OPTIMAL SHAPE AND NON-HOMOGENEITY OF A NONUNIFORMLY COMPRESSED COLUMN

The best possible distribution of Young's modulus and/or the cross-sectional area is found for a column which, for a given volume and length, carries the maximum possible axial loads which are non-uniformly distributed along its length and concentrated at the end-points. The column is elastically clamped at one end and free at the other, where the concentrated axial load is applied. The design variables are subject to upper and lower bounds. Sufficient optimality conditions are derived for a given function to be a solution of the optimization problem. The procedure to determine the optimal solutions is described. Numerical results are obtained by employing an iterative computational technique. © 1979.