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On the Homogenization of Nonlinear Shell

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Recent Developments in the Theory of Shells

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 110))

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Abstract

In this paper we propose a multiscale finite-strain shell theory for simulating the mechanical response of highly heterogeneous shell with varying thickness. To resolve this issue a higher-order stress-resultant shell formulation based on multiscale homogenization is considered. At the macroscopic scale level, we approximate the displacement field by a fifth-order Taylor-Young expansion in thickness. We take account of the microscale fluctuations by introducing a boundary value problem over the domain of a three-dimensional representative volume element (RVE). The geometrical form and the dimensions of the RVE are determined by the representative microstructure of the heterogeneity. In this way, an in-plane homogenization is directly combined with a through thickness stress integration. As a result the macroscopic stress resultants are the volume averages through RVE of microscopic stress. All microstructural constituents are modeled as first-order continua and three-dimensional continuum, described by the standard equilibrium and the constitutive equations. This type of theory is anxiously awaited.

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Authors and Affiliations

  1. Department of Mathematic, University of Lille, 59655, Villeneuve d’Ascq Cedex, France

    Erick Pruchnicki

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  1. Erick Pruchnicki
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Correspondence to Erick Pruchnicki .

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Editors and Affiliations

  1. Faculty of Mechanical Engineering, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Jacek Chróścielewski

  3. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Victor A. Eremeyev

  4. Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

    Krzysztof Wiśniewski

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Pruchnicki, E. (2019). On the Homogenization of Nonlinear Shell. In: Altenbach, H., Chróścielewski, J., Eremeyev, V., Wiśniewski, K. (eds) Recent Developments in the Theory of Shells . Advanced Structured Materials, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-030-17747-8_27

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