A review of meshless methods for laminated and functionally graded plates and shells

Composite Structures - Tập 93 Số 8 - Trang 2031-2041 - 2011
K.M. Liew1, Xin Zhao1, A.J.M. Ferreira2
1Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
2Faculdade de Engenharia da Universidade do Porto, Departamento de Engenharia Mecanica, Rua Dr Roberto Frias, 4200-465 Porto, Portugal

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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

Monaghan, 1988, An introduction to SPH, Comput Phys Commun, 48, 89, 10.1016/0010-4655(88)90026-4

Monaghan, 1982, Why particle methods work, SIAM J Sci Stat Comput, 3, 422, 10.1137/0903027

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

Chung, 1998, An error estimate in the EFG method, Comput Mech, 21, 91, 10.1007/s004660050286

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

Ferreira, 2009, Natural frequencies of thick plates made of orthotropic, monoclinic, and hexagonal materials by a meshless method, J Sound Vib, 319, 984, 10.1016/j.jsv.2008.06.034