Keywords: tension structures, form-finding, dynamic relaxation, force density, matrix methods, structural optimisation.

The concept of form-finding is well established in the field of tension structures, but is not explored sufficiently outside that field, with structural optimisation being the main contender to providing robust, functional and durable designs. Form-finding can be defined as an iterative process of shaping structures according to prescribed boundary configurations and forces acting on them. It is a process that may, or may not, involve the elastic response of the structure.

This paper presents a review of form-finding techniques, including a variety of computational approaches (preferred by engineers), and physical modelling (preferred by architects). Amongst the computational approaches, the best known are: dynamic relaxation, force density, stiffness matrix, and the updated reference strategy. The main characteristics of each method will be outlined in the context of their suitability to a given application. The role of soap-film analogy in form-finding of fabric structures will be discussed from the theoretical and practical perspectives, and contrasted with the idea of differentially stressed forms. This will be followed by a discussion of common misconceptions related to the design of fabric structures.

Form-finding, if properly implemented, has the potential to deliver 'minimal' structures, or minimum energy forms, characterised by maximum stability and strength with minimum weight. This minimal principle operates in the formation of highly optimised objects we find in nature. It will, therefore, be postulated that formfinding techniques should be used not only to model shapes of flexible fabric structures, but also rigid structural forms. Examples of applications to rigid structural forms will include biomedical and aerospace structures, modelled through computational form-finding using the soap-film analogy. The biomedical application will concern a bone replacement scaffold - a minimal structure of appropriate surface curvatures to promote rapid growth of bone-forming cells, porosity to transport nutrients and waste, and stiffness for load sharing with the host bone. The aerospace application will concern a family of compressor blades subjected to aerodynamic loading. Comparisons between the form-found, and aerodynamically optimized structures, will be given.

Structural optimisation is an established approach to finding optimal shapes of rigid structural forms with methods such as evolutionary structural optimisation having the potential for delivering natural, minimum energy objects. However, there are distinct differences between structural optimisation and form-finding, and while optimisation criteria are, in general, well understood, form-finding presents a challenge in knowing what set of forces should be used to model an optimal shape of a structure.

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