Keywords: Fibonacci spiral, stiffening ribs, thin-walled structure, phyllotaxis, structure design, bucking.

For a long period, phyllotaxis (the arrangement of leaves on a plant stem) has been observed as an interesting morphological property of various plants, and the phyllotactic spirals form a distinctive class of patterns in nature. These days, the unique patterns governed by the Fibonacci sequence, or the golden ratio in a deeper sense, have moved beyond the botanical system and came to be universal, occurring in architectural and structural design. In this work, we develop a design approach for curvilinear stiffening ribs which follow the Fibonacci spiral pattern. The parametric model of the designed ribs is built according to two parameters, one discrete and another continuous. Parametric studies on the two variables are performed to assess the potential mechanical advantages of the Fibonacci spiral pattern in stiffening structures. The deformation-, vibration- and buckling-resisting capacities are investigated for thin-walled stiffening plates with a central cut-out. Moreover, an attempt is devoted to clarifying the rationality of curvilinear employment in other designs. Lastly, we demonstrate that the developed protocol does not limit itself to planar structures with cut-outs, and it is easy to be extended to stiffening ribs on curved surfaces, where the gain in mechanical property is observed to be even more visible and pronounced.

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