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Prediction and control of buckling: the inverse bifurcation problems for von Karman equations. (English) Zbl 1425.74197
Dutta, Hemen (ed.) et al., Applied mathematical analysis: theory, methods, and applications. Cham: Springer. Stud. Syst. Decis. Control 177, 353-381 (2020).
Summary: 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.
For the entire collection see [Zbl 1417.00004].
74G60 Bifurcation and buckling
37N35 Dynamical systems in control
35Q74 PDEs in connection with mechanics of deformable solids
Full Text: DOI
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