The Meshless Element Free Galerkin Method for Buckling Analysis of Simply Supported Laminate Composite Plates

Pekbey, Yeliz; Malekı, Farshıd Khosravı; Yıldız, Hasan; Hesar, Goudarz Ghanizadeh

doi:10.1177/096369351202100602

Cited by 5 publications

(1 citation statement)

References 23 publications

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“…A straightforward solution is the use of micromodels in which the resolution is refined until the model can explicitly resolve all important microstructural details. This solution strategy has been utilised to model microstructurally heterogeneous materials such as composites using numerical techniques such as the Finite-Element method [1][2][3][4], Finite-Difference Method [5][6][7][8], and meshless methods such as the Element-free Galerkin method [9][10][11][12] to name just a few. This method of enriching the model suffers from several drawbacks amongst which include the fact that the microstructural details that plays important role in the response of the material may exist over wide orders of magnitude and explicit resolution of the microstructure for some applications may require computational resources that is prohibitively expensive.…”

Section: Introductionmentioning

confidence: 99%

A computational homogenization framework for non-ordinary state-based peridynamics

Galadima

Xia

Öterkuş

et al. 2022

Engineering with Computers

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Peridynamic theory has been shown to possess the capabilities of describing phenomena that theories based on partial differential equations are not capable of describing. These phenomena include nonlocal interactions and presence of singularities in system responses. To exploit the capabilities offered by peridynamics in the homogenization of heterogenous media, a nonlocal computational homogenization theory based on peridynamic correspondence model (non-ordinary state-based peridynamics) is proposed. To set the development of the theory on a rigorous mathematical framework and to ensure consistency with the nonlocal nature of the peridynamic theory, a nonlocal vector calculus was used in the analysis of the nonlocal homogenization theory. The proposed theory is a two-scale micro–macro-homogenization strategy in which the constitutive relation at the macroscale is derived from explicit solution of a nonlocal volume constraint problem at the microscale. To justify the coupling between the two scales, nonlocal analogues of the stress and strain average theorems as well as the Hill–Mandel macrohomogeneity condition were derived. Validation of the proposed theory is achieved via numerical solution of Representative Volume Elements (RVE) from composite materials and comparing the results with those obtained by means of established methodologies.

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