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Analysis Methods

Tensile structures are structures that have two major characteristics:

• They may have large displacements under expected loads.
• They are composed of large amounts of linear objects (bars) or surface (elements) that can only withstand tension. If these objects are subjected  to another type of loads (compression, bending,…),  these objects give up interacting with the structure (bent cables, wrinkled canvas, etc.).

Both characteristics will generate a nonlinear behavior of the structure. That is, actions and deformations are not directly proportional, as usually happens in most rigid structures we use in architecture like steel, concrete, stone, etc.

This is not going to accomplish something as basic as “double load corresponds twice deformation.” Nor can we use the superposition principle: “If deformation is DA under load A  and deformation is DB under load B, then deformation will be DA + DB with a load of A + B”. This means that we will not be able to do something as common as a combination of assumptions on when it comes to the results.

To cope with the calculation of this type of non-linear structures, today there are many numerical methods used in engineering. Each one of them, individually or in groups, is designed for a particular type of structure.

Firstly, we can classify structures according to the objects that form them. The most representatives are:

• Bars
Linear components. They can withstand different types of loads. If they only support tension then we are referring to cables, belts, etc. On the contrary, if they can support other type of loads (compression, bending, etc.), then we are talking about other objects: tubes, beams, etc.
• Elements
If you want to analyze a continuous (a surface, a mass, etc.) object, there are methods that discretizes this continuum into smaller and more limited objects that are often referred to as finite elements.

WinTess3 has used only bar structures to date. Although the membrane structures have a continuous component, the fact that the fabrics are not isotropic (rather they are orthotropic) makes them a difficult choice of finite element with the appropriate characteristics. Also the behavior of the element when it is subjected to compression (wrinkled) is not easy to implement.

Currently, popularized isotropic membranes (ETFE, for example) has made us to think reactivating the calculation by the finite element method (FEM) for those cases in which it can be useful. This is not yet active.

Thus, at this time, WinTess3 is a program that analyzes structures tensioned only by bars. The membrane is broken down into a mesh to analyze. The choice of the mesh is important, both the type (triangular, square, radial, … ) as its density.

Secondly, we can consider the way in which develops the non-linear calculation. There is always an iterative process to find the balance of the structure subject to certain loads. However, this process can be different:

• Matrix methods (including different methods of approximation to the final solution)
• Dynamic relaxation
• Force density
• etc.

WinTess3 can use different methods, but only the matrix method has activated in standard way. This is the quickest to find the solution but it has the disadvantage that for complex structures (very large stiffness matrix) the method can become slow and requires high-performance computers and may still become unstable. We must therefore control the size of the stiffness matrix of the structure for fast and reliable results.