×

Selection of radial basis functions for the accuracy of meshfree Galerkin method in rotating Euler-Bernoulli beam problem. (English) Zbl 1492.74141

MSC:

74S99 Numerical and other methods in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H45 Vibrations in dynamical problems in solid mechanics
Full Text: DOI

References:

[1] Kumar, M.; Yadav, N., Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey, Comput. Math. Appl., 62, 3796-3811 (2011) · Zbl 1236.65107 · doi:10.1016/j.camwa.2011.09.028
[2] Zou, Y.; Lie, G.; Shao, K.; Guo, Y.; Zhu, J.; Chen, X., Hybrid approach of radial basis function and finite element method for electromagnetic problems, IEEE Trans. Mag., 51, 1-4 (2015)
[3] Han, H.; Chen, Q.; Qiao, J., Research on an online self-organizing radial basis function neural network, Neural Comput. Appl., 19, 667-676 (2010) · doi:10.1007/s00521-009-0323-6
[4] Duan, Y., A note on the meshless method using radial basis functions, Comput. Math. Appl., 55, 66-75 (2008) · Zbl 1176.65133 · doi:10.1016/j.camwa.2007.03.011
[5] Duan, Y.; Tan, Y-J, A meshless Galerkin method for Dirichlet problems using radial basis functions, J. Comput. Appl. Math., 196, 394-401 (2006) · Zbl 1106.65103 · doi:10.1016/j.cam.2005.09.018
[6] Chinchapatnam, PP; Djidjeli, K.; Nair, PB, Radial basis function meshless method for the steady incompressible Navier-Stokes equations, Int. J. Comput. Math., 84, 1509-1526 (2007) · Zbl 1123.76048 · doi:10.1080/00207160701308309
[7] Wendland, H., Meshless Galerkin methods using radial basis functions, Math. Comput., 68, 1521-2153 (1999) · Zbl 1020.65084 · doi:10.1090/S0025-5718-99-01102-3
[8] Zhang, X.; Song, KZ; Lu, MW; Liu, X., Mehsless methods based on collocation with radial basis functions, Comput. Mech., 26, 333-343 (2000) · Zbl 0986.74079 · doi:10.1007/s004660000181
[9] Oruc, O., Two meshless methods based on local radial basis function and barycentric rational interpolation for solving 2D viscoelastic wave equation, Comput. Math. Appl., 79, 3272-3288 (2020) · Zbl 1440.74466 · doi:10.1016/j.camwa.2020.01.025
[10] Waters, J.; Pepper, DW, Global versus localized RBF meshless methods for solving incompressible fluid flow with heat transfer, Numer. Heat Transf. B., 68, 185-203 (2015) · doi:10.1080/10407790.2015.1021590
[11] Schaback, R.; Wendland, H., Kernel techniques: from machine learning to meshless methods, Acta Numer., 15, 1-97 (2006) · Zbl 1111.65108 · doi:10.1017/S0962492906270016
[12] Kadalbajoo, MK; Kumar, A.; Tripathi, LP, Application of radial basis function with L-stable Padé time marching scheme for pricing exotic option, Comput. Math. Appl., 66, 500-511 (2013) · Zbl 1360.91154 · doi:10.1016/j.camwa.2013.06.002
[13] Sarra, SA, Integrated multiquadric radial basis function approximation methods, Comput. Math. Appl., 51, 500-511 (2006) · Zbl 1146.65327 · doi:10.1016/j.camwa.2006.04.014
[14] Fornberg, B.; Lehto, E.; Powell, C., Stable calculation of Gaussian-based RBF-FD stencils, Comput. Math. Appl., 65, 627-637 (2013) · Zbl 1319.65011 · doi:10.1016/j.camwa.2012.11.006
[15] Bouhamidi, A.; Hached, M.; Jbilou, K., A meshless RBF method for computing a numerical solution of unsteady Burgers’-type equations, Comput. Math. Appl., 68, 238-256 (2014) · Zbl 1369.65125 · doi:10.1016/j.camwa.2014.05.022
[16] Piret, C., The orthogonal gradients method: a radial basis functions method for solving partial differential equations on arbitrary surfaces, J. Comput. Phys., 231, 4662-4675 (2012) · Zbl 1248.35009 · doi:10.1016/j.jcp.2012.03.007
[17] Marchi, SD; Santin, G., A new stable basis for radial basis function interpolation, J. Comput. Appl. Math., 253, 1-13 (2013) · Zbl 1288.65013 · doi:10.1016/j.cam.2013.03.048
[18] Sarra, SA, A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains, Appl. Math. Comput., 218, 9853-9865 (2012) · Zbl 1245.65144
[19] Kazem, S.; Rad, JA, Radial basis functions method for solving of a non-local boundary value problem with Neumann’s boundary conditions, Appl. Math. Model., 36, 2360-2369 (2012) · Zbl 1246.65229 · doi:10.1016/j.apm.2011.08.032
[20] Kadem, A.; Baleanu, D., Analytical method based on Walsh function combined with orthogonal polynomial for fractional transport equation, Commun. Nonlinear Sci. Numer. Simul., 15, 491-501 (2010) · Zbl 1221.45008 · doi:10.1016/j.cnsns.2009.05.024
[21] Baleanu, D.; Abadi, MH; Jajarmi, A.; Vahid, KZ; Nieto, JJ, A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects, Alexand. Eng. J., 61, 4779-4791 (2022) · doi:10.1016/j.aej.2021.10.030
[22] Baleanu, D.; Zibaei, S.; Namjoo, M.; Jajarmi, A., A nonstandard finite difference scheme for the modelling and nonidentical synchronization of a novel fractional chaotic system, Adv. Differ. Equ. (2021) · Zbl 1494.65060 · doi:10.1186/s13662-021-03454-1
[23] Erturk, VS; Godwe, E.; Baleanu, D.; Kumar, P.; Asad, J.; Jajarmi, A., Novel fractional-order Lagrangian to describe motion of beam on nanowire, Acta Phys. Polonica A., 140, 265-272 (2021) · doi:10.12693/APhysPolA.140.265
[24] Jajarmi, A.; Baleanu, D.; Vahid, KZ; Pirouz, HM; Asad, JH, A new and general fractional Lagrangian approach: a capacitor microphone case study, Results Phys. (2021) · doi:10.1016/j.rinp.2021.104950
[25] Baleanu, D.; Etemad, S.; Rezapour, S., On a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions by using three operators, Alexand. Eng. J., 59, 3019-3027 (2020) · doi:10.1016/j.aej.2020.04.053
[26] Baleanu, D.; Etemad, S.; Pourrazi, S.; Rezapour, S., On the new fractional hybrid boundary value problems with three-point integral hybrid conditions, Adv. Differ. Equ. (2019) · Zbl 1487.34008 · doi:10.1186/s13662-019-2407-7
[27] Baleanu, D., Hedayati, V., Rezapour, S., Qurashi, M. M. A.: On two fraction differential inclusions. Springer, New York (2016). doi:10.1186/s40064-016-2564-z
[28] Baleanu, D.; Etemad, S.; Rezapour, S., A hybrid Caputo fractional modelling for thermostat with hybrid boundary value conditions, Bound. Value Prob. (2020) · Zbl 1482.34016 · doi:10.1186/s13661-020-01361-0
[29] Mohammadi, H.; Kumar, S.; Rezapour, S.; Etemad, S., A theoretical study of the Caputo-Fabrizio fractional modelling for hearing loss due to Mumps virus with optimal control, Chaos Solitons Fractals. (2021) · doi:10.1016/j.chaos.2021.110668
[30] Alizadeh, S.; Baleanu, D.; Rezapour, S., Analyzing transient response of the parallel RCL circuit by using the Caputo-Fabrizio fractional derivative, Adv. Differ. Equ. (2020) · Zbl 1487.94202 · doi:10.1186/s13662-020-2527-0
[31] Matar, MM; Abbas, MI; Alzabut, J.; Kabar, MKA; Etemad, S.; Rezapour, S., Investigation of the p-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives, Adv. Differ. Equ. (2021) · Zbl 1487.34028 · doi:10.1186/s13662-021-03228-9
[32] Baleanu, D.; Rezapour, S.; Saberpour, Z., On fractional integro-differential inclusions via the extended fractional Caputo-Fabrizio derivation, Bound. Value Probl. (2019) · Zbl 1524.45012 · doi:10.1186/s13661-019-1194-0
[33] Aydogan, MS; Baleanu, D.; Mousalou, A.; Rezapour, S., On higher order integro-differential equations including the Caputo-Fabrizio derivative, Bound. Value Probl. (2018) · Zbl 1422.34019 · doi:10.1186/s13661-018-1008-9
[34] Baleanu, D.; Mohammadi, H.; Rezapour, S., Analysis of the model of HIV-1 infection of CD4+ T-Cell with a new approach of fractional derivative, Adv. Differ. Equ. (2020) · Zbl 1482.37090 · doi:10.1186/s13662-020-02544-w
[35] Hodges, HD; Rutkowski, MJ, Free-vibration analysis of rotating beams by a variable-order finite element method, AIAA J., 19, 1459-1466 (1981) · Zbl 0468.73093 · doi:10.2514/3.60082
[36] Nagaraj, VT; Shanthakumar, P., Rotor blade vibration by the Galerkin finite element method, J. Sound Vib., 43, 575-577 (1975) · doi:10.1016/0022-460X(75)90013-9
[37] Bauchau, OA; Hong, CH, Finite element approach to rotor blade modeling, J. Am. Helicop. Soc., 32, 60-67 (1987) · doi:10.4050/JAHS.32.60
[38] Hoa, SV, Vibration of a rotating beam with tip mass, J. Sound Vib., 67, 369-381 (1979) · Zbl 0428.73059 · doi:10.1016/0022-460X(79)90542-X
[39] Raju, I. S., Phillips, D. R., Krishnamurthy, T.: A radial basis function approach in the meshless local Petrov-Galerkin method for Euler-Bernoulli beam problems. Comput. Mech. 34, 464-474 (2204) · Zbl 1109.74375
[40] Wang, G.; Wereley, NM, Free vibration analysis of rotating blades with uniform tapers, AIAA J., 42, 2429-2437 (2004) · doi:10.2514/1.4302
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.