Form-finding and determining geodesic seam lines using the updated weight method for tensile membrane structures with strut and anchorage supports

Tensile membrane structures (TMS) consist of the membrane fabric, supporting frame, cables and strut elements. The initial shape of a TMS is not known beforehand and has to be found by a process of ‘form-finding’. The majority of form-finding research has focused on determining the initial shape due to a defined prestress for TMS having only membrane and cable elements, while there has been very little research on TMS supported with struts and anchorage cables. This study extends the updated weight method (UWM) for the form-finding of TMS with struts and anchorage supports. The modified approach provides a robust solution in comparison to constrained strut length approaches. Furthermore, the curved form-found shape is not developable and geodesic lines need to be identified on the final form-found shape to provide seam locations for cutting the fabric. To solve this issue, geodesic lines are included in the UWM as constraints, whereby the geodesic pseudo cable lengths are minimised tangent to the surface. A sequential process is developed to ensure both the equilibrium and the constraint conditions are satisfied. The proposed method is successfully tested on a wide variety of TMS shapes along with the patterning of the cut panels. The study provides an integrated solution for the form-finding and identification of geodesic seam line on TMS having different boundary types.