There is a great knowledge of the mechanical behavior of geometrically regular curved surfaces like most shells structures are formed by (Flugge [1]). This is mainly because these surfaces are relatively easily described by analytical mathematical functions. For describing irregu
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There is a great knowledge of the mechanical behavior of geometrically regular curved surfaces like most shells structures are formed by (Flugge [1]). This is mainly because these surfaces are relatively easily described by analytical mathematical functions. For describing irregular curved surfaces, like those in Free From Architecture, there are very little analytical mathematical functions available and there for it is very hard to derive formulas to describe their mechanical behavior. One way of dealing with this problem is to calculate the stresses and strains of these irregular curved structures with computer programs based on the finite element method. The problem with that is that you only obtain quantitative information about the results (like the magnitude of the forces) but not any qualitative information. It doesn’t always give clear insight into the structural behavior. For example, what is the relation between the shape of the curved surface and the flow of forces. In analytical formulas for regular curved surfaces there is a quantitative relation between the magnitude of the forces and the shape of the shell, like the radius. Because of the lack of insight it can be difficult to design irregular curved surfaces which have shell-like behavior, that is mainly extension forces and little bending moments.
The research tries the reveal some of the mysteries of the relationship between form and force of irregular curved surfaces. In 2D structures the load and the supports determine the line of thrust of the load. If the system line of a structure deviates from the line of thrust of the load it will cause “corrective” bending moments in the structure. In 3D structures like shells, for example a dome, the line of thrust of the load can be corrected by the hoop forces so to coincide with the system line of the shell so there are no bending moments in the dome. For a dome where the line of thrust of the load falls outside the system line the hoop forces are compression, and where the line of thrust of the load falls inside of the dome the hoop forces are tension (Figure 1). If we know the “3D line” (surface) of thrust of the load in regards to it’s supports and we combine this with any (irregular) curved surface it is possible to determine the forces in the shell. A way of determining the flow of forces of (irregular) curved surfaces is the “rain flow” analysis of the geometry of the curved surface.