The application of mesh-free method in the numerical simulation of beams with the size effect
type: Item
instance of: scholarly article
title: The application of mesh-free method in the numerical simulation of beams with the size effect
zbMATH Open document ID: 1407.74056
DOI: 10.1155/2014/590271
author: Yuan Tian
author: Caili Zhang
author: Yuzhou Sun
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The mesh-free method is employed to implement the numerical simulation of the bending behavior of beams with the size effect. On the basis of the classical Bernoulli-Euler beam theory, two higher-order strain components are involved in the beam model. The intrinsic bulk length and the directional surface length components are introduced into the constitutive relationship to describe the size effect, and the variation of the total potential is provided. The moving-least square approximation is used to construct the shape function and its second- and third-order derivatives, and the choice of the scaling factor is discussed in detail. A mesh-free scheme is built to implement numerical simulation, in which the higher-order strains are directly approximated with the nodal components due to the higher-order continuity of the shape function. The convergence of method is illustrated in virtue of an example of the simply supported beam, and the effect of the intrinsic bulk length and the directional surface length components are studied.
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74H15
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 7016798
Wikidata QID: Q59066298
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/590271
OpenAlex ID: W2130899622
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description: scientific article; zbMATH DE number 7016798