Theory of the multilayer thin anisotropic shells, based on the asymptotic analysis of the general equations for the elasticity theory

Dimitrienko, Yu. I.; Губарева, Е. А.; Pichugina, Anna E.

doi:10.1088/1742-6596/1141/1/012097

Cited by 2 publications

(2 citation statements)

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“…To solve the problems of macroscopic deformation of structural elements made of composites with small deformations, it is necessary to apply constitutive relations for composites, taking into account anisotropy. The direct use of the asymptotic averaging method for constructing constitutive relations is possible and was done in [13], the method is based on solving special problems of microscopic deformation on periodicity cells (PC). Calculations of macroscopic deformation, for example, by the finite element method, when at each node of the grid it is necessary to solve the problem on a periodicity cell, lead to very large amounts of calculations.…”

Section: Introductionmentioning

confidence: 99%

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Modeling of effective elastic-plastic properties of layered composites with a periodic structure in the framework of the anisotropic flow theory

Dimitrienko

Губарева²,

Cherkasova³

2023

E3S Web of Conf.

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The article is devoted to the development of a method for constructing theoretical strain diagrams. The method is based on the use of a model of effective constitutive relations for approximating the deformation diagrams of layered composites obtained using the asymptotic averaging method. To find the elastic constants of the model of a transversally isotropic composite, the method of minimizing the deviation of the approximation deformation diagrams from the diagrams obtained by the asymptotic homogenization (AH) method is used for a series of standard problems of deformation at small deformations. Minimization problems were solved using the Hooke-Jeeves method. The results of numerical simulation by the proposed method for layered composites are presented, which showed good approximation accuracy, which is achieved due to the proposed method for separating the coupled problems of micro- and macroscopic deformation.

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Section: Introductionmentioning

confidence: 99%

“…obtained by direct numerical solution of the problem in PC for some standard problems of macroscopic deformation, in which a homogeneous stress-strain state with ij and ij independent of coordinates is realized. A numerical method for solving a local problem in PL for a linearly elastic layered composite was implemented in [13].…”

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confidence: 99%