Prediction and Control of Buckling: The Inverse Bifurcation Problems for von Karman Equations

Ch. 11. P. 353–381.

Obodan N., Adlucky V., Gromov V.

The chapter presents novel approaches to predict and control buckling of thin-walled structures; mathematically, these approaches are formalized as the first and second inverse bifurcation problems for von Karman equations. Both approaches are based upon the method employed to solve the direct bifurcation problem for the equations in question. The approach considered was applied to several difficult problems of actual practice, viz., for the first inverse problem, to the problems of optimal thickness distribution and optimal external pressure distribution for a cylindrical shell, optimal curvature for a cylindrical panel as well; for the second inverse problem, to the problem to predict buckling of a cylindrical shell under an external pressure.

Keywords: identification of parameters, Buckling of thin-walled structures, Non-linear boundary problem for von Karman equations, The inverse bifurcation problem, Identification of pre-bifurcation state, Control of bifurcations, Early-warning signs

In book

Applied Mathematical Analysis: Theory, Methods, and Applications

Springer, 2020.