Multiscale eigenelement method for periodical composites: A review

Xing, Yufeng; Gao, Yahe

doi:10.1016/j.cja.2018.07.003

Cited by 6 publications

(2 citation statements)

References 35 publications

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“…In recent decades, many multiscale homogenization methods have been proposed to deal with composite structures, such as the two-scale asymptotic homogenization method (AHM) [1][2][3], the multiscale eigenelement method (MEM) [4][5][6], the heterogeneous multiscale method (HMM) [7,8], the variational asymptotic method (VAM) [9,10], and for many other multiscale homogenization methods referred to [11,12] and the references cited therein. Among the above numerical homogenization methods [1][2][3][4][5][6][7][8][9][10], the AHM [1][2][3] is one of the most representative ones with a rigorous mathematical foundation and has been widely used in the homogenization analysis of periodic composite structures for statics [13][14][15][16][17][18] and dynamics [19][20][21][22]. However, the AHM [1][2][3][13][14][15][16][17][18][19]…”

Section: Introductionmentioning

confidence: 99%

Two-Scale Asymptotic Homogenization Method for Composite Kirchhoff Plates with in-Plane Periodicity

2022

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This paper develops a two-scale asymptotic homogenization method for periodic composite Kirchhoff plates. In this method, a three-dimensional (3D) periodic plate problem is simplified as a Kirchhoff plate problem, which is governed by a fourth-order uniformly elliptic partial differential equation (PDE) with periodically oscillating coefficients. Then, a two-scale solution in an asymptotic expansion form is presented for the PDE, and it is found that the first-order perturbed displacement in the asymptotic solution is zero. Additionally, periodic boundary and normalization constraint conditions are proposed to determine the unique solution to unit cell problems. Moreover, standard finite element formulations for calculating the perturbed displacements are derived from the principle of virtual work. Physical interpretations of the influence functions are presented by analyzing the properties of self-balanced quasi-load vectors used for solving the influence functions. Numerical comparisons show that the present method is physically acceptable and highly accurate.

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Section: Introductionmentioning

confidence: 99%

Two-Scale Asymptotic Homogenization Method for Composite Kirchhoff Plates with in-Plane Periodicity

2022

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“…3D textile composites possessed the periodic microstructure, and the macroscopic mechanical properties of composites were affected by geometric factors such as fiber volume fraction, shape, and distribution of composites. 20 The representative volume method and the asymptotic homogenization method were two numerical methods for predicting the equivalent mechanical properties of periodic materials. 21 Therefore, scholars at home and abroad have done a lot of research on the models.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the classification and properties of three-dimensional textile fabrics

Zhang

Zhu

2019

Journal of Engineered Fibers and Fabrics

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Three-dimensional textile fabrics are used as the reinforcing phase of the textile structural composites, and their geometry affect the physical and mechanical properties of composites. Based on the curvature and directions of the fiber tows in three-dimensional textile fabrics, four representative geometric units are proposed, namely, the orthogonal geometric unit, the curved geometric unit, the skew geometric unit, and the uniform distribution unit, respectively. Other units are the combinations or derivations of these representative geometric units. The relationship and performance characteristics of these representative geometric units are discussed in section “The relationship of RGUs.” The structural features of three-dimensional textile fabrics are illustrated on the mesoscopic scale, and the models are established to predict the geometric properties. The concepts of fabrics with stable structure, flexible structure, elastoplastic structure, and uniform structure are proposed. The fiber volume fractions and elastic characteristics of different structural fabrics are discussed. The classification of three-dimensional textile fabrics is conducive to investigate the relationship between geometry and property, forming a technical system and providing a theoretical basis for the selection of three-dimensional structural textile composites with different performance.

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A novel stiffness prediction method with constructed microscopic displacement field for periodic beam-like structures

Gao

Huang

et al. 2022

Acta Mech. Sin.

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Multiscale eigenelement method for periodical composites: A review

Cited by 6 publications

References 35 publications

Two-Scale Asymptotic Homogenization Method for Composite Kirchhoff Plates with in-Plane Periodicity

Two-Scale Asymptotic Homogenization Method for Composite Kirchhoff Plates with in-Plane Periodicity

Investigation of the classification and properties of three-dimensional textile fabrics

A novel stiffness prediction method with constructed microscopic displacement field for periodic beam-like structures

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