Optimization of geometrically nonlinear structures with respect to both buckling and postbuckling constraints

In this paper the optimization of structures against instability is carried out, and nonlinear behaviour of designed elements is taken into account. The form of the deformation path for an optimal element is analysed to check whether that behaviour is stable or not. In the latter case the formulation of the design problem is modified with a view to include constraints that take care of a stable form of the postbuckling path of the structure. A suitable form of the postbuckling constraints is proposed depending on the type of instability. If bifurcation occurs the constraints will force the structure to behave in a stable way after buckling. When a limit point is reached without bifurcation of the equilibrium the formulation is modified in such a way that the resulting structure does not lose its stability at all. For structures for which design can modify postbuckling behaviour without affecting buckling load, the postbuckling constraints are chosen so as to ensure stable behaviour of the structures after buckling. When the critical state does not exist and instability occurs at finite displacements the minimum load value of the deformation path is maximized.