The present investigation presents an efficient meshless method based on the weak form of an element-free-Galerkin method. The formulation of the numerical solution was conducted using an artificial neural network (ANN) approach to compute the optimal number of nodes in the influence domain for each point of interest. The numerical results using the ANN model were tested and compared with different approaches in the literature. Results show a reduction in the computational cost and an enhancement in an error criterion of up to 11%.
Revised:
Accepted:
Published online:
Imane Hajjout 1; Manal Haddouch 1; El Mostapha Boudi 1
CC-BY 4.0
@article{CRMECA_2020__348_1_63_0,
author = {Imane Hajjout and Manal Haddouch and El Mostapha Boudi},
title = {Optimal influence cover for an element free {Galerkin} {MFree} method based on artificial neural network},
journal = {Comptes Rendus. M\'ecanique},
pages = {63--76},
publisher = {Acad\'emie des sciences, Paris},
volume = {348},
number = {1},
year = {2020},
doi = {10.5802/crmeca.5},
language = {en},
}
TY - JOUR AU - Imane Hajjout AU - Manal Haddouch AU - El Mostapha Boudi TI - Optimal influence cover for an element free Galerkin MFree method based on artificial neural network JO - Comptes Rendus. Mécanique PY - 2020 SP - 63 EP - 76 VL - 348 IS - 1 PB - Académie des sciences, Paris DO - 10.5802/crmeca.5 LA - en ID - CRMECA_2020__348_1_63_0 ER -
%0 Journal Article %A Imane Hajjout %A Manal Haddouch %A El Mostapha Boudi %T Optimal influence cover for an element free Galerkin MFree method based on artificial neural network %J Comptes Rendus. Mécanique %D 2020 %P 63-76 %V 348 %N 1 %I Académie des sciences, Paris %R 10.5802/crmeca.5 %G en %F CRMECA_2020__348_1_63_0
Imane Hajjout; Manal Haddouch; El Mostapha Boudi. Optimal influence cover for an element free Galerkin MFree method based on artificial neural network. Comptes Rendus. Mécanique, Volume 348 (2020) no. 1, pp. 63-76. doi : 10.5802/crmeca.5. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.5/
[1] FVM-BEM method based on the Green’s function theory for the heat transfer problem in buried co-axial exchanger, C. R. Mécanique, Volume 338 (2010) no. 4, pp. 220-229 | DOI | Zbl
[2] (“Structural topology optimisation based on the Boundary Element and Level Set methods”, Thesis, Durham University, May 2014)
[3] SPH modeling of adhesion in fast dynamics: Application to the Cold Spray process, C. R. Méc., Volume 344 (2016) no. 4, pp. 211-224 | DOI
[4] A new implementation of the element free Galerkin method, Comput. Methods Appl. Mech. Eng., Volume 113 (1994) no. 3–4, pp. 397-414 | DOI | MR | Zbl
[5] A numerical approach to the testing of the fission hypothesis, Astron. J., Volume 82 (1977), pp. 1013-1024 | DOI
[6] Generalizing the finite element method: diffuse approximation and diffuse elements, Comput. Mech., Volume 10 (1992) no. 5, pp. 307-318 | DOI | MR | Zbl
[7] Reproducing kernel particle methods, Int. J. Numer. Methods Fluids, Volume 20 (1995) no. 8-9, pp. 1081-1106 | DOI | MR | Zbl
[8] A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG), and Local Boundary Integral Equation (LBIE) methods, Comput. Mech., Volume 24 (1999) no. 5, pp. 348-372 | DOI | Zbl
[9] A local radial point interpolation method (LRPIM) for free vibration analyses of 2-D solids, J. Sound Vib., Volume 246 (2001) no. 1, pp. 29-46 | DOI
[10] A point interpolation method for two-dimensional solids, Int. J. Numer. Methods Eng., Volume 50 (2001) no. 4, pp. 937-951 | DOI | Zbl
[11] Element-free Galerkin methods, Int. J. Numer. Methods Eng., Volume 37 (1994) no. 2, pp. 229-256 | DOI | MR | Zbl
[12] An improved crack analysis technique by element-free Galerkin method with auxiliary supports, Int. J. Numer. Methods Eng., Volume 56 (2003) no. 9, pp. 1291-1314 | DOI | Zbl
[13] A numerical mesh-free model for elasto-plastic contact problems, Eng. Anal. Bound. Elem., Volume 82 (2017), pp. 68-78 | DOI | MR | Zbl
[14] Analysis of meshless weak and strong formulations for boundary value problems, Eng. Anal. Bound. Elem., Volume 80 (2017), pp. 1-17 | DOI | MR | Zbl
[15] Surface generated by moving least squares methods, Math. Comput., Volume 37 (1981) no. 155, pp. 141-158 | DOI | MR | Zbl
[16] An optimal radius of influence domain in element-free Galerkin method, 2018 6th International Renewable and Sustainable Energy Conference (IRSEC) (A. ElHibaoui; M. Essaaidi; Y. Zaz, eds.), IEEE, 345 E 47TH ST, New York, NY 10017 USA, 2018, pp. 911-914
[17] An introduction to programming the meshless element free Galerkin method, Arch. Comput. Methods Eng., Volume 207-241 (1998) no. 5, pp. 207-241 | DOI | MR
[18] On error control in the element-free Galerkin method, Eng. Anal. Bound. Elem., Volume 36 (2012) no. 3, pp. 351-360 | DOI | MR | Zbl
[19] An adaptive procedure based on background cells for meshless methods, Comput. Methods Appl. Mech. Eng., Volume 191 (2002) no. 17-18, pp. 1923-1943 | DOI | Zbl
[20] A simple technique to improve computational efficiency of meshless methods, Procedia Eng., Volume 31 (2012), pp. 1102-1107 | DOI
[21] Independent cover meshless method using a polynomial approximation, Int. J. Fract., Volume 203 (2017) no. 1-2, pp. 63-80 | DOI
[22] A modified method to determine the radius of influence domain in element-free Galerkin method, Proc. Inst. Mech. Eng. C, Volume 229 (2015) no. 5, pp. 795-805 | DOI
[23] An h-adaptive modified element-free Galerkin method, Eur. J. Mech. - A, Volume 24 (2005) no. 5, pp. 782-799 | DOI | MR | Zbl
[24] Imposing essential boundary conditions in mesh-free methods, Comput. Methods Appl. Mech. Eng., Volume 193 (2004) no. 12-14, pp. 1257-1275 | DOI | MR | Zbl
[25] Structural optimization based on meshless element free Galerkin and level set methods, Comput. Methods Appl. Mech. Eng., Volume 344 (2019), pp. 144-163 | DOI | MR
[26] An Introduction to Meshfree Methods and Their Programming, Springer-Verlag, Berlin/Heidelberg, 2005
[27] An error estimate in the EFG method, Comput. Mech., Volume 21 (1998) no. 2, pp. 91-100 | DOI | MR | Zbl
[28] Theory of Elasticity, Engineering Societies Monographs, 1951 | Zbl
[29] Neural networks and neuroscience-inspired computer vision, Curr. Biol., Volume 24 (2014) no. 18, p. R921-R929 | DOI
[30] ANFIS: adaptive-network-based fuzzy inference system, IEEE Trans. Syst. Man Cybern., Volume 23 (1993) no. 3, pp. 665-685 | DOI
[31] The Nature of Statistical Learning Theory, Springer-Verlag, New York, 2000 | DOI | Zbl
[32] Comparison of ANN (MLP), ANFIS, SVM, and RF models for the online classification of heating value of burning municipal solid waste in circulating fluidized bed incinerators, Waste Manag., Volume 68 (2017), pp. 186-197 | DOI
[33] Adam: a method for stochastic optimization, arXiv:1412.6980 [cs] (2014)
Cited by Sources:
Comments - Policy