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Asymptotic Justification of Equations for von Kármán Membrane Shells

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Abstract

The objective of this work is to study the asymptotic justification of the two- dimensional equations for membrane shells with boundary conditions of von Kármán’s type. More precisely, we consider a three-dimensional model for a nonlinearly elastic membrane shell of Saint Venant–Kirchhoff material, where only a portion of the lateral face is subjected to boundary conditions of von Kármán’s type. Using technics from formal asymptotic analysis with the thickness of the shell as a small parameter, we show that the scaled three-dimensional solution still leads to the so-called two-dimensional equations of von Kármán membrane shell.

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  1. Laboratoire de Mathématiques Appliquées, Université Kasdi Merbah, B. P. 511, Ouargla, 30000, Algérie

    M. Legougui & A. Ghezal

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  1. M. Legougui
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  2. A. Ghezal
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Correspondence to A. Ghezal.

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Legougui, M., Ghezal, A. Asymptotic Justification of Equations for von Kármán Membrane Shells. Math Notes 114, 536–552 (2023). https://doi.org/10.1134/S0001434623090237

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