The Stringer system: a truss model of membrane shells for analysis and design of boundary conditions

This paper deals with the problem: What sort of boundary conditions are to be prescribed on the edge of a shell that is to be in a statically determinate membrane state? Triangulated single layer trusses have been suggested as a model for membrane shells by (Calladine 1983) and have been investigated by (Szabo and Tarnai 1992). However, these efforts have not solved the problem completely. The paper presents a triangular single layer truss system - the stringer system - which differs from the above mentioned models in two ways: 1. the systematic topology makes it relatively simple to control whether or not the system is statically and geometrically/kinematically determinate. 2. the geometry corresponds to the curvature of the considered surface and ensures that the system can be applied as a valid static and geometric model for the membrane shell. In most cases, the stringer system regarded as a static model of membrane shells leads to the same results as the theory of partial differential equations, as investigated by (Tarnai 1980a, 1981, 1983). However, some new boundary conditions for shells with positive and zero Gaussian curvature have been found and the types of supports and the connection between statical and geometrical determinacy have been further generalised.