Sensitivity analysis and optimal redesign of columns in the state of initial distortions and prestress

The problem of the optimal distribution of the reinforcing material added to an existing column with the aim to increase its buckling load is considered in the paper. It is assumed that the stress-strain relation is nonlinear elastic. The authors employ the variational formulation to derive the sensitivity gradients with respect to variable reinforcement distribution, prestress and initial distortions. The formulation of optimal redesign allows for uni- and bimodal buckling. Numerical examples for various geometrical constraints illustrate the theory.