A larger plot of a gradient from vertical to lateral force exposure.
Exposure of a surface to pure tensile force, plot of von Mises stress (far left), optimized structure (second from left), exposure to pure transverse force, von Mises stress plot (second from right) and optimized structure (far right).
Above, bottom row: The exposure of a surface to a gradient field, from tensile to transverse force. Plot of von Mises stress. Top row: At each extreme, optimized structure under exposure to transverse force (left) and tensile force (right), and the transitional pattern that develops between which is not a simple blend or morph between these extremes.
A surface exposed to a gradient voiding pattern which shifts from orthagonal to hexagonal in organization and loaded in tension. Left: von Mises stress plot. Right: optimized structure. Note transitional pattern.
Variation of optimized structure of a dome with a distributed vertical load as aperature size varies.
A 3-dimensional elaboration of the first experiment: exposing a structure to a gradient environment from cantilever to catenary condition. A structure supported by piles which wrap around its length,such that it cantilevers at one end and is vertically supported at the other. The structure is optimized to minimize volume based on maximum allowable stress. Blue piles may be removed from the optimized structure. The result is not a gradient pattern of pilings from the cantilevering to the vertically supported end. Gradient environmental conditions thus do not result in gradient (ie smoothly morphing) structures.