Shown here are several experiments conducted with a structural optimization software program (topological optimization based on finite element analysis). In each test case, the locaton of restraints, the magnitude, location and direction of loads, and material properties are specified. A an optimized structure (of minimum volume) is computed, given maximum von Mises stress. I was interested in creating a gradient environment and then observing how optimal structure evolves along this gradient as a critique of operations of morphing or blending, which I would argue offer an impoverished understanding of transitional mechanisms within complex systems. Above is an environmental gradient from a paradigmatic cantilever condition to catenary condition: from exposure to entirely lateral loads to vertical loads. Note that the optimized structure which develops as one moves between these two paradigmatic conditions is not a simple morphing of extreme shapes, but that there are unexpected jumps or shifts in morphology as one moves across this gradient.
Above (top row): a gradient between an ideal case of exposure to tensile force and to twisting. Bottom row: from lateral force to twisting.
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.
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