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Paper's Title:

On the Optimal Buckling Loads of Clamped Columns


Samir Karaa

Department of Mathematics and Statistics
Sultan Qaboos University, P.O. Box 36, Alkhod 123
Muscat, Sultanate of Oman



We consider the problem of determining the optimal shape of a clamped column of given length and volume, without minimum cross section constraints. We prove that the necessary condition of optimality derived by Olhoff and Rasmussen is sufficient when 0<α<1. The number alpha appears in Equation 2.1. For the case α =1 it is shown that the value 48 is optimal. We also determine the exact values of the optimal shape at the extremities, and take advantage of a robust nonlinear ordinary differential equation solver COLSYS to compute the optimal buckling load with a high accuracy.

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