Stability optimization for a simultaneously twisted and compressed rod

What is it about?

We present the compressed and twisted rod of the minimal mass and maximal buckling resistance. The optimal shape of the rod is roughly parabolic along its length. The optimal shape of cross-section, which leads to the maximal buckling attempt among the rods of the equal mass, is the equilateral triangle. Curiously, that the common rods with the circular cross-section present the worst case, namely the minimal buckling resistance.

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