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Multiscale computational homogenization of heterogeneous shells at small strains with extensions to finite displacements and buckling
Author(s) -
Cong Yu,
Nezamabadi Saeid,
Zahrouni Hamid,
Yvonnet Julien
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4927
Subject(s) - homogenization (climate) , buckling , boundary value problem , finite element method , shell (structure) , geometry , context (archaeology) , structural engineering , mathematics , computer science , mechanics , materials science , mathematical analysis , physics , geology , composite material , engineering , biodiversity , ecology , paleontology , biology
Summary In this paper, a framework for computational homogenization of shell structures is proposed in the context of small‐strain elastostatics, with extensions to large displacements and large rotations. At the macroscopic scale, heterogeneous thin structures are modeled using a homogenized shell model, based on a versatile three‐dimensional seven‐parameter shell formulation, incorporating a through‐thickness and pre‐integrated constitutive relationship. In the context of small strains, we show that the local solution on the elementary cell can be decomposed into six strains and six‐strain gradient modes, associated with corresponding boundary conditions. The heterogeneities can have arbitrary morphology but are assumed to be periodically distributed in the tangential direction of the shell. We then propose an extension of the small‐strain framework to geometrical nonlinearities. The procedure is purely sequential and does not involve coupling between scales. The homogenization method is validated and illustrated through examples involving large displacements and buckling of heterogeneous plates and shells. Copyright © 2015 John Wiley & Sons, Ltd.