On the Bifurcation and Initial Post-buckling Behaviour of Structures with Bimodal Optimum Buckling Loads




<正> The formulation of structural buckling eigenvalue optimization problems allowing for bimodal optimum solutions is considered in terms of elastic columns resting on an elastic foundation of given stiffness modulus. It is first shown that bimodal optimum solutions can be obtained for columns with clamped-clamped and clamped-simply supported boundary conditions. Then the equilibrium equation for a non-extensible, geometrically nonlinear elastic columns is derived, and the initial post-buckling behaviour of a bimodal optimum column near the bifurcation point is studied using a perturbation method. It is shown that there may be up to four post-buckling paths emanating from the trivial equilibrium state. Each of these paths may be either supercritical or subcriticai. The conditions for stability of these post-buckling paths are established. In the end of the paper, numerical results for the post-buckling behaviour of columns with bimodal optimum buckling eigenvalues are presented and discussed.


bifurcation, initial post-buckling, post-buckling paths, stability, bimodal optimum buckling loads, bimodal structural eigenvalues, optimum structural design


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