Numerical analysis for multi-group neutron-diffusion equation using Radial Point Interpolation Method (RPIM)

Kim, Kyung-O; Jeong, Hae Sun; Jo, Daeseong

doi:10.1016/j.anucene.2016.08.021

Cited by 8 publications

(2 citation statements)

References 10 publications

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“…The RPIM is a more complex version of the Point Interpolation Method (PIM) (Liu and Gu, 2001), using both the polynomial basis function (as the PIM) and an additional RBF, allowing the construction of stable and more robust interpolation shape functions. This meshless method has been used in many fields of application such as inelastic analysis of 2D solids (Dai et al ., 2006), 3D contact problems (Qian et al ., 2014), crack growth modelling in elastic solids (Nguyen et al ., 2014), homogenization techniques (Rodrigues et al ., 2018b), non-local constitutive damage models (Farahani et al ., 2016), the analysis for multi-group neutron-diffusion equation (Kim et al ., 2017) or the static (Belinha et al ., 2016; Belinha et al ., 2013) and dynamic (Phan-Dao, 2016; Pilafkan et al ., 2013; Phan-Dao et al ., 2016) analysis of composite plates and shells.…”

Section: Meshless Methodsmentioning

confidence: 99%

Numerical simulation of the extrusion process of viscoplastic materials using a radial point interpolation method

Rodrigues,

Belinha,

Natal Jorge

2023

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PurposeFused Filament Fabrication (FFF) is an extrusion-based manufacturing process using fused thermoplastics. Despite its low cost, the FFF is not extensively used in high-value industrial sectors mainly due to parts' anisotropy (related to the deposition strategy) and residual stresses (caused by successive heating cycles). Thus, this study aims to investigate the process improvement and the optimization of the printed parts.Design/methodology/approachIn this work, a meshless technique – the Radial Point Interpolation Method (RPIM) – is used to numerically simulate the viscoplastic extrusion process – the initial phase of the FFF. Unlike the FEM, in meshless methods, there is no pre-established relationship between the nodes so the nodal mesh will not face mesh distortions and the discretization can easily be modified by adding or removing nodes from the initial nodal mesh. The accuracy of the obtained results highlights the importance of using meshless techniques in this field.FindingsMeshless methods show particular relevance in this topic since the nodes can be distributed to match the layer-by-layer growing condition of the printing process.Originality/valueUsing the flow formulation combined with the heat transfer formulation presented here for the first time within an in-house RPIM code, an algorithm is proposed, implemented and validated for benchmark examples.

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Section: Meshless Methodsmentioning

confidence: 99%

Numerical simulation of the extrusion process of viscoplastic materials using a radial point interpolation method

Rodrigues,

Belinha,

Natal Jorge

2023

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“…Additionally, the shape functions have virtually a higher order, allowing a higher continuity and reproducibility. 12 Recently developed meshless methods showed a wide range of applications, such as the analysis of dental implants, 13 crack path prediction, 14 bone remodelling, 12 elasto-plastic analyses, 15 inelastic analysis of 2D solids, 16 3D contact problems, 17 crack growth modelling in elastic solids, 18 non-local constitutive damage models, 19 the analysis for multi-group neutron-diffusion equation, 20 the static 21,22 and dynamic [23][24][25] analysis of composite plates and shells or the analysis of a composite representative volume element model. 26 In this work, meshless methods are used to construct an elasto-plastic algorithm to simulate the non-linear material behaviour of thermoplastics used in the FDM/FFF process.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of compression and tensile tests on thermoplastics: A meshless approach

Rodrigues

Belinha

Jorge

et al. 2018

Proceedings of the IMechE

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Thermoplastics, such as the polypropylene, often have different behaviours when subjected to traction or compression loads. Thermoplastics are also used in additive manufacturing processes, such as the fused filament fabrication, allowing to build complex structures possessing structural elements with an intricate internal architecture (foams and functionally graded material deposition). Thus, yield criterions have to be appropriately chosen in order to capture the homogenised material non-linear behaviour. In this work, polypropylene regular specimens are discretised and analysed assuming traction and compression tests. The non-linear elastoplastic analyses are performed considering three distinct discrete numerical approaches. Thus, the stress-strain curves obtained using two different meshless methods and the finite element method are compared with experimental data. In the end, a comparative study is performed between the results obtained using meshless methods and the finite element method, and the accuracy of the meshless methods is demonstrated.

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A mesh-free treatment for even parity neutron transport equation

Alizadeh

Abbasi

Minuchehr

et al. 2021

Annals of Nuclear Energy

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Numerical analysis for multi-group neutron-diffusion equation using Radial Point Interpolation Method (RPIM)

Cited by 8 publications

References 10 publications

Numerical simulation of the extrusion process of viscoplastic materials using a radial point interpolation method

Numerical simulation of the extrusion process of viscoplastic materials using a radial point interpolation method

Numerical simulation of compression and tensile tests on thermoplastics: A meshless approach

A mesh-free treatment for even parity neutron transport equation

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