Abstract
In this section we shall use the results presented so far to formulate several variational principles for t he equations describing deformations and the optimal shape of elastic columns. We shall use the classical (Bernoulli-Euler) rod theory as well as generalized rod theories. The variational principles that we will formulate will be used to (a) estimate the critical (buckling) load of a column, (b) determine post critical shape of the column using Ritz method, (c) determine the optimal shape of the column, that is, the shape of the column having smallest volume and being stable against buckling. This constitutes the so-called Lagrange problem formulated in 1773 (see [31], [100]).
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