Form Finding : Soap Film

The commonest method of form-finding is with Triangles or Quads which have been given a uniform pretension and whose stiffnesses have been set to zero. Because the elements have no stiffness, the pretension is unaffected by changes of strain and so is “locked in” to the elements. They therefore behave like a soap film. If the pressure on the elements is zero they will form the “least area” surface within their boundary. A popular example of such a surface is the hyperbolic paraboloid; this is formed in a square in which two opposite corners have been raised. If the elements have a uniform pressure load, they will simulate an inflated bubble. The elements will only converge within conditions where a soap film could be formed; each point on their perimeter must be prevented from shifting inwards and they cannot be restrained internally at an isolated node since this would act like a pinpoint in a soap film. Equally in a surface that is being formed between a ring and a large base, the elements below the ring may form a narrow neck and collapse inwards if the ring is too small or too high.

If the pressure on the elements is zero, the shape that is form found is not affected by the size of the pretension and the pretension may be set to any reasonable value. If the elements have a pressure load, the curvature of the surface formed depends on the pretension. The greater the pretension, the flatter will be the form found surface. The pretension that will provide a given curvature can be estimated from the following equations.

For a spherical surface

For a cylindrical surface

A problem with “soap film” form-finding is that nodes that are only attached to Triangles and Quads tend to wander over the surface that is being formed. One method of controlling them is to put them on “greasy poles” i.e. restrain them so that they can only move in a line. The line should be approximately normal to the surface being formed. However Spacers offer a better means of controlling nodes. Advantages of using Spacers are that they position nodes on smooth curves with regular spacing and that the positioning of the nodes adapts automatically when the boundary of a surface is changed. Also if one uses a geodesic Spacer to form the boundary of a strip from a surface that will be flattened to make a cutting pattern, the curvature of the edges of the cutting pattern will be minimised and fabric wastage reduced.

Soap Film boundaries

In the absence of external load, the soap film surface is entirely dependent on its boundary conditions. Sometimes the boundary is a fixed line or point representing connection to a rigid structural beam or support point. More often, the boundary is a constant tension tie (defined using 1D soap film properties) which controls the edges of the surface of soap film triangles and quads. In reality this represents clamping the fabric to a cable spanning between fixed boundary points. The boundary cables should not be confused with the sliding cable element.

In the form finding process these boundary cables can be thought of as elastic bands. They are used when the precise length of the members they represent is not critical. They are modelled by a line of Ties whose Young’s modulus has been set to zero using 1D soap film properties. The prestress in the ties is set to a constant tension using 1D soap film properties. The ties’ forces are unaffected by their lengths and their nodes will shift to a position where the ties’ forces are in equilibrium with the tension of the surface of which they form the edge.

As with 2D soap film form finding elements, nodes in constant tension cables may need to be prevented from wandering. They can be controlled by duplicating the Ties with a “free” spacer or by restraining them to move in a plane approximately normal to the cable.

The required prestress in the cable depends on the desired curvature of the cable. For a boundary cable to “soap film” Triangles and Quads