Simulation of CNT Composites using Fast Multipole BEM

Yao, Z. H.; Xu, Jun-Dong; Wang, H. T.

doi:10.1007/978-3-540-75999-7_158

Cited by 5 publications

(5 citation statements)

References 3 publications

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“…In addition, the IIMLS method was also performed in the The proposed method can be extended to other problems and 3D problems. Coupling the presented method with the fast multipole method [37][38][39] for large-scale computations is under research. It is also possible to solve problems with body force by coupling the presented method with methods for domain integrals [40][41][42] in the BEM.…”

Section: Discussionmentioning

confidence: 99%

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

Yang

Chen

2017

Mathematical Problems in Engineering

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The presented study proposed an improved interpolating boundary node method (IIBNM) for 2D potential problems. The improved interpolating moving least-square (IIMLS) method was applied to construct the shape functions, of which the delta function properties and boundary conditions were directly implemented. In addition, any weight function used in the moving least-square (MLS) method was also applicable in the IIMLS method. Boundary cells were required in the computation of the boundary integrals, and additional discretization error was not avoided if traditional cells were used to approximate the geometry. The present study applied the parametric cells created in the parameter space to preserve the exact geometry, and the geometry was maintained due to the number of cells. Only the number of nodes on the boundary was required as additional information for boundary node construction. Most importantly, the IIMLS method can be applied in the parameter space to construct shape functions without the requirement of additional computations for the curve length.

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Section: Discussionmentioning

confidence: 99%

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

Yang

Chen

2017

Mathematical Problems in Engineering

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“…The well-known numerical solution of integral equations is by the BEM and by its more effective form, FMBEM [4,[7][8][9][10][11]. However, no one formulation was used for composites reinforced by fibres with large aspect ratio and authors of this paper do not know any publications to problems like those shown below.…”

Section: Methods Of Continuous Source Functions For Simulation Of Fibresmentioning

confidence: 99%

“…The FMBEM is the only numerical method which enables solving representative volume element (RVE) of the matrix containing two to five thousand short fibres (three to eleven million degrees of freedom (d.o.f.)). The problems have been solved on a supercomputers, or on clusters of PCs [9][10][11]. If a matrix reinforced by carbon nanotubes (CNTs) having 1% volume of CNTs 1 mm long and 20 nm diameter will contain 3.2 × 10 7 tubes and the CNTs can have general form (curvature and orientation) and can be randomly distributed, then the control volume element (CVE) for homogenisation would contain several millions of CNTs for correct assessment of homogenized properties of the composite.…”

Section: Introductionmentioning

confidence: 99%

Thermal Properties of Short Fibre Composites Modeled by Meshless Method

Kompiš

Murčínková

2014

Advances in Materials Science and Engineering

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Computational model using continuous source functions along the fibre axis is presented for simulation of temperature/heat flux in composites reinforced by short fibres with large aspect ratio. The aspect ratio of short fibres reinforcing composite material is often as large as 103 : 1–106 : 1, or even larger. 1D continuous source functions enable simulating the interaction of each fibre with the matrix and also with other fibres. The developed method of continuous source functions is a boundary meshless method reducing the problem considerably comparing to other methods like FEM, BEM, meshless methods, or fast multipole BEM formulation.

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“…The effective nonlinear stress-strain relation was obtained. Yao et al [16] analysed an effect of non-ideal interfacial conditions or additional interfacial layer between deformable fibres and the matrix of carbon nanotube composites on effective Young's modulus using the FMBEM.…”

Section: Introductionmentioning

confidence: 99%

Effective elastic properties of composites with randomly distributed thin rigid fibres

Fedeliński

2020

Arch Appl Mech

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The aim of the work is to analyse the effective elastic properties of composites with randomly distributed thin rigid fibres. The matrix is linear-elastic, homogenous and isotropic, and the fibres are perfectly connected to the matrix. Two-dimensional models of composites are analysed using the boundary element method (BEM). The method requires division of fibres and external boundaries of the plate into boundary elements. The boundary quantities are interpolated using quadratic shape functions. The direct solutions are: displacements and tractions along the external boundaries, displacements of fibres and interaction forces between the fibres and the matrix. Three numerical examples are presented in the paper: a single fibre in a circular disc, uniformly distributed parallel fibres and randomly distributed and oriented fibres in a square plate. The influence of distribution and orientation of fibres on effective Young’s moduli, Poisson’s ratios and Kirchhoff’s moduli is analysed. The examples demonstrate the accuracy and efficiency of the method.

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Simulation of CNT Composites using Fast Multipole BEM

Cited by 5 publications

References 3 publications

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

Thermal Properties of Short Fibre Composites Modeled by Meshless Method

Effective elastic properties of composites with randomly distributed thin rigid fibres

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