An inherently consistent reproducing kernel gradient smoothing framework toward efficient Galerkin meshfree formulation with explicit quadrature

Computer Methods in Applied Mechanics and Engineering - Tập 349 - Trang 628-672 - 2019
Dongdong Wang1, Junchao Wu1
1Department of Civil Engineering, Xiamen University, Xiamen, Fujian, 361005, China

Tài liệu tham khảo

Belytschko, 1996, Meshless methods: an overview and recent developments, Comput. Methods Appl. Mech. Engrg., 139, 3, 10.1016/S0045-7825(96)01078-X

Chen, 2017, Meshfree methods: progress made after 20 years, J. Eng. Mech.-ASCE, 143, 04017001, 10.1061/(ASCE)EM.1943-7889.0001176

Nayroles, 1992, Generalizing the finite element method: diffuse approximation and diffuse elements, Comput. Mech., 10, 307, 10.1007/BF00364252

Lancaster, 1981, Surfaces generated by moving least squares methods, Math. Comp., 37, 141, 10.1090/S0025-5718-1981-0616367-1

Belytschko, 1994, Element-free Galerkin methods, Internat. J. Numer. Methods Engrg., 37, 229, 10.1002/nme.1620370205

Belytschko, 1995, Crack propagation by element-free Galerkin methods, Eng. Fract. Mech., 51, 295, 10.1016/0013-7944(94)00153-9

Liu, 1995, Reproducing kernel particle methods, Internat. J. Numer. Methods Fluids, 20, 1081, 10.1002/fld.1650200824

Chen, 1996, Reproducing kernel particle methods for large deformation analysis of nonlinear structures, Comput. Methods Appl. Mech. Engrg., 139, 195, 10.1016/S0045-7825(96)01083-3

Duarte, 1996, An hp adaptive method using clouds, Comput. Methods Appl. Mech. Engrg., 139, 237, 10.1016/S0045-7825(96)01085-7

Babuška, 1997, The partition of unity method, Internat. J. Numer. Methods Engrg., 40, 727, 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N

Sukumar, 1998, The natural element method in solid mechanics, Internat. J. Numer. Methods Engrg., 43, 839, 10.1002/(SICI)1097-0207(19981115)43:5<839::AID-NME423>3.0.CO;2-R

Atluri, 1998, A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics, Comput. Mech., 22, 117, 10.1007/s004660050346

De, 2000, The method of finite spheres, Comput. Mech., 25, 329, 10.1007/s004660050481

Wang, 2002, A point interpolation meshless method based on radial basis functions, Internat. J. Numer. Methods Engrg., 54, 1623, 10.1002/nme.489

Strouboulis, 2000, The design and analysis of the generalized finite element method, Comput. Methods Appl. Mech. Engrg., 181, 43, 10.1016/S0045-7825(99)00072-9

Chen, 2003, A reproducing kernel method with nodal interpolation property, Internat. J. Numer. Methods Engrg., 56, 935, 10.1002/nme.592

Gu, 2003, Moving kriging interpolation and element-free Galerkin method, Internat. J. Numer. Methods Engrg., 56, 1, 10.1002/nme.553

Liu, 2004, Reproducing kernel element method. Part I: theoretical formulation, Comput. Methods Appl. Mech. Engrg., 193, 933, 10.1016/j.cma.2003.12.001

Sukumar, 2004, Construction of polygonal interpolants: a maximum entropy approach, Internat. J. Numer. Methods Engrg., 61, 2159, 10.1002/nme.1193

Arroyo, 2006, Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods, Internat. J. Numer. Methods Engrg., 65, 2167, 10.1002/nme.1534

Liu, 2007, A smoothed finite element method for mechanics problems, Comput. Mech., 39, 859, 10.1007/s00466-006-0075-4

Li, 2010, Optimal transportation meshfree approximation schemes for fluid and plastic flows, Internat. J. Numer. Methods Engrg., 83, 1541, 10.1002/nme.2869

Guan, 2011, Semi-Lagrangian reproducing kernel particle method for fragment-impact problems, Int. J. Impact Eng., 38, 1033, 10.1016/j.ijimpeng.2011.08.001

Wu, 2011, A generalized approximation for the meshfree analysis of solids, Internat. J. Numer. Methods Engrg., 85, 693, 10.1002/nme.2991

Bessa, 2014, A meshfree unification: reproducing kernel peridynamics, Comput. Mech., 53, 1251, 10.1007/s00466-013-0969-x

Wang, 2014, Quasi-convex reproducing kernel meshfree method, Comput. Mech., 54, 689, 10.1007/s00466-014-1022-4

Wu, 2015, A displacement smoothing induced strain gradient stabilization for the meshfree Galerkin nodal integration method, Comput. Mech., 56, 19, 10.1007/s00466-015-1153-2

Metsis, 2015, A new hierarchical partition of unity formulation of EFG meshless methods, Comput. Methods Appl. Mech. Engrg., 283, 782, 10.1016/j.cma.2014.10.016

Yreux, 2017, A quasi-linear reproducing kernel particle method, Internat. J. Numer. Methods Engrg., 109, 1045, 10.1002/nme.5319

Wu, 2018, Simulation of impact penetration and perforation of metal targets using the smoothed particle Galerkin method, J. Eng. Mech.-ASCE, 144, 04018057, 10.1061/(ASCE)EM.1943-7889.0001470

Atluri, 2002

Babuška, 2003, Survey of meshless and generalized finite element methods: a unified approach, Acta Numer., 12, 1, 10.1017/S0962492902000090

Li, 2004

Zhang, 2004

Nguyen, 2008, Meshless methods: a review and computer implementation aspects, Math. Comput. Simulation, 79, 763, 10.1016/j.matcom.2008.01.003

Liu, 2009

Hughes, 2000

Zienkiewicz, 2015

Dolbow, 1999, Numerical integration of the Galerkin weak form in meshfree methods, Comput. Mech., 23, 219, 10.1007/s004660050403

Chen, 2001, A stabilized conforming nodal integration for Galerkin meshfree methods, Internat. J. Numer. Methods Engrg., 50, 435, 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A

Chen, 2002, Nonlinear version of stabilized conforming nodal integration for Galerkin meshfree methods, Internat. J. Numer. Methods Engrg., 53, 2587, 10.1002/nme.338

Babuška, 2008, Quadrature for meshless methods, Internat. J. Numer. Methods Engrg., 76, 1434, 10.1002/nme.2367

Karatarakis, 2013, GPU-Acceleration of stiffness matrix calculation and efficient initialization of EFG meshless methods, Comput. Methods Appl. Mech. Engrg., 258, 63, 10.1016/j.cma.2013.02.011

Peco, 2015, Efficient implementation of Galerkin meshfree methods for large-scale problems with an emphasis on maximum entropy approximants, Comput. Struct., 150, 52, 10.1016/j.compstruc.2014.12.005

Beissl, 1996, Nodal integration of the element-free Galerkin method, Comput. Methods Appl. Mech. Engrg., 139, 49, 10.1016/S0045-7825(96)01079-1

Dyka, 1997, Stress points for tension instability in SPH, Internat. J. Numer. Methods Engrg., 40, 2325, 10.1002/(SICI)1097-0207(19970715)40:13<2325::AID-NME161>3.0.CO;2-8

Rabczuk, 2004, Stable particle methods based on Lagrangian kernels, Comput. Methods Appl. Mech. Engrg., 193, 1035, 10.1016/j.cma.2003.12.005

Wu, 2016, Strain gradient stabilization with dual stress points for the meshfree nodal integration method in inelastic analyses, Internat. J. Numer. Methods Engrg., 107, 3, 10.1002/nme.5147

Wu, 2018, A stable and convergent Lagrangian particle method with multiple nodal stress points for large strain and material failure analyses in manufacturing processes, Finite Elem. Anal. Des., 146, 96, 10.1016/j.finel.2018.04.007

Carpinteri, 2002, The partition of unity quadrature in meshless methods, Internat. J. Numer. Methods Engrg., 54, 987, 10.1002/nme.455

Griebel, 2002, A particle-partition of unity method. Part II: efficient cover construction and reliable integration, SIAM J. Sci. Comput., 23, 1655, 10.1137/S1064827501391588

Kwon, 2006, The support integration scheme in the least-squares mesh-free method, Finite Elem. Anal. Des., 43, 127, 10.1016/j.finel.2006.08.005

Liu, 2010, A new support integration scheme for the weakform in mesh-free methods, Internat. J. Numer. Methods Engrg., 82, 699, 10.1002/nme.2780

Chen, 2000, Regularization of material instabilities by meshfree approximations with intrinsic length scales, Internat. J. Numer. Methods Engrg., 47, 1301, 10.1002/(SICI)1097-0207(20000310)47:7<1303::AID-NME826>3.0.CO;2-5

Wang, 2004, Locking-free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation, Comput. Methods Appl. Mech. Eng., 193, 1065, 10.1016/j.cma.2003.12.006

Chen, 2006, A constrained reproducing kernel particle formulation for shear deformable shell in Cartesian coordinates, Internat. J. Numer. Methods Engrg., 68, 151, 10.1002/nme.1701

Wang, 2006, Extended meshfree analysis of transverse and inplane loading of a laminated anisotropic plate of general planform geometry, Int. J. Solids Struct., 43, 144, 10.1016/j.ijsolstr.2005.03.068

Wang, 2008, An efficient Galerkin meshfree analysis of shear deformable cylindrical panels, Interact. Multiscale Mech., 1, 339, 10.12989/imm.2008.1.3.339

Wang, 2011, A Galerkin meshfree method with stabilized conforming nodal integration for geometrically nonlinear analysis of shear deformable plates, 8, 685

Wang, 2011, Three dimensional efficient meshfree simulation of large deformation failure evolution in soil medium, Sci. China Technol. Sci., 54, 573, 10.1007/s11431-010-4287-7

Wu, 2014, Three dimensional fragmentation simulation of concrete structures with a nodally regularized meshfree method, Theor. Appl. Fract. Mech., 72, 89, 10.1016/j.tafmec.2014.04.006

Wu, 2016, A direct displacement smoothing meshfree particle formulation for impact failure modeling, Int. J. Impact Eng., 87, 169, 10.1016/j.ijimpeng.2015.03.013

Hillman, 2016, Nodally integrated implicit gradient reproducing kernel particle method for convection dominated problems, Comput. Methods Appl. Mech. Engrg., 299, 381, 10.1016/j.cma.2015.11.004

Wang, 2008, A Hermite reproducing kernel approximation for thin-plate analysis with sub-domain stabilized conforming integration, Internat. J. Numer. Methods Engrg., 74, 368, 10.1002/nme.2175

Wang, 2010, Free vibration analysis of thin plates using Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration, Comput. Mech., 46, 703, 10.1007/s00466-010-0511-3

Wang, 2011, Dispersion and transient analyses of hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures, Comput. Mech., 48, 47, 10.1007/s00466-011-0580-y

Wang, 2013, A hermite reproducing kernel galerkin meshfree approach for buckling analysis of thin plates, Comput. Mech., 51, 1013, 10.1007/s00466-012-0784-9

Wang, 2015, A circumferentially enhanced hermite reproducing kernel meshfree method for buckling analysis of Kirchhoff–love cylindrical shells, Int. J. Struct. Stab. Dyn., 15, 1450090, 10.1142/S0219455414500904

Chen, 2007, Stability in Lagrangian and semi-Lagrangian reproducing kernel discretizations using nodal integration in nonlinear solid mechanics, 55

Duan, 2012, Second-order accurate derivatives and integration schemes for meshfree methods, Internat. J. Numer. Methods Engrg., 92, 399, 10.1002/nme.4359

Duan, 2014, A four-point integration scheme with quadratic exactness for three-dimensional element-free Galerkin method based on variationally consistency formulation, Comput. Methods Appl. Mech. Engrg., 280, 84, 10.1016/j.cma.2014.07.015

Chen, 2013, An arbitrary order variationally consistent integration for Galerkin meshfree methods, Internat. J. Numer. Methods Engrg., 95, 387, 10.1002/nme.4512

Hillman, 2014, Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems, Comput. Part. Mech., 1, 245, 10.1007/s40571-014-0024-5

Ruter, 2013, Corrected stabilized non-conforming nodal integration in meshfree methods, Lect. Notes Comput. Sci. Eng., 89, 75, 10.1007/978-3-642-32979-1_5

Wang, 2016, An efficient nesting sub-domain gradient smoothing integration algorithm with quadratic exactness for Galerkin meshfree methods, Comput. Methods Appl. Mech. Engrg., 298, 485, 10.1016/j.cma.2015.10.008

Hillman, 2016, An accelerated convergent and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics, Internat. J. Numer. Methods Engrg., 107, 603, 10.1002/nme.5183

Li, 1998, Synchronized reproducing kernel interpolant via multiple wavelet expansion, Comput. Mech., 21, 28, 10.1007/s004660050281

Li, 1999, Reproducing kernel hierarchical partition of unity part I: formulation and theory, Internat. J. Numer. Methods Engrg., 45, 251, 10.1002/(SICI)1097-0207(19990530)45:3<251::AID-NME583>3.0.CO;2-I

Li, 1999, Reproducing kernel hierarchical partition of unity part II: applications, Internat. J. Numer. Methods Engrg., 45, 289, 10.1002/(SICI)1097-0207(19990530)45:3<289::AID-NME584>3.0.CO;2-P

Chi, 2013, A gradient reproducing kernel collocation method for boundary value problems, Internat. J. Numer. Methods Engrg., 93, 1381, 10.1002/nme.4432

Wachspress, 1975

Eisenberg, 1973, On finite element integration in natural co-ordinates, Internat. J. Numer. Methods Engrg., 7, 574, 10.1002/nme.1620070421

Dunavant, 1985, High degree efficient symmetrical Gaussian quadrature-rules for the triangle, Internat. J. Numer. Methods Engrg., 21, 1129, 10.1002/nme.1620210612

Gellert, 1991, Moderate degree cubature formulas for 3-D tetrahedral finite-element approximations, Commun. Appl. Numer. Methods, 7, 487, 10.1002/cnm.1630070609

Conway, 2006, Packing, tiling, and covering with tetrahedra, 10612

Schrijver, 1998

Fernández-Méndez, 2004, Imposing essential boundary conditions in mesh-free methods, Comput. Methods Appl. Mech. Engrg., 193, 1257, 10.1016/j.cma.2003.12.019

Timoshenko, 1970

Wei, 1984, Area calculation of three dimensional polygon, Chin. Math. Bull., 2, 18

Thông tin
Thông tin xuất bản

Computer Methods in Applied Mechanics and Engineering

Tập 349

628-672

Thông tin tác giả