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A model of layered prismatic shells

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Abstract

The present paper is devoted to a model for elastic layered prismatic shells which is constructed by means of a suggested in the paper approach which essentially differs from the known approaches for constructing models of laminated structures. Using Vekua’s dimension reduction method after appropriate modifications, hierarchical models for elastic layered prismatic shells are constructed. We get coupled governing systems for the whole structure in the projection of the structure. The advantage of this model consists in the fact that we solve boundary value problems separately for each ply. In addition, beginning with the second ply, we use a solution of a boundary value problem of the preceding ply. We indicate ways of investigating boundary value problems for the governing systems. For the sake of simplicity, we consider the case of two plies, in the zeroth approximation. However, we also make remarks concerning the cases when either the number of plies is more than two or higher-order approximations (hierarchical models) should be applied. As an example, we consider a special case of deformation and solve the corresponding boundary value problem in the explicit form.

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Authors and Affiliations

  1. Faculty of Exact and Natural Sciences, I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    George Jaiani

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  1. George Jaiani
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Correspondence to George Jaiani.

Additional information

Communicated by Andreas Öchsner.

The paper was supported by the Shota Rustaveli National Science Foundation (SRNSF) Grant # 30/28.

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Jaiani, G. A model of layered prismatic shells. Continuum Mech. Thermodyn. 28, 765–784 (2016). https://doi.org/10.1007/s00161-015-0414-9

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  • DOI: https://doi.org/10.1007/s00161-015-0414-9

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