A review of meshless methods for laminated and functionally graded plates and shells
Tóm tắt
Từ khóa
Tài liệu tham khảo
Zienkiewicz, 2000
Bath, 1996
Lucy, 1977, A numerical approach to the testing of the fission hypothesis, J Astron, 82, 1013, 10.1086/112164
Gingold, 1977, Smoothed particle hydrodynamics: theory and allocation to non-spherical stars, Mon Not Roy Astron Soc, 181, 375, 10.1093/mnras/181.3.375
Randles, 1996, Smoothed particle hydrodynamics: some recent improvements and applications, Comput Methods Appl Mech Eng, 139, 375, 10.1016/S0045-7825(96)01090-0
Dilts, 1999, Moving-least-squares-particle hydrodynamics—I: consistency and stability, Int J Numer Methods Eng, 44, 1115, 10.1002/(SICI)1097-0207(19990320)44:8<1115::AID-NME547>3.0.CO;2-L
Dilts, 2000, Moving-least-squares-particle hydrodynamics—II: conservation and boundaries, Int J Numer Methods Eng, 48, 1503, 10.1002/1097-0207(20000810)48:10<1503::AID-NME832>3.0.CO;2-D
Johnson, 1996, Normalized smoothing functions for SPH impact computations, Int J Numer Methods Eng, 39, 2725, 10.1002/(SICI)1097-0207(19960830)39:16<2725::AID-NME973>3.0.CO;2-9
Johnson, 1996, SPH for high velocity impact computations, Comput Methods Appl Mech Eng, 139, 347, 10.1016/S0045-7825(96)01089-4
Morris, 2000, Simulating surface tension with smoothed particle hydrodynamics, Int J Numer Methods Eng, 33, 333, 10.1002/1097-0363(20000615)33:3<333::AID-FLD11>3.0.CO;2-7
Bonet, 2000, Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations, Int J Numer Methods Eng, 47, 1189, 10.1002/(SICI)1097-0207(20000228)47:6<1189::AID-NME830>3.0.CO;2-I
Nayroles, 1992, Generalizing the finite element method: diffuse approximation and diffuse elements, Comput Mech, 10, 307, 10.1007/BF00364252
Belytschko, 1994, Element-free Galerkin methods, Int J Numer Methods Eng, 37, 229, 10.1002/nme.1620370205
Belytschko, 1996, Meshless methods: an overview and recent developments, Comput Methods Appl Mech Eng, 139, 3, 10.1016/S0045-7825(96)01078-X
Krysl, 1996, Analysis of thin plates by the element-free Galerkin method, Comput Mech, 17, 26, 10.1007/BF00356476
Krysl, 1996, Analysis of thin shells by the element-free Galerkin method, Int J Solids Struct, 33, 3057, 10.1016/0020-7683(95)00265-0
Belytschko, 1996, Dynamic fracture using element-free Galerkin methods, Int J Numer Methods Eng, 39, 923, 10.1002/(SICI)1097-0207(19960330)39:6<923::AID-NME887>3.0.CO;2-W
Belytschko, 1995, Element-free Galerkin methods for static and dynamic fracture, Int J Solids Struct, 32, 2547, 10.1016/0020-7683(94)00282-2
Liu, 1995, Reproducing kernel particle methods, Int J Numer Methods Fluids, 20, 1081, 10.1002/fld.1650200824
Chen, 1996, Reproducing kernel particle methods for large deformation analysis of non-linear structures, Comput Methods Appl Mech Eng, 139, 195, 10.1016/S0045-7825(96)01083-3
Liu, 1996, Overview and applications of reproducing kernel particle methods, Arch Comput Methods Eng, 3, 3, 10.1007/BF02736130
Liu, 1997, Moving least-square reproducing kernel methods (I) methodology and convergence, Comput Methods Appl Mech Eng, 143, 113, 10.1016/S0045-7825(96)01132-2
Liu, 1996, Moving least-square reproducing kernel methods part II: Fourier analysis, Comput Methods Appl Mech Eng, 139, 159, 10.1016/S0045-7825(96)01082-1
Liu, 1995, Reproducing kernel particle methods for structural dynamics, Int J Numer Methods Eng, 38, 1655, 10.1002/nme.1620381005
Jun, 1998, Explicit reproducing kernel particle methods for large deformation problems, Int J Numer Methods Eng, 41, 137, 10.1002/(SICI)1097-0207(19980115)41:1<137::AID-NME280>3.0.CO;2-A
Chen, 1997, Large deformation analysis of rubber based on a reproducing kernel particle method, Comput Mech, 19, 211, 10.1007/s004660050170
Chen, 1998, A Lagrangian reproducing kernel particle method for metal forming analysis, Comput Mech, 22, 289, 10.1007/s004660050361
Chen, 1998, Analysis of metal forming process based on meshless method, J Mater Process Technol, 80–81, 642, 10.1016/S0924-0136(98)00171-X
Donning, 1998, Meshless methods for shear-deformable beams and plates, Comput Methods Appl Mech Eng, 152, 47, 10.1016/S0045-7825(97)00181-3
Li, 2000, Numerical simulations of large deformation of thin shell structures using meshfree methods, Comput Mech, 25, 102, 10.1007/s004660050463
Duarte, 1996, Hp cloud-an hp meshless method, Numer Methods Part Differ Equat, 12, 673, 10.1002/(SICI)1098-2426(199611)12:6<673::AID-NUM3>3.0.CO;2-P
Duarte, 1996, An hp adaptive method using clouds, Comput Methods Appl Mech Eng, 139, 237, 10.1016/S0045-7825(96)01085-7
Liszka, 1996, Hp-meshless cloud method, Comput Methods Appl Mech Eng, 139, 263, 10.1016/S0045-7825(96)01086-9
Babuška, 1996, The partition of unity finite element method: basic theory and applications, Comput Methods Appl Mech Eng, 139, 289, 10.1016/S0045-7825(96)01087-0
Babuška, 1997, The partition of unity method, Int J Numer Methods Eng, 40, 727, 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N
Babuška, 1998, The partition of unity method for the elastically supported beam, Comput Methods Appl Mech Eng, 152, 1, 10.1016/S0045-7825(97)00231-4
Atluri, 1998, A new meshless local Petrov–Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation, Comput Model Eng Sci, 3, 187
Atluri, 1998, A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics, Comput Mech, 22, 117, 10.1007/s004660050346
Atluri, 2000, The meshless local Petrov–Galerkin (MLPG) approach for solving problems in elasto-statics, Comput Mech, 25, 169, 10.1007/s004660050467
Atluri, 1999, A critical assessment of the truly meshless local Petrov–Galerkin (MLPG), and local boundary integral equation (LBIE) methods, Comput Mech, 24, 348, 10.1007/s004660050457
Li, 2002, Meshfree and particle methods and their application, Appl Mech Rev, 55, 1, 10.1115/1.1431547
Nguyen, 2008, Meshless methods: a review and computer implementation aspects, Math Comput Simul, 79, 763, 10.1016/j.matcom.2008.01.003
Reissner, 1945, The effect of transverse shear deformation on the bending of elastic plates, J Appl Mech, 12, A69, 10.1115/1.4009435
Reissner E. Small bending and stretching of sandwich type shells. NACA-TN-1832, 1949.
Mindlin, 1951, Influence of rotary inertia and shear in flexural motion of isotropic elastic plates, ASME J Appl Mech, 18, 31, 10.1115/1.4010217
Whitney, 1973, Shear correction factors for orthotropic laminates under static loads, J Appl Mech, 40, 302, 10.1115/1.3422950
Whitney, 1969, The effect of transverse shear deformation in the bending of laminated plates, J Compos Mater, 3, 534, 10.1177/002199836900300316
Whitney, 1970, Shear deformation in heterogeneous anisotropic plates, J Appl Mech, 37, 1031, 10.1115/1.3408654
Reissner, 1972, A consistent treatment of transverse shear deformations in laminated anisotropic plates, AIAA J, 10, 716, 10.2514/3.50194
Yang, 1966, Elastic wave propagation in heterogeneous plates, Int J Solids Struct, 2, 665, 10.1016/0020-7683(66)90045-X
Bert, 1978, Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates, Int J Solids Struct, 14, 465, 10.1016/0020-7683(78)90011-2
Fortier, 1973, On the vibration of shear deformable curved anisotropic composite plates, J Appl Mech, 40, 299, 10.1115/1.3422948
Liew, 1998
Reddy, 1984, Exact solutions of moderately thick laminated shells, J Eng Mech, 110, 794, 10.1061/(ASCE)0733-9399(1984)110:5(794)
Noor, 1975, Stability of multilayered composite plates, Fibre Sci Technol, 8, 81, 10.1016/0015-0568(75)90005-6
Murthy MVV. An improved transverse shear deformation theory for laminated antisotropic plates. NASA Technical Paper 1903 1981; 1-37.
Levinson, 1980, An accurate simple theory of the static and dynamics of elastic plates, Mech Res Commun, 7, 343, 10.1016/0093-6413(80)90049-X
Reddy, 1984, A simple higher-order theory for laminated composite plates, J Appl Mech, 51, 745, 10.1115/1.3167719
Reddy, 1985, A higher-order shear deformation theory of laminated elastic shells, Int J Eng Sci, 23, 319, 10.1016/0020-7225(85)90051-5
Reddy, 1985, Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory, J Sound Vib, 98, 157, 10.1016/0022-460X(85)90383-9
Phan, 1985, Analysis of laminated composite plates using a higher-order shear deformation theory, Int J Numer Methods Eng, 21, 2201, 10.1002/nme.1620211207
Khdeir, 1991, Analytical solutions of refined plate theories of cross-ply composite laminates, J Press Ves, 113, 570, 10.1115/1.2928797
Reddy, 1989, Buckling and vibration of laminated composite plates using various plate theories, AIAA J, 27, 1808, 10.2514/3.10338
Palazotto, 1991, Vibration and buckling characteristics of composite cylindrical panels incorporating the effects of a higher-order shear theory, Int J Solids Struct, 28, 341, 10.1016/0020-7683(91)90198-O
Huang, 1994, Influence of shear correction factors in the higher-order shear deformation laminated shell theory, Int J Solids Struct, 31, 1263, 10.1016/0020-7683(94)90120-1
Di, 1998, Solution of laminated cylindrical shells using an unconstrained third-order theory, Comput Struct, 69, 291, 10.1016/S0045-7949(98)00137-0
Nayak, 2002, Free vibration analysis of composite sandwich plates based on Reddy’s higher-order theory, Composites Part B, 33, 505, 10.1016/S1359-8368(02)00035-5
Noor, 1989, Assessment of shear deformation theories for multilayered composite plates, Appl Mech Rev, 42, 1, 10.1115/1.3152418
Reddy, 1990, A general non-linear third-order theory of plates with moderate thickness, Int J Non Linear Mech, 25, 677, 10.1016/0020-7462(90)90006-U
Reddy JN. Overview of shear deformation theories and their relationships to the classical theory. ASME Mechanical Behavior of Advanced Materials MD-Vol 84, 1998.
Reddy, 2004
Kapania, 1989, A review of the analysis of laminated shells, ASME J Press Ves, 111, 88, 10.1115/1.3265662
Reddy, 2004, Shear deformation plate and shell theories: from Starvsky to present, Mech Adv Mater Struct, 11, 535, 10.1080/15376490490452777
Reddy, 1987, A generalization of two dimensional theories of laminated composite plates, Commun Appl Numer Methods, 3, 173, 10.1002/cnm.1630030303
Reddy, 1992, Layer-wise shell theory for postbuckling of laminated circular cylindrical shells, AIAA J, 30, 2148, 10.2514/3.11193
Di Sciuva, 1987, An improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates, J Appl Mech, 54, 589, 10.1115/1.3173074
Di Sciuva, 1986, Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model, J Sound Vib, 105, 425, 10.1016/0022-460X(86)90169-0
Robbins, 1991, Analysis of piezoelectrically actuated beams using layer-wise displacement theory, Comput Struct, 41, 265, 10.1016/0045-7949(91)90430-T
Barbero, 1991, Modeling of delamination in composite laminates using a layer-wise plate theory, Int J Solids Struct, 28, 373, 10.1016/0020-7683(91)90200-Y
Singh, 1996, Composite shaft rotodynamic analysis using a layer wise theory, J Sound Vib, 191, 739, 10.1006/jsvi.1996.0153
Xavier, 1993, An improved zig-zag model for the bending of laminated composite shells, Compos Struct, 26, 123, 10.1016/0263-8223(93)90061-T
Kim, 2002, Buckling analysis for delaminated composites using plate bending elements based on higher-order zig-zag theory, Int J Numer Methods Eng, 55, 1323, 10.1002/nme.545
Cho, 2000, Higher order zig-zag theory for fully coupled thermo-electric-mechanical smart composite plates, Int J Solids Struct, 41, 1331, 10.1016/j.ijsolstr.2003.10.020
Averill, 1996, Thick beam theory and finite element model with zig-zag sublaminate approximations, AIAA J, 34, 1627, 10.2514/3.13281
Lancaster, 1981, Surfaces generated by moving least squares methods, Math Comput, 37, 141, 10.1090/S0025-5718-1981-0616367-1
Belytschko, 1998, On the completeness of meshfree particle methods, Int J Numer Methods Eng, 43, 785, 10.1002/(SICI)1097-0207(19981115)43:5<785::AID-NME420>3.0.CO;2-9
Dolbow, 1998, An introduction to programming the meshless element free Galerkin method, Arch Comput Methods Eng, 5, 207, 10.1007/BF02897874
Krysl, 1997, Element-free Galerkin method: convergence of the continuous and discontinuous shape functions, Comput Methods Appl Mech Eng, 148, 257, 10.1016/S0045-7825(96)00007-2
Cordes, 1996, Treatment of material discontinuity in the element-free Galerkin method, Comput Methods Appl Mech Eng, 139, 75, 10.1016/S0045-7825(96)01080-8
Belytschko, 1996, Smoothing and accelerated computations in the element free Galerkin method, J Comput Appl Math, 74, 111, 10.1016/0377-0427(96)00020-9
Fleming, 1997, Enriched element-free Galerkin methods for crack tip fields, Int J Numer Methods Eng, 40, 1483, 10.1002/(SICI)1097-0207(19970430)40:8<1483::AID-NME123>3.0.CO;2-6
Rao, 2000, An efficient meshless method for fracture analysis of cracks, Comput Mech, 26, 398, 10.1007/s004660000189
Liu, 1996, Generalized multiple scale reproducing kernel particle methods, Comput Methods Appl Mech Eng, 139, 91, 10.1016/S0045-7825(96)01081-X
Uras, 1997, Multiresolution reproducing kernel particle methods in acoustics, J Comput Acoust, 5, 71, 10.1142/S0218396X9700006X
Suleau, 2000, One-dimensional dispersion analysis for the element-free Galerkin method for the Helmholtz equation, Int J Numer Methods Eng, 47, 1169, 10.1002/(SICI)1097-0207(20000228)47:6<1169::AID-NME824>3.0.CO;2-9
Organ, 1996, Continuous meshless approximations for nonconvex bodies by diffraction and transparency, Comput Mech, 18, 225, 10.1007/BF00369940
Anderson, 1991
Krongauz, 1998, EFG approximation with discontinuous derivatives, Int J Numer Methods Eng, 41, 1215, 10.1002/(SICI)1097-0207(19980415)41:7<1215::AID-NME330>3.0.CO;2-#
Shepard D. A two dimentsional interpolation function for irregularly-spaced data. Proceedings-1968 ACM National Conference.
Krongauz, 1997, Consistent pseudo-derivatives in meshless methods, Comput Methods Appl Mech Eng, 146, 371, 10.1016/S0045-7825(96)01234-0
Swegle, 1995, Smoothed particle hydrodynamics stability analysis, J Comput Phys, 116, 123, 10.1006/jcph.1995.1010
Swegle JW, Attaway SW, Heinsein MW, Mello FJ, Hicks DL. An analysis of smoothed particle hydrodynamics. Report No. SAND93-2513-UC-705, Sandia National Laboratories, Albuquerque, NM 1994.
Wen Y, Hicks DL, Swegle JW. Stabilizing SPH with conservative smoothing. Report No. SAND94-1932-UC-705, Sandia National Laboratories, Albuquerque, NM 1994.
Morris JP. A study of the stability properties of SPH. Applied Mathematics Reports and Reprints. Monash University, 1994.
Morris JP. A study of the stability properties of smoothed particle hydrodynamics. Publications of the Astronomical Society of Austrilia 1996; 13.
Beissel, 1996, Nodal integration of the element-free Galerkin methods, Comput Methods Appl Mech Eng, 139, 49, 10.1016/S0045-7825(96)01079-1
Belytschko, 2000, A unified stability analysis of meshless particle methods, Int J Numer Methods Eng, 48, 1359, 10.1002/1097-0207(20000730)48:9<1359::AID-NME829>3.0.CO;2-U
Liu, 1997, Multiresolution reproducing kernel particle method, Comput Mech, 20, 295, 10.1007/s004660050252
Han, 2001, Error analysis of the reproducing kernel particle method, Comput Methods Appl Mech Eng, 190, 6157, 10.1016/S0045-7825(01)00214-6
Voth, 2001, Discretization errors associated with reproducing kernel methods: one-dimensional domains, Comput Methods Appl Mech Eng, 190, 2429, 10.1016/S0045-7825(00)00245-0
Mukherjee, 1997, On boundary conditions in the element-free Galerkin method, Comput Mech, 19, 264, 10.1007/s004660050175
Krongauz, 1996, Enforcement of essential boundary conditions in meshless approximations using finite elements, Comput Methods Appl Mech Eng, 131, 133, 10.1016/0045-7825(95)00954-X
Belytschko, 1994, Fracture and crack growth by element-free Galerkin methods, Modell Simul Mater Sci Eng, 2, 519, 10.1088/0965-0393/2/3A/007
Zhu, 1998, A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method, Comput Mech, 21, 211, 10.1007/s004660050296
Fernández-Méndez, 2004, Imposing essential boundary conditions in mesh-free methods, Comput Methods Appl Mech Eng, 193, 1257, 10.1016/j.cma.2003.12.019
Chen, 2000, New boundary condition treatments in meshfree computation of contact problems, Comput Methods Appl Mech Eng, 187, 441, 10.1016/S0045-7825(00)80004-3
Günther, 1998, Implementation of boundary conditions for meshless methods, Comput Methods Appl Mech Eng, 163, 205, 10.1016/S0045-7825(98)00014-0
Gosz, 1996, Admissible approximations for essential boundary conditions in the reproducing kernel particle method, Comput Mech, 19, 120, 10.1007/BF02824850
Wagner, 2000, Application of essential boundary conditions in mesh-free methods: a corrected collocation method, Int J Numer Methods Eng, 47, 1367, 10.1002/(SICI)1097-0207(20000320)47:8<1367::AID-NME822>3.0.CO;2-Y
Dolbow, 1999, Numerical integration of the Galerkin weak form in meshfree methods, Comput Mech, 23, 219, 10.1007/s004660050403
Bonet, 1999, Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulation, Int J Numer Methods Eng, 47, 1189, 10.1002/(SICI)1097-0207(20000228)47:6<1189::AID-NME830>3.0.CO;2-I
De, 2001, The method of finite spheres with improved numerical integration, Comput Struct, 79, 2183, 10.1016/S0045-7949(01)00124-9
Chen, 2001, A stabilized conforming nodal integration for Galerkin mesh-free methods, Int J Numer Methods Eng, 50, 435, 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
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, 2002, Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods, Int J Numer Methods Eng, 53, 2587, 10.1002/nme.338
Chen, 2006, A constrained reproducing kernel particle formulation for shear deformable shell in Cartesian coordinates, Int J Numer Methods Eng, 68, 151, 10.1002/nme.1701
Zhao, 2009, A linearly conforming radial point interpolation method (LC-RPIM) for shells, Comput Mech, 43, 321, 10.1007/s00466-008-0313-z
Zhao, 2008, Geometric nonlinear analysis of plates and cylindrical shells via a linearly conforming radial point interpolation method, Comput Mech, 42, 133, 10.1007/s00466-008-0242-x
Liu, 2008, A conforming radial point interpolation method for static and free vibration analysis of laminated composite plates, Compos Sci Technol, 68, 354, 10.1016/j.compscitech.2007.07.014
Gavete, 2000, Penalty functions in constrained variational principles for element free Galerkin method, Eur J Mech A/Solids, 19, 699, 10.1016/S0997-7538(00)00168-6
Wang, 2004, Extended immersed boundary method using FEM and RKPM, Comput Methods Appl Mech Eng, 193, 1305, 10.1016/j.cma.2003.12.024
Liu, 2004, Reproducing kernel element method. Part I: theoretical formulation, Comput Meth Appl Mech Eng, 193, 933, 10.1016/j.cma.2003.12.001
Li, 2004, Reproducing kernel element method. Part II: globally conforming Im/Cm hierarchies, Comput Methods Appl Mech Eng, 193, 953, 10.1016/j.cma.2003.12.002
Lu, 2004, Reproducing kernel element method. Part III: generalized enrichment and application, Comput Methods Appl Mech Eng, 193, 989, 10.1016/j.cma.2003.12.003
Belytschko, 1999, Smoothing, enrichment and contact in the element-free Galerkin method, Comput Struct, 71, 173, 10.1016/S0045-7949(98)00205-3
Breitkopf, 2000, Explicit form and efficient computation of MLS shape functions and their derivatives, Int J Numer Methods Eng, 48, 451, 10.1002/(SICI)1097-0207(20000530)48:3<451::AID-NME892>3.0.CO;2-1
Lu, 1994, A new implementation of the element free Galerkin method, Comput Methods Appl Mech Eng, 113, 397, 10.1016/0045-7825(94)90056-6
Belytschko, 1995, A coupled finite element free Galerkin methods, Comput Mech, 17, 186, 10.1007/BF00364080
Barry, 1999, A three-dimensional element-free Galerkin elastic and elastoplastic formulation, Int J Numer Methods Eng, 46, 671, 10.1002/(SICI)1097-0207(19991020)46:5<671::AID-NME650>3.0.CO;2-9
Kim, 2003, Point collocation methods using the fast moving least-square reproducing kernel approximation, Int J Numer Methods Eng, 56, 1445, 10.1002/nme.618
Aluru, 2000, A point collocation method based on reproducing kernel approximations, Int J Numer Methods Eng, 47, 1083, 10.1002/(SICI)1097-0207(20000228)47:6<1083::AID-NME816>3.0.CO;2-N
Ponthot, 1998, Arbitrary Lagrangian-Eulerian formulation for element-free Galerkin method, Comput Methods Appl Mech Eng, 152, 19, 10.1016/S0045-7825(97)00180-1
Liew, 2002, Meshless method for modeling of human proximal femur: treatment of nonconvex boundaries and stress analysis, Comput Mech, 28, 390, 10.1007/s00466-002-0303-5
Liew, 2002, The element-free kp-Ritz method for vibration of laminated rotating cylindrical panels, Int J Struct Stab Dyn, 2, 523, 10.1142/S0219455402000701
Ren, 2002, Mesh-free method revisited: two new approaches for the treatment of essential boundary conditions, Int J Comput Eng Sci, 3, 219, 10.1142/S1465876302000617
Ren, 2002, Modelling and simulation of the superelastic behaviour of shape memory alloys using the element-free Galerkin method, Int J Mech Sci, 44, 2393, 10.1016/S0020-7403(02)00169-8
Wang, 2002, Analysis of rectangular laminated composite plates via FSDT meshless method, Int J Mech Sci, 44, 1275, 10.1016/S0020-7403(02)00057-7
Rajendran, 2003, A novel unsymmetric 8-node plane element immune to mesh distortion under a quadratic displacement field, Int J Numer Methods Eng, 58, 1713, 10.1002/nme.836
Liew, 2004, Mesh-free radial basis function method for buckling analysis of non-uniformly loaded arbitrarily shaped shear deformable plates, Comput Methods Appl Mech Eng, 193, 205, 10.1016/j.cma.2003.10.002
Liew, 2004, Mesh-free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in-plane point loads, Int J Numer Methods Eng, 60, 1861, 10.1002/nme.1027
Liew, 2004, Dynamic analysis of laminated composite plates with piezoelectric sensor/actuator patches using the FSDT mesh-free method, Int J Mech Sci, 46, 411, 10.1016/j.ijmecsci.2004.03.011
Liew, 2004, Analysis of the pseudoelastic behavior of a SMA beam by the element-free Galerkin method, Eng Anal Boundary Elem, 28, 497, 10.1016/S0955-7997(03)00103-6
Liew, 2004, Free vibration and buckling analyses of shear deformable plates based on FSDT meshfree method, J Sound Vib, 276, 997, 10.1016/j.jsv.2003.08.026
Ren, 2005, Meshfree modelling and characterisation of thermomechanical behaviour of NiTi alloys, Eng Anal Boundary Elem, 29, 29, 10.1016/j.enganabound.2004.09.004
Ren, 2005, Meshfree modeling and simulation of thermomechanical behaviors of shape memory alloys, Smart Mater Struct, 14, S302, 10.1088/0964-1726/14/5/020
Liew, 2006, A quadratic plane triangular element immune to quadratic mesh distortions under quadratic displacement fields, Comput Methods Appl Mech Eng, 195, 1207, 10.1016/j.cma.2005.04.012
Liu, 2006, A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems, Int J Numer Methods Eng, 66, 1153, 10.1002/nme.1587
Liew, 2007, Analyzing the 2D fracture problems via the enriched boundary element-free method, Int J Solids Struct, 44, 4220, 10.1016/j.ijsolstr.2006.11.018
Liew, 2007, Complex variable moving least-squares method: a meshless approximation technique, Int J Numer Methods Eng, 70, 46, 10.1002/nme.1870
Liew, 2007, Dynamic stability analysis of composite laminated cylindrical panels via mesh-free kp-Ritz method, Int J Mech Sci, 49, 1156, 10.1016/j.ijmecsci.2007.02.005
Liew, 2007, Nonlinear analysis of corrugated plates using a FSDT and a meshfree method, Comput Methods Appl Mech Eng, 196, 2358, 10.1016/j.cma.2006.11.018
Sun, 2008, Mesh-free simulation of single-walled carbon nanotubes using higher order Cauchy-Born rule, Comput Mater Sci, 42, 444, 10.1016/j.commatsci.2007.08.008
Sun, 2008, The buckling of single-walled carbon nanotubes upon bending: the higher order gradient continuum and mesh-free method, Comput Methods Appl Mech Eng, 197, 3001, 10.1016/j.cma.2008.02.003
Sun, 2008, Application of the higher-order Cauchy-Born rule in mesh-free continuum and multiscale simulation of carbon nanotubes, Int J Numer Methods Eng, 75, 1238, 10.1002/nme.2299
Zhang, 2008, Coupling of the improved element-free Galerkin and boundary element methods for 2D elasticity problems, Eng Anal Boundary Elem, 32, 100, 10.1016/j.enganabound.2007.06.006
Zhao, 2008, Free vibration analysis of functionally graded plates using the element-free kp-Ritz method, J Sound Vib, 319, 918, 10.1016/j.jsv.2008.06.025
Liew, 2009, Vibration analysis of corrugated Reissner–Mindlin plates using a mesh-free Galerkin method, Int J Mech Sci, 51, 642, 10.1016/j.ijmecsci.2009.06.005
Liew, 2009, Complex variable boundary element-free method for two-dimensional elastodynamic problems, Comput Methods Appl Mech Eng, 198, 3925, 10.1016/j.cma.2009.08.020
Zhang, 2009, Improved element-free Galerkin method for two-dimensional potential problems, Eng Anal Boundary Elem, 33, 547, 10.1016/j.enganabound.2008.08.004
Zhang, 2009, Analyzing three-dimensional potential problems with the improved element-free Galerkin method, Comput Mech, 44, 273, 10.1007/s00466-009-0364-9
Rajendran, 2010, A partition of unity-based ‘FE-meshfree’ QUAD4 element for geometric non-linear analysis, Int J Numer Methods Eng, 82, 1574, 10.1002/nme.2820
Zhang, 2010, Improved element-free method (IEFG) for solving three-dimensional elasticity problems, Interact Multiscale Mech, 3, 123, 10.12989/imm.2010.3.2.123
Zhao, 2010, A mesh-free method for analysis of the thermal and mechanical buckling of functionally graded cylindrical shell panels, Comput Mech, 45, 297, 10.1007/s00466-009-0446-8
Krysl, 1999, The element free Galerkin method for dynamic propagation of arbitrary 3-D cracks, Int J Numer Methods Eng, 44, 767, 10.1002/(SICI)1097-0207(19990228)44:6<767::AID-NME524>3.0.CO;2-G
Ventura, 2002, A vector level set method and new discontinuity approximations for crack growth by EFG, Int J Numer Methods Eng, 54, 923, 10.1002/nme.471
Rabczuk, 2004, Cracking particles: a simplified meshfree method for arbitrary evolving cracks, Int J Numer Methods Eng, 61, 2316, 10.1002/nme.1151
Rao, 2003, Mesh-free analysis of cracks in isotropic functionally graded materials, Eng Fract Mech, 70, 1, 10.1016/S0013-7944(02)00038-3
Rabczuk, 2007, A three-dimensional large deformation meshfree method for arbitrary evolving cracks, Comput Methods Appl Mech Eng, 196, 2777, 10.1016/j.cma.2006.06.020
Belytschko, 2000, Element-free Galerkin methods for dynamic fracture in concrete, Comput Methods Appl Mech Eng, 187, 385, 10.1016/S0045-7825(00)80002-X
Askes, 2000, Dispersion analysis and element-free Galerkin solutions of second- and fourth-order gradient enhanced damaged models, Int J Numer Methods Eng, 49, 811, 10.1002/1097-0207(20001030)49:6<811::AID-NME985>3.0.CO;2-9
Li, 2002, Mesh-free Galerkin simulation of dynamic shear band propagation and failure mode transition, Int J Solids Struct, 39, 1213, 10.1016/S0020-7683(01)00188-3
Li, 2000, Mesh-free shear banding in large deformation, Int J Solids Struct, 37, 7185, 10.1016/S0020-7683(00)00195-5
Jun, 2000, Multiple-scale meshfree adaptivity for the simulation of adiabatic shear band formation, Comput Mech, 25, 257, 10.1007/s004660050474
Hao, 2004, Modeling and simulation of intersonic crack growth, Int J Solids Struct, 41, 1773, 10.1016/j.ijsolstr.2003.10.025
Sun, 2007, A mesh-free simulation of cracking and failure using the cohesive segments method, Int J Eng Sci, 45, 541, 10.1016/j.ijengsci.2007.03.004
Zhang, 2008, Analyzing 2D fracture problems with the improved element-free Galerkin method, Eng Anal Boundary Elem, 32, 242, 10.1016/j.enganabound.2007.08.012
Sun, 2006, Analyzing the interaction between collinear interfacial cracks by an efficient boundary element-free method, Int J Eng Sci, 44, 37, 10.1016/j.ijengsci.2005.08.005
Liew, 2007, Boundary element-free method for fracture analysis of 2-D piezoelectric solids, Int J Numer Methods Eng, 69, 729, 10.1002/nme.1786
Noguchi, 2000, Element free analyses of shell and spatial structures, Int J Numer Methods Eng, 47, 1215, 10.1002/(SICI)1097-0207(20000228)47:6<1215::AID-NME834>3.0.CO;2-M
Dolbow, 1999, Volumetric locking in the element free Galerkin method, Int J Numer Methods Eng, 46, 925, 10.1002/(SICI)1097-0207(19991030)46:6<925::AID-NME729>3.0.CO;2-Y
Huerta, 2001, Locking in the incompressible limit for the element-free Galerkin method, Int J Numer Methods Eng, 51, 1361, 10.1002/nme.213
Kanok-Nukulchai, 2001, On elimination of shear locking in the element-free Galerkin method, Int J Numer Methods Eng, 52, 705, 10.1002/nme.223
Askes, 1999, Conditions for locking-free elasto-plastic analyses in the element-free Galerkin method, Comput Methods Appl Mech Eng, 173, 99, 10.1016/S0045-7825(98)00259-X
Liew, 2002, Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method, Comput Mech, 29, 486, 10.1007/s00466-002-0358-3
Liew, 2009, Analysis of symmetrically laminated folded plate structures using the meshfree Galerkin method, Mech Adv Mater Struct, 16, 69, 10.1080/15376490802544301
Peng, 2006, Bending analysis of folded plates by the FSDT meshless method, Thin-walled Struct, 44, 1138, 10.1016/j.tws.2006.10.007
Peng, 2005, Analysis of rectangular stiffened plates under uniform lateral load based on FSDT and element-free Galerkin method, Int J Mech Sci, 63, 1014
Peng, 2007, Analysis of stiffened corrugated plates based on the FSDT via the mesh-free method, Int J Mech Sci, 49, 364, 10.1016/j.ijmecsci.2006.08.018
Dai, 2005, Thermomechanical analysis of functionally graded material (FGM) plates using element-free Galerkin method, Comput Struct, 83, 1487, 10.1016/j.compstruc.2004.09.020
Rabczuk, 2004, Numerical analysis of prestressed concrete beams using a coupled element free Galerkin/finite element approach, Int J Solids Struct, 41, 1061, 10.1016/j.ijsolstr.2003.09.040
Lee, 2009, Thermoelastic analysis of functionally graded plates using the element free kp-Ritz method, Smart Mater Struct, 18, 035007, 10.1088/0964-1726/18/3/035007
Zhao, 2009, Thermoelastic and vibration analysis of functionally graded cylindrical shells, Int J Mech Sci, 51, 694, 10.1016/j.ijmecsci.2009.08.001
Liu, 2008, A semi-analytic meshfree method for Almansi–Michell problems of piezoelectric cylinders, Int J Solids Struct, 45, 2379, 10.1016/j.ijsolstr.2007.12.001
Bobaru, 2002, Meshless approach to shape optimization of linear thermoelastic solids, Int J Numer Methods Eng, 53, 765, 10.1002/nme.311
Bobaru, 2001, Shape sensitivity analysis and shape optimization in planar elasticity using the element-free Galerkin method, Comput Methods Appl Mech Eng, 190, 4319, 10.1016/S0045-7825(00)00321-2
Zhang, 2005, Shape optimization using reproducing kernel particle method and an enriched genetic algorithm, Comput Methods Appl Mech Eng, 194, 4048, 10.1016/j.cma.2004.10.004
Kim, 2003, Meshfree analysis and design sensitivity analysis for shell structures, Int J Numer Methods Eng, 53, 2087, 10.1002/nme.385
Kim, 2002, A material derivative approach in design sensitivity of three-dimensional contact problems, Int J Solids Struct, 39, 2087, 10.1016/S0020-7683(02)00083-5
Liew, 2006, Buckling of folded plate structures subjected to partial in-plane edge loads by the FSDT meshfree Galerkin method, Int J Numer Methods Eng, 65, 1495, 10.1002/nme.1505
Liew, 2006, Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory, Comput Mech, 38, 61, 10.1007/s00466-005-0721-2
Peng, 2006, Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method, J Sound Vib, 289, 421, 10.1016/j.jsv.2005.02.023
Zhao, 2009, Mechanical and thermal buckling analysis of functionally graded plates, Compos Struct, 90, 161, 10.1016/j.compstruct.2009.03.005
Liu, 2001, A mesh-free method for static and free vibration analysis of thin plates of complicated shape, J Sound Vib, 241, 839, 10.1006/jsvi.2000.3330
Chen, 2003, An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape, Compos Struct, 59, 279, 10.1016/S0263-8223(02)00034-X
Liu, 2002, Element free method for static and free vibration analysis of spatial thin shell structures, Comput Meth Appl Mech Eng, 191, 5923, 10.1016/S0045-7825(02)00504-2
Zhao, 2003, Vibration analysis of laminated composite cylindrical panels via a mesh-free approach, Int J Solids Struct, 40, 161, 10.1016/S0020-7683(02)00475-4
Zhao, 2004, Free vibration of laminated two-side simply-supported cylindrical panels via the kp-Ritz method, Int J Mech Sci, 46, 123, 10.1016/j.ijmecsci.2004.02.010
Liew, 2002, Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells, Comput Methods Appl Mech Eng, 191, 37, 10.1016/S0045-7825(02)00358-4
Liew, 2005, Free vibration analysis of conical shells via the element-free kp-Ritz method, J Sound Vib, 281, 627, 10.1016/j.jsv.2004.01.005
Zhao, 2006, The element-free kp-Ritz method for free vibration analysis of conical shell panels, J Sound Vib, 295, 906, 10.1016/j.jsv.2006.01.045
Zhao, 2009, Free vibration analysis of functionally graded plates using element free kp-Ritz method, J Sound Vib, 319, 918, 10.1016/j.jsv.2008.06.025
Liew, 2006, Dynamic stability analysis of composite laminated cylindrical shells via the mesh-free kp-Ritz method, Comput Methods Appl Mech Eng, 196, 147, 10.1016/j.cma.2006.02.007
Liew, 2006, Dynamic stability of rotating cylindrical shells subjected to periodic axial loads, Int J Solids Struct, 43, 7553, 10.1016/j.ijsolstr.2006.03.016
Peng, 2007, Free vibration analysis of folded plate structures by the FSDT mesh-free method, Comput Mech, 39, 799, 10.1007/s00466-006-0070-9
Amirani, 2009, Free vibration analysis of sandwich beam with FG core using the element free Galerkin method, Compos Struct, 90, 373, 10.1016/j.compstruct.2009.03.023
Liu, 1997, Multiplesolution reproducing kernel particle methods, Comput Mech, 20, 295, 10.1007/s004660050252
Liu, 1995, Wavelet and multiple scale reproducing kernel particle methods, Int J Numer Methods Fluids, 21, 901, 10.1002/fld.1650211010
Liu, 1996, Advances in multiple scale kernel particle methods, Comput Mech, 18, 73, 10.1007/BF00350529
Liu, 2000, Multi-scale methods, Int J Numer Methods Eng, 47, 1343, 10.1002/(SICI)1097-0207(20000310)47:7<1343::AID-NME828>3.0.CO;2-W
Liu, 1998, Multiple-scale reproducing kernel particle methods for large deformation problems, Int J Numer Methods Eng, 41, 1339, 10.1002/(SICI)1097-0207(19980415)41:7<1339::AID-NME343>3.0.CO;2-9
Liu, 1999, Multiple scale meshfree methods for damage fracture and localization, Comput Mater Sci, 16, 197, 10.1016/S0927-0256(99)00062-2
Li, 2001, A meshfree contact-detection algorithm, Comput Methods Appl Mech Eng, 190, 3271, 10.1016/S0045-7825(00)00392-3
Park, 2004, An introduction and tutorial on multiple-scale analysis in solids, Comput Methods Appl Mech Eng, 193, 1733, 10.1016/j.cma.2003.12.054
Lee, 2000, Two scale meshfree method for the adaptivity of 3-D stress concentration problems, Comput Mech, 26, 376, 10.1007/s004660000186
Xiong, 2005, Simulation of bulk metal forming processes using the reproducing kernel particle method, Comput Struct, 83, 574, 10.1016/j.compstruc.2004.11.008
Yoon, 2002, Accelerated meshfree method for metal forming simulation, Finite Elem Anal Des, 38, 937, 10.1016/S0168-874X(02)00086-0
Shangwu, 2003, On the the utilization of reproducing kernel particle method for the numerical simulation of plane strain rolling, Int J Mach Tools Manuf, 43, 89, 10.1016/S0890-6955(02)00134-7
Liew, 2002, Meshfee method for large deformation analysis-a reproducing kernel particle approach, Eng Struct, 24, 543, 10.1016/S0141-0296(01)00120-1
Liew, 2005, Numerical simulation of thermomechanical behaviours of shape memory alloys via a non-linear mesh-free Galerkin formulation, Int J Numer Methods Eng, 63, 1014, 10.1002/nme.1320
Liew, 2004, Nonlinear analysis of laminated plates using the mesh-free kp-Ritz method based on FSDT, Comput Methods Appl Mech Eng, 193, 4763, 10.1016/j.cma.2004.03.013
Liew, 2006, Postbuckling analysis of laminated composite plates using the mesh-free kp-Ritz method, Comput Methods Appl Mech Eng, 195, 551, 10.1016/j.cma.2005.02.004
Zhao, 2007, Geometrically nonlinear analysis of cylindrical shells using the element-free kp-Ritz method, Eng Anal Boundary Elem, 31, 783, 10.1016/j.enganabound.2007.01.003
Zhao, 2009, Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method, Comput Methods Appl Mech Eng, 198, 2796, 10.1016/j.cma.2009.04.005
Zhao, 2009, Geometrically nonlinear analysis of functionally graded shells, Int J Mech Sci, 51, 131, 10.1016/j.ijmecsci.2008.12.004
Belinha, 2007, Nonlinear analysis of plates and laminates using the element free Galerkin method, Compos Struct, 78, 337, 10.1016/j.compstruct.2005.10.007
Ren, 2002, Modelling and simulation of the superelastic behaviour of shape memeory alloys using the element-free Galerkin method, Int J Mech Sci, 44, 2393, 10.1016/S0020-7403(02)00169-8
Liew, 2007, Geometric non-linear analysis of folded plate structures by the spline strip kernel particle method, Int J Numer Methods Eng, 71, 1102, 10.1002/nme.1984
Chen, 2008, Lower bound shakedown analysis by using the element free Galerkin method and non-linear programming, Comput Methods Appl Mech Eng, 197, 3911, 10.1016/j.cma.2008.03.009
Barbieri, 2009, Nonlinear wave propagation in damaged hysteretic materials using a frequency domain-based PM space formulation, Int J Solids Struct, 46, 165, 10.1016/j.ijsolstr.2008.08.025
Areias, 2007, A meshfree thin shell method for non-linear dynamic fracture, Int J Numer Methods Eng, 72, 524, 10.1002/nme.2013
Li, 1999, Reproducing kernel hierarchical partition of unity, part I- formulation and theory, Int J Numer Methods Eng, 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, Int J Numer Methods Eng, 45, 289, 10.1002/(SICI)1097-0207(19990530)45:3<289::AID-NME584>3.0.CO;2-P
Rahman, 2001, An element-free Galerkin method for probalistic mechanics and reliability, Int J Solids Struct, 38, 9313, 10.1016/S0020-7683(01)00193-7
Liew, 2006, Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems, Int J Numer Methods Eng, 65, 1310, 10.1002/nme.1489
Liew, 2005, Boundary element-free (BEFM) for two-dimensional elastodynamic analysis using Laplace transform, Int J Numer Methods Eng, 64, 1610, 10.1002/nme.1417
Kitipornchai, 2005, A boundary element-free method (BEFM) for three-dimensional elasticity problems, Comput Mech, 36, 13, 10.1007/s00466-004-0638-1
Karim, 2002, Analysis of transient response of saturated porus elstic soil under cyclic loading using element-free Galerkin method, Int J Solids Struct, 39, 6011, 10.1016/S0020-7683(02)00497-3
Shishvan, 2009, A time integration algorithm for linear transient analysis based on the reproducing kernel method, Comput Methods Appl Mech Eng, 198, 3361, 10.1016/j.cma.2009.06.011
Danielson, 2000, Parallel computing of meshless methods for explicit dynamic analysis, Int J Numer Methods Eng, 47, 1323, 10.1002/(SICI)1097-0207(20000310)47:7<1323::AID-NME827>3.0.CO;2-0
Rabczuk, 2005, Adaptivity of structured meshfree particle methods in 2D and 3D, Int J Numer Methods Eng, 63, 1559, 10.1002/nme.1326
Qian, 2004, Static and dynamic deformations of thick functionally graded elastic plate by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method, Compos Part B-Eng, 35, 685, 10.1016/j.compositesb.2004.02.004
Qian, 2004, Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov-Galerkin method, Comput Mech, 33, 263, 10.1007/s00466-003-0527-z
Qian, 2005, Design of bidirectional functionally graded plate for pptimal natural frequencies, J Sound Vib, 280, 415, 10.1016/j.jsv.2004.01.042
Qian, 2004, Transient thermoelastic deformations of a thick functionally graded plate, J Therm Stresses, 27, 705, 10.1080/01495730490440145
Ferreira, 2005, Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method, Compos Struct, 69, 449, 10.1016/j.compstruct.2004.08.003
Qian, 2005, Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method, Comput Mech, 35, 214, 10.1007/s00466-004-0617-6
Ferreira, 2006, Natural frequencies of functionally graded plates by a meshless method, Compos Struct, 75, 593, 10.1016/j.compstruct.2006.04.018
Gilhooley, 2007, Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions, Compos Struct, 80, 539, 10.1016/j.compstruct.2006.07.007
Ferreira, 2008, Static deformations and vibration analysis of composite and sandwich plates using a Layerwise theory and RBF-PS discretizations with optimal shape parameter, Compos Struct, 86, 328, 10.1016/j.compstruct.2008.07.025