The surface stress density method as a form-finding tool for tensile membranes

Abstract

Form-finding for membrane tension structures is a delicate operation which must ensure both the absence of compressive areas and interactive control of the forms generated. Until now, methods have generally been based on large displacements and strain analysis that provide non-linear formulations; resolution and computation are, therefore, too complex and cumbersome. This paper describes a new method of form-finding which reflects a wish to provide architects with a simple, effective and reliable investigation suited to their needs. The surface stress density method uses surface triangular elements with an isotropic stress tensor and leads to an iterative procedure which converges on configurations that satisfy the laws of static equilibrium. Mathematical considerations ensure the convergence conditions. This method enables the designer to generate a broad range of structures (pneumatic membranes or cable-reinforced membranes), while conserving control of shape and internal stress distribution. Moreover, the formulation draws a parallel with the force density method and a combined approach may be specified, particularly for the monitoring of reinforcing cable.