I need guidance on the analytical model and calculation for shape (cross-section) optimization of Euler Bernoulli cantilever column under buckling with a point load. It may be using variational methods, with the use of Rayleigh Quotient.

For it, I found a similar case in "Haftka, Raphael & Gurdal, Zafer & Kamat, Manohar. Elements of structural optimization. 2nd revised ed." but with different boundary conditions, I have attached the scans of the procedure used in the text for reference.

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