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In this paper geometrically nonlinear structures are optimized against instability. The postbuckling analysis performed for structures optimally designed for only buckling constraints shows that in many cases their behaviour after buckling is unstable. That is a weakness of the design and therefore, the alternative design philosophy is proposed, in which the postbuckling analysis is implemented directly into the formulation of optimization problem. As the result the modified optimal structure is created, for which previously unstable behaviour becomes stable. The effect of modification of postbuckling behaviour in most of the known cases has been obtained by changing sizing variables. In this paper a new approach is proposed, namely stabilization of the postbuckling path is obtained by application of additional forces acting on the optimized element. Numerical results are presented for the design of finite-degree-of-freedom systems that model the behaviour of real elastic frame and shell structures.

In this paper, the optimization problem of helical springs against instability is considered. An initial distribution of helix angle and radius of a spring is sought which ensures maximal value of the critical axial compressive force under equality and inequality constraints. As the equality constraints a volume of a spring material, an initial compression rigidity and also a volume taken up by a spring are considered. The inequality constraints are connected with: a strength condition, a condition of closing up of neighbouring coils, geometrical conditions in initial and compressed state (7 inequality constraints).Variational optimization using the Pontriagin maximum principle is considered. It turned out that the main profit of optimization is connected with the optimal distribution of a helix angle. The influence of the optimal variable radius on the critical axial force is much lower: the profit reaches here a few per cent only whereas that obtained by optimization of the helix angle can be even over 100%.