Searching form (“form-finding”) of a tensostructure is one of the basic tasks in the design of tensile structures: those made with membranes, cables, belts, etc. Ensuring that the whole structure is in tension is not something immediate since we can easily meet with warped surfaces, wrinkles even at rest under the load of self weight.

According to actions which are always in one direction (pneumatic structures, structures with heavy surfaces, snow) or having opposite direction (mainly wind), we use synclastic2 or anticlastic3 forms.

Methods of generation of forms.

There are many ways of generating these surfaces. We are going to quote some of them:

1. 1. Surfaces of known geometry.
      We have already commented on some of them in the definitions of the terms synclastic and anticlastic. In general, most forms of revolution, whether with a positive Gauss curvature or negative, can be built with any CAD program and may be subject to tension. But not all work the same.The surface of a baluster is a surface of revolution but can only be prestressed with internal pressure. Therefore, it cannot be a tensioned membrane structure, but a presostructure.
      

      Baluster

   2. Soap bubbles.
      Frei Otto in his IL lab, studied tensable surfaces very thoroughly applying force of surface tension of soapy membranes. The main problem of this method is the their volatile nature.
      

      Soap films

   3. Ruled surfaces.
      The ruled surfaces formed by straight lines of which ends run any two curves are capable of being tensables in the direction of the straight line of course. In the other direction, it depends on the generatrix curves. Technology of concrete shells can be a good reference for the generation of forms using this method.
      

      Ruled surfaces

   4. Models.
      This is one of the most commonly used methods (along with the next) as the realization of a model with a membrane made of a very deformable material (lycra, for example). This method allows you to not only find ways, but being able to prove their structural behavior, analyze uniformity of the prestress, show model to customer, take pictures, etc.
      

      Model using lycra

   5. Simulation with software.
      It is without doubt the most common method used today in the professional field due to the speed and the possibility to continue with the manufacture. (From design to manufacture by numerical control). Nevertheless it has an obvious disadvantage: the possibility of committing serious errors on not having appreciated impossible forms or of very low resistance that they appear as perfectly valid on screen. Of the quality of the software and especially on the quality of the user of the software the obtained result will depend.However, it has an obvious drawback: the possibility of committing serious mistakes by not appreciating impossible or very low resistance forms that appear as perfectly valid on screen. The result obtained depends on the quality of software and mostly on the competency of the software user.
      

      Forms obtained with software

Forms by simulation

How does a computer program seeks a tensioned form? There are various ways of doing this. In fact, each one can invent their own, but the truth is that the majority of programs (also WinTess3) use one of these two:

1. 1. Force density
      The force density term is used in physics, especially in fluid mechanics concepts (https://en.wikipedia.org/wiki/Force_density) that have nothing to do with the tensile structures. It was H.J. Tschiang who first made reference to this term to describe the method in 1974. It’s creating a linear system of equations where the unknowns are (X, Y, Z) position of the nodes of a mesh, while the parameters of these equations are the lengths of the segments that join each node on the mesh with another. If we only use these lengths we would get smooth mesh (no peaks) but with highly deformed free edges.In order to create ridges and valleys on the one hand and to decide on the curvature of the edges on the other hand, we need to change these lengths by applying a certain coefficient. Hence the term density.It is necessary that there are some fixed points, otherwise the system of equations would be indeterminate, and there wouldn’t be any solution.
      

      Form obtained with force density method

      In the previous figure, segments of the edge (in blue) have a coefficient of 5, while others (in black) have a coefficient equal to 1.
      NOTE: In WinTess3, this is the method used when the dropdown in the top toolbar is in “Form finding”.

   2. Deformation by force applied
      In this method, the aim is to simulate the deformation of a very deformable mesh (imagine a mesh formed by rubber bands) against the loads applied. If these loads are punctual (applied to only one point) we obtain forms with apexes or corners, while if the loads are applied superficially we obtain pneumatic forms.One of the drawbacks of this method is that it is a non-linear, therefore, slower calculation than the previous, but it reproduces faithfully what we can experience with a deformable model.
      

      Form obtained by applying pressure to all points of the mesh

NOTE: In WinTess3, this is the method used when the dropdown in the top toolbar is in “Analysis”.

1. ---

   ¹ Term invented to refer to the tensile structures, i.e. subjected to tension on most of them. It is sometimes confused with the term presostructures, which would be tensile structures subjected to internal pressure as a method of prestressing.

2. ² Surfaces with a single curvature: cylinder, cone, … (Gauss curvature is equal to zero) or double curvature in the same direction (positive Gauss curvature): forms of revolution as sphere, ellipsoid, paraboloid, …

3. ³ Surfaces with double curvature in opposite directions, i.e. negative Gauss curvature (one of the best known is hyperbolic paraboloid form, … )