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Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

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International Applied Mechanics Aims and scope

Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff–Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress–strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)

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Authors and Affiliations

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

    V. A. Maksimyuk, E. A. Storozhuk & I. S. Chernyshenko

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  1. V. A. Maksimyuk
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  2. E. A. Storozhuk
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  3. I. S. Chernyshenko
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Correspondence to V. A. Maksimyuk.

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Translated from Prikladnaya Mekhanika, Vol. 48, No. 6, pp. 3–80, November–December 2012.

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Maksimyuk, V.A., Storozhuk, E.A. & Chernyshenko, I.S. Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review). Int Appl Mech 48, 613–687 (2012). https://doi.org/10.1007/s10778-012-0544-8

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