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Nonlinear Deformation of Discretely Inhomogeneous Shallow Shells Based on the Generalized Method of Finite Integral Transforms*

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A numerical analytical approach to the study of the nonlinear deformation of shallow shells under subcritical loads is proposed. The approach rationally combines the generalized method of finite integral transforms and the Newton–Kantorovich–Raphson linearization method. The static stiffness and load–deflection relationship of flexible shallow shells with various boundary conditions in a wide range of changes in their Gaussian curvature and the presence of discrete inclusions are analyzed. It is shown that the dependence of the upper critical values of external pressure on the location of discrete inclusions is nonmonotonic, which makes it possible to determine their optimal location in terms of the static stability and bearing capacity of the shells.

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St, Kyiv, 03057, Ukraine

    O. I. Bespalova

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  1. O. I. Bespalova
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Correspondence to O. I. Bespalova.

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Translated from Prykladna Mekhanika, Vol. 58, No. 5, pp. 81–96, September–October 2022

This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).

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Bespalova, O.I. Nonlinear Deformation of Discretely Inhomogeneous Shallow Shells Based on the Generalized Method of Finite Integral Transforms*. Int Appl Mech 58, 569–582 (2022). https://doi.org/10.1007/s10778-023-01181-6

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