A NEW CONCEPT OF OPTIMIZATION FOR POSTBUCKLING BEHAVIOUR

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.     

OPTIMIZATION OF GEOMETRICALLY NONLINEAR STUCTURES 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 iose 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.