×

The elastoplastic large deformation analysis based on meshless radial basis reproducing kernel particle method. (English) Zbl 1537.74377


MSC:

74S60 Stochastic and other probabilistic methods applied to problems in solid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65D12 Numerical radial basis function approximation
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
Full Text: DOI

References:

[1] Liu, F. B.; Wu, Q.; Cheng, Y. M., A meshless method based on the nonsingular weight functions for elastoplastic large deformation problems, Int J Appl Mech, 11, 1, Article 1950006 pp. (2019)
[2] Li, D. M.; Liew, K. M.; Cheng, Y. M., Analyzing elastoplastic large deformation problems with the complex variable element-free Galerkin method, Comput Mech, 53, 6, 1149-1162 (2014)
[3] Liu, Z.; Wei, G. F.; Wang, Z. M., Geometrically nonlinear analysis of functionally graded materials based on reproducing kernel particle method, Int J Mech Mater Des, 16, 487-502 (2020)
[4] Liu, Z.; Wei, G. F.; Wang, Z. M., The radial basis reproducing kernel particle method for geometrically nonlinear problem of functionally graded materials, Appl Math Model, 85, 244-272 (2020) · Zbl 1481.74124
[5] Roque, C. M.C.; Grasa, J., Geometrically nonlinear analysis of laminated composite plates using RBF-PS meshless method, Compos Struct, 267, Article 113830 pp. (2021)
[6] He, C.; Wu, X. H.; Wang, T.; He, H., Geometrically nonlinear analysis for elastic beam using point interpolation meshless method, Shock Vib, 2019, Article 9065365 pp. (2019)
[7] Sun, D. W.; Liu, C.; Hu, H. Y., Dynamic computation of 2D segment-to-segment frictional contact for a flexible multibody system subject to large deformations, Mech Mach Theory, 158, Article 104197 pp. (2021)
[8] Liu, Z.; Wei, G. F.; Qin, S. P.; Wang, Z. M., The elastoplastic analysis of functionally graded materials using a meshfree RB-RKPM, Appl Math Comput, 413, Article 126651 pp. (2022) · Zbl 1510.74013
[9] DJr, Soares; Sladek, J.; Sladek, V., Non-linear dynamic analyses by meshless local Petrov-Galerkin formulations, Int J Numer Meth Eng, 81, 13, 1687-1699 (2010) · Zbl 1183.74369
[10] Wu, Q.; Liu, F. B.; Cheng, Y. M., The interpolating element-free Galerkin method for three-dimensional elastoplasticity problems, Eng Anal Bound Elem, 115, C, 156-167 (2020) · Zbl 1464.74218
[11] Yu, S. Y.; Peng, M. J.; Cheng, H.; Cheng, Y. M., The improved element-free Galerkin method for three-dimensional elastoplasticity problems, Eng Anal Bound Elem, 104, 215-224 (2019) · Zbl 1464.74225
[12] Liu, N.; Hsu, M. C.; Lua, J.; Phan, N., A large deformation isogeometric continuum shell formulation incorporating finite strain elastoplasticity, Comput Mech, 70, 5, 965-976 (2022) · Zbl 1503.74115
[13] Nam, H. K.; Kyung, K. C.; Jiun, S. C., Die shape design optimization of sheet metal stamping process using meshfree method, Int J Numer Meth Eng, 51, 12, 1385-1405 (2001) · Zbl 1065.74584
[14] Liu, W. K.; Guo, Y.; Tang, S.; Belytschko, T., A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis, Comput Method Appl M, 154, 1, 69-132 (1998) · Zbl 0935.74068
[15] Yoo, W. S.; Park, S. J.; Dmitrochenko, O. N.; Pogorelov, D. Y., Verification of absolute nodal coordinate formulation in flexible multibody dynamics via physical experiments of large deformation problems, J Comput Nonlin Dyn, 1, 1, 81-93 (2006)
[16] Yoshihiro, O., Meshless large plastic deformation analysis considering with a friction coefficient by triple-reciprocity boundary element method, Int J Comput Method Exp Meas, 6, 989-999 (2018)
[17] Peng, Y. X.; Zhang, A. M.; Ming, F. R.; Wang, S. P., A meshfree framework for the numerical simulation of elasto-plasticity deformation of ship structure, Ocean Eng, 192, C, Article 106507 pp. (2019)
[18] Zhang, S. D.; Long, Z. L.; Yang, X. Y., Reaction force of ship stern bearing in hull large deformation based on stochastic theory, Int J Nav Arch Ocean, 12, 723-732 (2020)
[19] Wang, Z. Y.; Mei, G. X., Numerical analysis of seismic performance of embankment supported by micropiles, Mar Georesour Geotechnol, 30, 1, 52-62 (2012)
[20] Zheng, Y.; Usami, T.; Ge, H. B., Ductility of thin-walled steel box stub-columns, J Struct Eng, 126, 11, 1304-1311 (2000)
[21] Nemer, R.; Larcher, A.; Coupez, T.; Hachem, E., Stabilized finite element method for incompressible solid dynamics using an updated Lagrangian formulation, Comput Method Appl M, 384, Article 113923 pp. (2021) · Zbl 1506.74423
[22] Ho, I. H.; Li, S.; Ma, L., Analysis of partially saturated clayey slopes using finite element method, Soil Mech Found Eng, 56, 6, 382-389 (2020)
[23] Zheng, Z. B.; Beer, M.; Dai, H. Z., Nackenhorst U. A weak-intrusive stochastic finite element method for stochastic structural dynamics analysis, Comput Method Appl M, 399, Article 115360 pp. (2022) · Zbl 1507.65193
[24] Li, L. M.; Lapin, A.; Zhang, S. H., Alternating direction implicit finite element method for multi-dimensional black-scholes models, Adv Appl Math Mech, 11, 2, 535-558 (2019) · Zbl 1488.65435
[25] Zhu, X. G.; Yuan, Z. B.; Wang, J. G.; Nie, Y. F.; Yang, Z. Z., Finite element method for time-space-fractional Schrodinger equation, Electron J Differ Eq, 2017, 166, 1-18 (2017) · Zbl 1372.65278
[26] Hajiazizi, M.; Graili, A., A novel hybrid meshless method for seepage flows in non-homogeneous and anisotropic soils, Eng Comput, 35, 2, 867-886 (2018)
[27] Panchore, V.; Ganguli, R.; Omkar, S. N., Meshless local Petrov-Galerkin method for rotating timoshenko beam: a locking-free shape function formulation, Com Model Eng, 108, 4, 215-237 (2015)
[28] Ma, J. C.; Gao, H. F.; Wei, G. F.; Qiao, J. W., The meshless analysis of wave propagation based on the Hermit-type RB-RKPM, Soil Dyn Earthq Eng, 134, Article 106154 pp. (2020)
[29] Chen, J. S.; Hu, W.; Hu, H. Y., Reproducing kernel enhanced local radial basis collocation method, Int J Numer Meth Eng, 75, 600-627 (2008) · Zbl 1195.74278
[30] Liu, F. B.; Cheng, Y. M., The improved element-free Galerkin method based on the nonsingular weight functions for inhomogeneous swelling of polymer gels, Int J Appl Mech, 10, 4, Article 1850047 pp. (2018)
[31] Gao, H. F.; Wei, G. F., Complex variable meshless manifold method for transient heat conduction problems, Int J Appl Mech, 9, Article 1750067 pp. (2017)
[32] Peng, P. P.; Wu, Q.; Cheng, Y. M., The dimension splitting reproducing kernel particle method for three-dimensional potential problems, Int J Numer Meth Eng, 121, 1, 146-164 (2020) · Zbl 1537.65171
[33] Liu, Z.; Wei, G. F.; Wang, Z. M., Numerical analysis of functionally graded materials using reproducing kernel particle method, Int J Appl Mech, 11, 6, Article 1950060 pp. (2019)
[34] Yang, J. P.; JY, Chen, Strong-form formulated generalized displacement control method for large deformation analysis, Int J Appl Mech, 9, 7, Article 1750101 pp. (2017)
[35] Yang, J. P.; Su, W. T., Strong-form framework for solving boundary value problems with geometric nonlinearity, Appl Math Mech Engl Ed, 37, 12, 1707-1720 (2016) · Zbl 1374.74131
[36] Yang, J. P.; Su, W. T., Investigation of radial basis collocation method for incremental-iterative analysis, Int J Appl Mech, 8, 1, Article 1650007 pp. (2016)
[37] Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M., The hybrid element-free Galerkin method for three-dimensional wave propagation problems, Int J Numer Method Eng, 117, 15-37 (2019) · Zbl 07865092
[38] Chen, J. S.; Wang, L. H.; Hu, H. Y.; Chi, S. W., Subdomain radial basis collocation method for heterogeneous media, Int J Numer Method Eng, 80, 163-190 (2009) · Zbl 1176.74207
[39] Yang, J. P.; Chen, Y. C., Gradient enhanced localized radial basis collocation method for inverse analysis of Cauchy problems, Int J Appl Mech, 12, 9, Article 2050107 pp. (2020)
[40] Malgorzata, A. J., On elastoplastic analysis of some plane stress problems with meshless methods and successive approximations method, Eng Anal Bound Elem, 95, 12-24 (2018) · Zbl 1403.74018
[41] Zhu, H. H.; Liu, W. J.; Cai, Y. C.; Miao, Y. B., A meshless local natural neighbor interpolation method for two-dimension incompressible large deformation analysis, Eng Anal Bound Elem, 31, 10, 856-862 (2007) · Zbl 1195.74283
[42] Gu, Y. T., An adaptive local meshfree updated lagrangian approach for large deformation analysis of metal forming, Adv Mater Res, 905, 97-101, 2664-2667 (2010)
[43] Liu, Z.; Gao, H. F.; Wei, G. F.; Wang, Z. M., The meshfree analysis of elasticity problem utilizing radial basis reproducing kernel particle method, Results Phys, 17, Article 103037 pp. (2020)
[44] Liu, Z.; Wei, G. F.; Wang, Z. M.; Qiao, J. W., The meshfree analysis of geometrically nonlinear problem based on radial basis reproducing kernel particle method, Int J Appl Mech, 12, 4, Article 2050044 pp. (2020)
[45] Liu, Z.; Wei, G. F.; Wang, Z. M., Numerical solution of functionally graded materials based on radial basis reproducing kernel particle method, Eng Anal Bound Elem, 111, 32-43 (2020) · Zbl 1464.65262
[46] Zhang, T.; Wei, G. F.; Ma, J. C.; Gao, H. F., Radial basis reproducing kernel particle method for piezoelectric materials, Eng Anal Bound Elem, 92, 171-179 (2018) · Zbl 1403.74331
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.