Tension membranes modelled by curvi-linear bicubic splines

One of the unique features of tension membrane structures (used as architectural roofing forms) is that their shape under tension has to be determined through an iterative, computational process, known as form‐finding. This paper describes the spline analysis approach, which makes use of general curvilinear co‐ordinates in Cartesian system, to model surface‐stretched tension membranes and inflatable structures. Surface‐stretched membranes are characterized by zero pressure difference between their outer and inner surfaces, while inflatable structures derive their shape and surface tension from the respective pressure differences. Examples presented in the paper include applications to both types of tension membranes and, for inflatable structures, include the case where the pressure difference is non‐uniform. The method can be applied to finding natural forms of shell structures. Copyright © 2007 John Wiley & Sons, Ltd.