A continuous stress-based form finding approach for compressed membranes

The need for highly efficient structures necessitates the development of innovative design approaches that lower the environmental impact of the construction industry. The efficient use of mechanical material properties represents a good basis to enable significant material reduction and reduce material waste. For materials with negligible tensile capacity, designing a purely compressed form enables the structure to work efficiently through membrane action under design load resulting in minimum structural thickness. Most shell and vault form-finding methods are based on discrete approaches, whose solutions are linked to the initial discretisation or mesh estimations. Such discretisation strategies might provide valuable aesthetic solutions but do not prioritise the shell’s optimal internal stress state. To overcome the challenge of inefficient mesh discretisation in a form-finding process for shell or vault forms with boundary arches, an optimised and continuous form-finding approach based on Pucher’s formulation of membrane equilibrium, is presented that achieves a compressed configuration with minimum principal stresses. Four case studies are presented where the applied vertical loads, the shape of the plan and geometrical constraints are varied.