Membrane Roof in Cardiff Bay. It is impossible to work with complex doubly curved surfaces without understanding the geometry or without the tools to manipulate the form of the surface. The surface is represented as a mesh. The representative mesh is analysed using non linear FEA (finite element analysis) to determine the forces in the membrane, the perimeter cables and the loads to the main supporting elements. The elements are usually masts and cables, but beams, concrete members or even timber can provide support. Non linear analysis is used where displacement may not equal the applied force depending on scale.
The membrane should ideally have double curvature, as in a saddle, where the centre of radius of curvature in two principle directions is on opposite sides of the surface. This forms a shape known as an anticlastic surface. Tension structures use a double curvature that is anticlastic (in opposite directions), while the air supported structure is generally synclastic (curved in the same direction).
The form must not only represent the design intended, but allow for heavy weather conditions such as ponding (water collection) high displacement under high loads and the efect of the membrane strching over a period of years.