Reciprocal diagrams for membrane structures, an intuitive approach for membrane form-finding

Abstract

In this paper, a connection between reciprocal diagrams and typical features in membrane structures is drawn. Although numerous form-finding techniques have been developed in the field of tensile membrane structures, the introduction of reciprocal diagrams allows for an intuitive understanding and can therefore facilitates the development in early design stages. To begin with, we introduce relevant basic concepts, including planar reciprocal diagrams and force density method. The second part of the paper focuses on the construction of planar reciprocal diagrams for typical membrane features including membrane patches, ridge/valley cables (cables that go through a patch of membrane) and edge cables. The concept of anchoring force polygon is introduced. The third part of the paper discusses form-finding in 3D with force densities found in the planar reciprocal construction, followed by progressive steps of updating force densities based on current geometry. Several benchmark studies were undertaken. Comparisons to analytical solutions or finite-element results were done, showing good agreement.