The Australian Journal of Mathematical Analysis and Applications


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ISSN 1449-5910  

 

Paper Information

Paper Title:

On the Optimal Buckling Loads of Clamped Columns

Author(s):

Samir Karaa

Department of Mathematics and Statistics
Sultan Qaboos University, P.O. Box 36, Alkhod 123
Muscat, Sultanate of Oman
skaraa@squ.edu.om

URL: http://ajmaa.org/EditorsU/SKaraa.php


Abstract:

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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