern of Fabric Membranes with the Stress Composition Method

Abstract

Study of fabric membranes emphasises on numerous difficulties which have to be overcome according to the willingness of reducing errors. We meet hence the first step of form-finding which must be achieved such as it ensures the determination of tensile shapes characterised by the lack of compressive areas. Therefore, it implies the knowledge of both the whole geometry and the prestress tensor at each point of the surface. Nevertheless, these considerations may be regarded as theoretical ones since the designer must then focus on the realisation of the membrane, in other words, on the determination the plane fabric strips which once assembled together and placed into position in space with anchorage points define the required configuration. This paper thus describes a new method devoted to the calculation of the strips with the aim of overcoming the drawbacks of the traditional processes. The used mechanical approaches allow to reduce distortions and errors by taking into account the whole geometrical characteristics of the strip, its stress distribution and the material constitutive laws. The theoretical formulation associates the operations of development and reduction and is based upon an iterative numerical procedure which converges to appropriate plane strips where distortions are minimised by least square methods. Several illustrative applications point out the efficiency of the method.