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

Composite Structures

Volumn 93, Issue 8, 2011, Pages 2031-2041

  Liew, K M ^a   Zhao, Xin ^a   Ferreira, Antonio J M ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF PORTO   (Portugal)

Author keywords

Functionally graded plates and shells; Laminated plates and shells; Meshless methods

Indexed keywords

COMPOSITE STRUCTURES; COMPUTATIONAL MECHANICS; GALERKIN METHODS; LAMINATING; SHELLS (STRUCTURES); STRUCTURE (COMPOSITION); VIBRATION ANALYSIS;

ELEMENT FREE GALERKIN METHODS; FUNCTIONALLY GRADED PLATES; HIGHER-ORDER THEORY; LAMINATED PLATE; MESH-LESS METHODS; POSSIBLE FUTURES; REPRODUCING KERNEL PARTICLE METHOD; STATIC AND DYNAMIC ANALYSIS;

PLATES (STRUCTURAL COMPONENTS);

EID: 79960784906     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2011.02.018     Document Type: Article

References (273)

1. Zienkiewicz OC, Taylor RL. The finite element method, volume 1: the basis. 5th ed. Butterworth-Heinemann; 2000.
2. Bath KJ. Finite element procedures. New Jersey: Printice hall; 1996.
3. Lucy LB. A numerical approach to the testing of the fission hypothesis. J Astron 1977;82:1013-24.
4. Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory and allocation to non-spherical stars. Mon Not Roy Astron Soc 1977;181:375-89.
5. Monaghan JJ. An introduction to SPH. Comput Phys Commun 1988;48:89-96.
6. Monaghan JJ. Why particle methods work. SIAM J Sci Stat Comput 1982;3:422-33.
7. Randles PW, Libersky LD. Smoothed particle hydrodynamics: some recent improvements and applications. Comput Methods Appl Mech Eng 1996;139:375-408.
8. Dilts GA. Moving-least-squares-particle hydrodynamics-I: consistency and stability. Int J Numer Methods Eng 1999;44:1115-55.
9. Dilts GA. Moving-least-squares-particle hydrodynamics-II: conservation and boundaries. Int J Numer Methods Eng 2000;48:1503-24.
10. Johnson GR, Beissel SR. Normalized smoothing functions for SPH impact computations. Int J Numer Methods Eng 1996;39:2725-41.
11. Johnson GR, Stryk RA, Beissel SR. SPH for high velocity impact computations. Comput Methods Appl Mech Eng 1996;139:347-73.
12. Morris JP. Simulating surface tension with smoothed particle hydrodynamics. Int J Numer Methods Eng 2000;33:333-53.
13. Bonet J, Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. Int J Numer Methods Eng 2000;47:1189-214.
14. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech 1992;10:307-18.
15. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. Int J Numer Methods Eng 1994;37:229-56.
16. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 1996;139:3-47.
17. Krysl P, Belytschko T. Analysis of thin plates by the element-free Galerkin method. Comput Mech 1996;17:26-35.
18. Krysl P, Belytschko T. Analysis of thin shells by the element-free Galerkin method. Int J Solids Struct 1996;33:3057-80.
19. Belytschko T, Tabbara M. Dynamic fracture using element-free Galerkin methods. Int J Numer Methods Eng 1996;39:923-38.
20. Belytschko T, Lu YY, Gu L, Tabbara M. Element-free Galerkin methods for static and dynamic fracture. Int J Solids Struct 1995;32:2547-70.
21. Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. Int J Numer Methods Fluids 1995;20:1081-106.
22. Chen JS, Pan C, Wu T, Liu WK. Reproducing kernel particle methods for large deformation analysis of non-linear structures. Comput Methods Appl Mech Eng 1996;139:195-227.
23. Liu WK, Chen Y, Jun S, Chen JS, Belytschko T, Pan C, et al. Overview and applications of reproducing kernel particle methods. Arch Comput Methods Eng 1996;3:3-80.
24. Liu WK, Li S, Belytschko T. Moving least-square reproducing kernel methods (I) methodology and convergence. Comput Methods Appl Mech Eng 1997;143:113-54.
25. Liu WK, Li S. Moving least-square reproducing kernel methods part II: Fourier analysis. Comput Methods Appl Mech Eng 1996;139:159-93.
26. Liu WK, Jun S, Li S, Adee J, Belytschko T. Reproducing kernel particle methods for structural dynamics. Int J Numer Methods Eng 1995;38:1655-79.
27. Jun S, Liu WK, Belytschko T. Explicit reproducing kernel particle methods for large deformation problems. Int J Numer Methods Eng 1998;41:137-66.
28. Chen JS, Wu CT. Large deformation analysis of rubber based on a reproducing kernel particle method. Comput Mech 1997;19:211-27.
29. Chen JS, Pan C, Roque CMOL, Wang HP. A Lagrangian reproducing kernel particle method for metal forming analysis. Comput Mech 1998;22:289-307.
30. Chen JS, Roque CMOL, Pan C, Button ST. Analysis of metal forming process based on meshless method. J Mater Process Technol 1998;80-81:642-6.
31. Donning BM, Liu WK. Meshless methods for shear-deformable beams and plates. Comput Methods Appl Mech Eng 1998;152:47-71.
32. Li S, Hao W, Liu WK. Numerical simulations of large deformation of thin shell structures using meshfree methods. Comput Mech 2000;25:102-16.
33. Duarte CA, Oden JT. Hp cloud-an hp meshless method. Numer Methods Part Differ Equat 1996;12:673-705.
34. Duarte CA, Oden JT. An hp adaptive method using clouds. Comput Methods Appl Mech Eng 1996;139:237-62.
35. Liszka T, Duarte CAM, Tworzydlo WW. Hp-meshless cloud method. Comput Methods Appl Mech Eng 1996;139:263-88.
36. Babuška I, Melenk JM. The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 1996;139:289-314.
37. Babuška I, Melenk JM. The partition of unity method. Int J Numer Methods Eng 1997;40:727-58.
38. Babuška I, Zhang Z. The partition of unity method for the elastically supported beam. Comput Methods Appl Mech Eng 1998;152:1-18.
39. Atluri S, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation. Comput Model Eng Sci 1998;3:187-96.
40. Atluri S, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech 1998;22:117-27.
41. Atluri S, Zhu T. The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Comput Mech 2000;25:169-79.
42. Atluri S, Kim HG, Cho JY. A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods. Comput Mech 1999;24:348-72.
43. Li S, Liu WK. Meshfree and particle methods and their application. Appl Mech Rev 2002;55:1-34.
44. Nguyen VP, Rabczuk T, Bordas S, Duflot M. Meshless methods: a review and computer implementation aspects. Math Comput Simul 2008;79:763-813.
45. Reissner E. The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech 1945;12:A69-77.
46. Reissner E. Small bending and stretching of sandwich type shells. NACA-TN-1832, 1949.
47. Mindlin RD. Influence of rotary inertia and shear in flexural motion of isotropic elastic plates. ASME J Appl Mech 1951;18:31-8.
48. Whitney JM. Shear correction factors for orthotropic laminates under static loads. J Appl Mech 1973;40:302-4.
49. Whitney JM. The effect of transverse shear deformation in the bending of laminated plates. J Compos Mater 1969;3:534-47.
50. Whitney JM, Pagano NJ. Shear deformation in heterogeneous anisotropic plates. J Appl Mech 1970;37:1031-6.
51. Reissner E. A consistent treatment of transverse shear deformations in laminated anisotropic plates. AIAA J 1972;10:716-8.
52. Yang PC, Norris CH, Stavsky Y. Elastic wave propagation in heterogeneous plates. Int J Solids Struct 1966;2:665-84.
53. Bert CW, Chen TL. Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates. Int J Solids Struct 1978;14:465-73.
54. Fortier RC, Rossetto JN. On the vibration of shear deformable curved anisotropic composite plates. J Appl Mech 1973;40:299-301.
55. Liew KM, Wang CM, Xiang Y, Kitipornchai S. Vibration of Mindlin plates: programming the p-version Ritz method. Amsterdam; New York: Elsevier; 1998.
56. Reddy JN. Exact solutions of moderately thick laminated shells. J Eng Mech 1984;110:794-805.
57. Noor AK. Stability of multilayered composite plates. Fibre Sci Technol 1975;8:81-9.
58. Murthy MVV. An improved transverse shear deformation theory for laminated antisotropic plates. NASA Technical Paper 1903 1981; 1-37.
59. Levinson M. An accurate simple theory of the static and dynamics of elastic plates. Mech Res Commun 1980;7:343-50.
60. Reddy JN. A simple higher-order theory for laminated composite plates. J Appl Mech 1984;51:745-52.
61. Reddy JN, Liu CF. A higher-order shear deformation theory of laminated elastic shells. Int J Eng Sci 1985;23:319-30.
62. Reddy JN, Phan ND. Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. J Sound Vib 1985;98:157-70.
63. Phan ND, Reddy JN. Analysis of laminated composite plates using a higher-order shear deformation theory. Int J Numer Methods Eng 1985;21:2201-19.
64. Khdeir AA, Reddy JN. Analytical solutions of refined plate theories of cross-ply composite laminates. J Press Ves 1991;113:570-8.
65. Reddy JN, Khdeir AA. Buckling and vibration of laminated composite plates using various plate theories. AIAA J 1989;27:1808-17.
66. Palazotto AN, Linnemann PE. Vibration and buckling characteristics of composite cylindrical panels incorporating the effects of a higher-order shear theory. Int J Solids Struct 1991;28:341-61.
67. Huang NN. Influence of shear correction factors in the higher-order shear deformation laminated shell theory. Int J Solids Struct 1994;31:1263-77.
68. Di S, Rothert H. Solution of laminated cylindrical shells using an unconstrained third-order theory. Comput Struct 1998;69:291-303.
69. Nayak AK, Moy SJ, Shenoi RA. Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory. Composites Part B 2002;33:505-19.
70. Noor AK, Burton WS. Assessment of shear deformation theories for multilayered composite plates. Appl Mech Rev 1989;42:1-13.
71. Reddy JN. A general non-linear third-order theory of plates with moderate thickness. Int J Non Linear Mech 1990;25:677-86.
72. Reddy JN. Overview of shear deformation theories and their relationships to the classical theory. ASME Mechanical Behavior of Advanced Materials MD-Vol 84, 1998.
73. Reddy JN. Mechanics of laminated composite plates and shells: theory and analysis. 2nd ed. CRC press; 2004.
74. Kapania RK. A review of the analysis of laminated shells. ASME J Press Ves 1989;111:88-96.
75. Reddy JN, Arciniega RA. Shear deformation plate and shell theories: from Starvsky to present. Mech Adv Mater Struct 2004;11:535-82.
76. Reddy JN. A generalization of two dimensional theories of laminated composite plates. Commun Appl Numer Methods 1987;3:173-80.
77. Reddy JN, Savoia M. Layer-wise shell theory for postbuckling of laminated circular cylindrical shells. AIAA J 1992;30:2148-54.
78. Di Sciuva M. An improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates. J Appl Mech 1987;54:589-96.
79. Di Sciuva M. Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model. J Sound Vib 1986;105:425-42.
80. Robbins DH, Reddy JN. Analysis of piezoelectrically actuated beams using layer-wise displacement theory. Comput Struct 1991;41:265-79.
81. Barbero EJ, Reddy JN. Modeling of delamination in composite laminates using a layer-wise plate theory. Int J Solids Struct 1991;28:373-88.
82. Singh SP, Gupta K. Composite shaft rotodynamic analysis using a layer wise theory. J Sound Vib 1996;191:739-56.
83. Xavier PB, Lee KH, Chew CH. An improved zig-zag model for the bending of laminated composite shells. Compos Struct 1993;26:123-38.
84. Kim JS, Cho MH. Buckling analysis for delaminated composites using plate bending elements based on higher-order zig-zag theory. Int J Numer Methods Eng 2002;55:1323-43.
85. Cho M, Oh J. Higher order zig-zag theory for fully coupled thermo-electric-mechanical smart composite plates. Int J Solids Struct 2000;41:1331-56.
86. Averill RC, Yip YC. Thick beam theory and finite element model with zig-zag sublaminate approximations. AIAA J 1996;34:1627-42.
87. Lancaster P, Salkauskas K. Surfaces generated by moving least squares methods. Math Comput 1981;37:141-58.
88. Belytschko T, Krongauz Y, Dolbow J, Gerlach C. On the completeness of meshfree particle methods. Int J Numer Methods Eng 1998;43:785-819.
89. Dolbow J, Belytschko T. An introduction to programming the meshless element free Galerkin method. Arch Comput Methods Eng 1998;5:207-41.
90. Krysl P, Belytschko T. Element-free Galerkin method: convergence of the continuous and discontinuous shape functions. Comput Methods Appl Mech Eng 1997;148:257-77.
91. Cordes LW, Morgan D. Treatment of material discontinuity in the elementfree Galerkin method. Comput Methods Appl Mech Eng 1996;139:75-89.
92. Belytschko T, Krongauz Y, Fleming M, Organ D, Liu WK. Smoothing and accelerated computations in the element free Galerkin method. J Comput Appl Math 1996;74:111-26.
93. Fleming M, Chu YA, Morgan B, Belytschko T. Enriched element-free Galerkin methods for crack tip fields. Int J Numer Methods Eng 1997;40:1483-504.
94. Rao BN, Rahman S. An efficient meshless method for fracture analysis of cracks. Comput Mech 2000;26:398-408.
95. Liu WK, Chen Y, Uras RA, Chang CT. Generalized multiple scale reproducing kernel particle methods. Comput Methods Appl Mech Eng 1996;139:91-157.
96. Uras RA, Chang CT, Chen Y, Liu WK. Multiresolution reproducing kernel particle methods in acoustics. J Comput Acoust 1997;5:71-94.
97. Suleau S, Bouillard Ph. One-dimensional dispersion analysis for the element-free Galerkin method for the Helmholtz equation. Int J Numer Methods Eng 2000;47:1169-88.
98. Organ D, Fleming M, Terry T, Belytschko T. Continuous meshless approximations for nonconvex bodies by diffraction and transparency. Comput Mech 1996;18:225-35.
99. Anderson TL. Fracture mechanics: fundamentals and applications. 1st ed. Boca Raton (FL): CRC press; 1991.
100. Krongauz Y, Belytschko T. EFG approximation with discontinuous derivatives. Int J Numer Methods Eng 1998;41:1215-33.
101. Shepard D. A two dimentsional interpolation function for irregularly-spaced data. Proceedings-1968 ACM National Conference.
102. Krongauz Y, Belytschko T. Consistent pseudo-derivatives in meshless methods. Comput Methods Appl Mech Eng 1997;146:371-86.
103. Swegle JW, Hicks DL, Attaway SW. Smoothed particle hydrodynamics stability analysis. J Comput Phys 1995;116:123-34.
104. 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.
105. Wen Y, Hicks DL, Swegle JW. Stabilizing SPH with conservative smoothing. Report No. SAND94-1932-UC-705, Sandia National Laboratories, Albuquerque, NM 1994.
106. Morris JP. A study of the stability properties of SPH. Applied Mathematics Reports and Reprints. Monash University, 1994.
107. Morris JP. A study of the stability properties of smoothed particle hydrodynamics. Publications of the Astronomical Society of Austrilia 1996; 13.
108. Beissel S, Belytschko T. Nodal integration of the element-free Galerkin methods. Comput Methods Appl Mech Eng 1996;139:49-74.
109. Belytschko T, Guo Y, Liu WK, Xiao SP. A unified stability analysis of meshless particle methods. Int J Numer Methods Eng 2000;48:1359-400.
110. Liu WK, Hao Y, Chen Y, Gosz J. Multiresolution reproducing kernel particle method. Comput Mech 1997;20:295-309.
111. Han W, Meng X. Error analysis of the reproducing kernel particle method. Comput Methods Appl Mech Eng 2001;190:6157-81.
112. Chung HJ, Belytschko T. An error estimate in the EFG method. Comput Mech 1998;21:91-100.
113. Voth TH, Christon MA. Discretization errors associated with reproducing kernel methods: one-dimensional domains. Comput Methods Appl Mech Eng 2001;190:2429-46.
114. Mukherjee YX, Mukherjee S. On boundary conditions in the element-free Galerkin method. Comput Mech 1997;19:264-70.
115. Krongauz Y, Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite elements. Comput Methods Appl Mech Eng 1996;131:133-45.
116. Belytschko T, Lu YY, Gu L. Fracture and crack growth by element-free Galerkin methods. Modell Simul Mater Sci Eng 1994;2:519-34.
117. Zhu T, Atluri SN. A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Comput Mech 1998;21:211-22.
118. Fernández-Méndez S, Huerta A. Imposing essential boundary conditions in mesh-free methods. Comput Methods Appl Mech Eng 2004;193:1257-73.
119. Chen JS, Wang HP. New boundary condition treatments in meshfree computation of contact problems. Comput Methods Appl Mech Eng 2000;187:441-68.
120. Günther FC, Liu WK. Implementation of boundary conditions for meshless methods. Comput Methods Appl Mech Eng 1998;163:205-30.
121. Gosz J, Liu WK. Admissible approximations for essential boundary conditions in the reproducing kernel particle method. Comput Mech 1996;19:120-35.
122. Wagner G, Liu WK. Application of essential boundary conditions in mesh-free methods: a corrected collocation method. Int J Numer Methods Eng 2000;47:1367-79.
123. Dolbow J, Belytschko T. Numerical integration of the Galerkin weak form in meshfree methods. Comput Mech 1999;23:219-30.
124. Bonet J, Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulation. Int J Numer Methods Eng 1999;47:1189-214.
125. De S, Bath KJ. The method of finite spheres with improved numerical integration. Comput Struct 2001;79:2183-96.
126. Chen JS, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. Int J Numer Methods Eng 2001;50:435-66.
127. Wang DD, Chen JS. Locking-free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation. Comput Methods Appl Mech Eng 2004;193:1065-83.
128. Chen JS, Yoon S, Wu CT. Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods. Int J Numer Methods Eng 2002;53:2587-615.
129. Chen JS, Wang DD. A constrained reproducing kernel particle formulation for shear deformable shell in Cartesian coordinates. Int J Numer Methods Eng 2006;68:151-72.
130. Zhao X, Liu GR, Dai KY, Zhong ZH, Li GY, Han X. A linearly conforming radial point interpolation method (LC-RPIM) for shells. Comput Mech 2009;43(3):321-441.
131. Zhao X, Liu GR, Dai KY, Zhong ZH, Li GY, Han X. Geometric nonlinear analysis of plates and cylindrical shells via a linearly conforming radial point interpolation method. Comput Mech 2008;42:133-44.
132. Liu GR, Zhao X, Dai KY, Zhong ZH, Li GY, Han X. A conforming radial point interpolation method for static and free vibration analysis of laminated composite plates. Compos Sci Technol 2008;68:354-66.
133. Gavete L, Benito JJ, Falćon S, Ruiz A. Penalty functions in constrained variational principles for element free Galerkin method. Eur J Mech A/Solids 2000;19:699-720.
134. Wang X, Liu WK. Extended immersed boundary method using FEM and RKPM. Comput Methods Appl Mech Eng 2004;193:1305-21.
135. Liu WK, Han W, Li S, Cao J. Reproducing kernel element method. Part I: theoretical formulation. Comput Meth Appl Mech Eng 2004;193:933-51.
136. Li S, Lu H, Han W, Liu WK, Simikins D. Reproducing kernel element method. Part II: globally conforming Im/Cm hierarchies. Comput Methods Appl Mech Eng 2004;193:953-87.
137. Lu H, Li S, Simkins Jr DC, Liu WK, Cao J. Reproducing kernel element method. Part III: generalized enrichment and application. Comput Methods Appl Mech Eng 2004;193:989-1011.
138. Belytschko T, Fleming M. Smoothing, enrichment and contact in the element-free Galerkin method. Comput Struct 1999;71:173-95.
139. Breitkopf P, Rassineux A, Touzot G, Villion P. Explicit form and efficient computation of MLS shape functions and their derivatives. Int J Numer Methods Eng 2000;48:451-66.
140. Lu YY, Belytschko T, Gu L. A new implementation of the element free Galerkin method. Comput Methods Appl Mech Eng 1994;113:397-414.
141. Belytschko T, Organ D, Krongauz Y. A coupled finite element free Galerkin methods. Comput Mech 1995;17:186-95.
142. Barry W, Saigal S. A three-dimensional element-free Galerkin elastic and elastoplastic formulation. Int J Numer Methods Eng 1999;46:671-93.
143. Kim DW, Kim Y. Point collocation methods using the fast moving least-square reproducing kernel approximation. Int J Numer Methods Eng 2003;56:1445-64.
144. Aluru NR. A point collocation method based on reproducing kernel approximations. Int J Numer Methods Eng 2000;47:1083-121.
145. Ponthot JP, Belytschko T. Arbitrary Lagrangian-Eulerian formulation for element-free Galerkin method. Comput Methods Appl Mech Eng 1998;152:19-46.
146. Liew KM, Wu HY, Ng TY. Meshless method for modeling of human proximal femur: treatment of nonconvex boundaries and stress analysis. Comput Mech 2002;28:390-400.
147. Liew KM, Zhao X, Ng TY. The element-free kp-Ritz method for vibration of laminated rotating cylindrical panels. Int J Struct Stab Dyn 2002;2:523-58.
148. Ren J, Liew KM. Mesh-free method revisited: two new approaches for the treatment of essential boundary conditions. Int J Comput Eng Sci 2002;3:219-33.
149. Ren J, Liew KM, Meguid SA. Modelling and simulation of the superelastic behaviour of shape memory alloys using the element-free Galerkin method. Int J Mech Sci 2002;44:2393-413.
150. Wang J, Liew KM, Tan MJ, Rajendran S. Analysis of rectangular laminated composite plates via FSDT meshless method. Int J Mech Sci 2002;44:1275-93.
151. Rajendran S, Liew KM. A novel unsymmetric 8-node plane element immune to mesh distortion under a quadratic displacement field. Int J Numer Methods Eng 2003;58:1713-48.
152. Liew KM, Chen XL. Mesh-free radial basis function method for buckling analysis of non-uniformly loaded arbitrarily shaped shear deformable plates. Comput Methods Appl Mech Eng 2004;193:205-24.
153. Liew KM, Chen XL. Mesh-free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in-plane point loads. Int J Numer Methods Eng 2004;60:1861-77.
154. Liew KM, He XQ, Tan MJ, Lim HK. Dynamic analysis of laminated composite plates with piezoelectric sensor/actuator patches using the FSDT mesh-free method. Int J Mech Sci 2004;46:411-31.
155. Liew KM, Ren J, Kitipornchai S. Analysis of the pseudoelastic behavior of a SMA beam by the element-free Galerkin method. Eng Anal Boundary Elem 2004;28:497-507.
156. Liew KM, Wang J, Ng TY, Tan MJ. Free vibration and buckling analyses of shear deformable plates based on FSDT meshfree method. J Sound Vib 2004;276:997-1017.
157. Ren J, Liew KM. Meshfree modelling and characterisation of thermomechanical behaviour of NiTi alloys. Eng Anal Boundary Elem 2005;29:29-40.
158. Ren J, Liew KM. Meshfree modeling and simulation of thermomechanical behaviors of shape memory alloys. Smart Mater Struct 2005;14:S302-11.
159. Liew KM, Rajendran S, Wang J. A quadratic plane triangular element immune to quadratic mesh distortions under quadratic displacement fields. Comput Methods Appl Mech Eng 2006;195:1207-23.
160. Liu Y, Hon YC, Liew KM. A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems. Int J Numer Methods Eng 2006;66:1153-78.
161. Liew KM, Cheng Y, Kitipornchai S. Analyzing the 2D fracture problems via the enriched boundary element-free method. Int J Solids Struct 2007;44:4220-33.
162. Liew KM, Feng C, Cheng Y, Kitipornchai S. Complex variable moving leastsquares method: a meshless approximation technique. Int J Numer Methods Eng 2007;70:46-70.
163. Liew KM, Lee YY, Ng TY, Zhao X. Dynamic stability analysis of composite laminated cylindrical panels via mesh-free kp-Ritz method. Int J Mech Sci 2007;49:1156-65.
164. Liew KM, Peng LX, Kitipornchai S. Nonlinear analysis of corrugated plates using a FSDT and a meshfree method. Comput Methods Appl Mech Eng 2007;196:2358-76.
165. Sun YZ, Liew KM. Mesh-free simulation of single-walled carbon nanotubes using higher order Cauchy-Born rule. Comput Mater Sci 2008;42:444-52.
166. Sun YZ, Liew KM. The buckling of single-walled carbon nanotubes upon bending: the higher order gradient continuum and mesh-free method. Comput Methods Appl Mech Eng 2008;197:3001-13.
167. Sun YZ, Liew KM. Application of the higher-order Cauchy-Born rule in meshfree continuum and multiscale simulation of carbon nanotubes. Int J Numer Methods Eng 2008;75:1238-58.
168. Zhang Z, Liew KM, Cheng YM. Coupling of the improved element-free Galerkin and boundary element methods for 2D elasticity problems. Eng Anal Boundary Elem 2008;32:100-7.
169. Zhao X, Lee YY, Liew KM. Free vibration analysis of functionally graded plates using the element-free kp-Ritz method. J Sound Vib 2008;319:918-39.
170. Liew KM, Peng LX, Kitipornchai S. Vibration analysis of corrugated Reissner-Mindlin plates using a mesh-free Galerkin method. Int J Mech Sci 2009;51:642-52.
171. Liew KM, Cheng YM. Complex variable boundary element-free method for two-dimensional elastodynamic problems. Comput Methods Appl Mech Eng 2009;198:3925-33.
172. Zhang Z, Zhao P, Liew KM. Improved element-free Galerkin method for two-dimensional potential problems. Eng Anal Boundary Elem 2009;33:547-54.
173. Zhang Z, Zhao P, Liew KM. Analyzing three-dimensional potential problems with the improved element-free Galerkin method. Comput Mech 2009;44:273-84.
174. Rajendran S, Zhang BR, Liew KM. A partition of unity-based 'FE-meshfree' QUAD4 element for geometric non-linear analysis. Int J Numer Methods Eng 2010;82:1574-608.
175. Zhang Z, Liew KM. Improved element-free method (IEFG) for solving three-dimensional elasticity problems. Interact Multiscale Mech 2010;3:123-44.
176. Zhao X, Liew KM. A mesh-free method for analysis of the thermal and mechanical buckling of functionally graded cylindrical shell panels. Comput Mech 2010;45:297-310.
177. Krysl P, Belytschko T. The element free Galerkin method for dynamic propagation of arbitrary 3-D cracks. Int J Numer Methods Eng 1999;44:767-800.
178. Ventura G, Xu JX, Belytschko T. A vector level set method and new discontinuity approximations for crack growth by EFG. Int J Numer Methods Eng 2002;54:923-44.
179. Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 2004;61:2316-43.
180. Rao BN, Rahman S. Mesh-free analysis of cracks in isotropic functionally graded materials. Eng Fract Mech 2003;70:1-27.
181. Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Comput Methods Appl Mech Eng 2007;196:2777-99.
182. Belytschko T, Organ D, Gerlach C. Element-free Galerkin methods for dynamic fracture in concrete. Comput Methods Appl Mech Eng 2000;187:385-99.
183. Askes H, Pamin J, Borst R. Dispersion analysis and element-free Galerkin solutions of second- and fourth-order gradient enhanced damaged models. Int J Numer Methods Eng 2000;49:811-32.
184. Li S, Liu WK, Rosakis AJ, Belytschko T. Mesh-free Galerkin simulation of dynamic shear band propagation and failure mode transition. Int J Solids Struct 2002;39:1213-40.
185. Li S, Hao W, Liu WK. Mesh-free shear banding in large deformation. Int J Solids Struct 2000;37:7185-206.
186. Jun S, Im S. Multiple-scale meshfree adaptivity for the simulation of adiabatic shear band formation. Comput Mech 2000;25:257-66.
187. Hao S, Liu WK, Klein PA, Rosakis AJ. Modeling and simulation of intersonic crack growth. Int J Solids Struct 2004;41:1773-99.
188. Sun Y, Hu YG, Liew KM. A mesh-free simulation of cracking and failure using the cohesive segments method. Int J Eng Sci 2007;45:541-53.
189. Zhang Z, Liew KM, Cheng YM, Lee YY. Analyzing 2D fracture problems with the improved element-free Galerkin method. Eng Anal Boundary Elem 2008;32:242-50.
190. Sun YZ, Zhang Z, Kitipornchai S, Liew KM. Analyzing the interaction between collinear interfacial cracks by an efficient boundary element-free method. Int J Eng Sci 2006;44:37-48.
191. Liew KM, Sun Y, Kitipornchai S. Boundary element-free method for fracture analysis of 2-D piezoelectric solids. Int J Numer Methods Eng 2007;69:729-49.
192. Noguchi H, Kawashima T, Miyamura T. Element free analyses of shell and spatial structures. Int J Numer Methods Eng 2000;47:1215-40.
193. Dolbow J, Belytschko T. Volumetric locking in the element free Galerkin method. Int J Numer Methods Eng 1999;46:925-42.
194. Huerta A, Fernan dez-Mendez S. Locking in the incompressible limit for the element-free Galerkin method. Int J Numer Methods Eng 2001;51:1361-83.
195. Kanok-Nukulchai W, Barry W, Saran-Yasoontorn K, Bouillard PH. On elimination of shear locking in the element-free Galerkin method. Int J Numer Methods Eng 2001;52:705-25.
196. Askes H, Borst R, Heeres O. Conditions for locking-free elasto-plastic analyses in the element-free Galerkin method. Comput Methods Appl Mech Eng 1999;173:99-109.
197. Liew KM, Lim HK, Tan MJ, He XQ. Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method. Comput Mech 2002;29:486-97.
198. Liew KM, Peng LX, Kitipornchai S. Analysis of symmetrically laminated folded plate structures using the meshfree Galerkin method. Mech Adv Mater Struct 2009;16:69-81.
199. Peng LX, Kitipornchai S, Liew KM. Bending analysis of folded plates by the FSDT meshless method. Thin-walled Struct 2006;44:1138-60.
200. Peng LX, Kitipornchai S, Liew KM. Analysis of rectangular stiffened plates under uniform lateral load based on FSDT and element-free Galerkin method. Int J Mech Sci 2005;63:1014-40.
201. Peng LX, Liew KM, Kitipornchai S. Analysis of stiffened corrugated plates based on the FSDT via the mesh-free method. Int J Mech Sci 2007;49:364-78.
202. Dai KY, Liu GR, Han X, Lim KM. Thermomechanical analysis of functionally graded material (FGM) plates using element-free Galerkin method. Comput Struct 2005;83:1487-502.
203. Rabczuk T, Eibl J. Numerical analysis of prestressed concrete beams using a coupled element free Galerkin/finite element approach. Int J Solids Struct 2004;41:1061-80.
204. Lee YY, Zhao X, Liew KM. Thermoelastic analysis of functionally graded plates using the element free kp-Ritz method. Smart Mater Struct 2009;18:035007.
205. Zhao X, Lee YY, Liew KM. Thermoelastic and vibration analysis of functionally graded cylindrical shells. Int J Mech Sci 2009;51:694-707.
206. Liu CW, Taciroglu E. A semi-analytic meshfree method for Almansi-Michell problems of piezoelectric cylinders. Int J Solids Struct 2008;45:2379-98.
207. Bobaru F, Mukherjee S. Meshless approach to shape optimization of linear thermoelastic solids. Int J Numer Methods Eng 2002;53:765-96.
208. Bobaru F, Mukherjee S. Shape sensitivity analysis and shape optimization in planar elasticity using the element-free Galerkin method. Comput Methods Appl Mech Eng 2001;190:4319-37.
209. Zhang ZQ, Zhou JX, Zhou N, Wang XM, Zhang L. Shape optimization using reproducing kernel particle method and an enriched genetic algorithm. Comput Methods Appl Mech Eng 2005;194:4048-70.
210. Kim NH, Choi KK, Chen JS, Botkin ME. Meshfree analysis and design sensitivity analysis for shell structures. Int J Numer Methods Eng 2003;53:2087-116.
211. Kim NH, Yi K, Choi KK. A material derivative approach in design sensitivity of three-dimensional contact problems. Int J Solids Struct 2002;39:2087-108.
212. Liew KM, Peng LX, Kitipornchai S. Buckling of folded plate structures subjected to partial in-plane edge loads by the FSDT meshfree Galerkin method. Int J Numer Methods Eng 2006;65:1495.
213. Liew KM, Peng LX, Kitipornchai S. Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory. Comput Mech 2006;38:61-75.
214. Peng LX, Liew KM, Kitipornchai S. Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method. J Sound Vib 2006;289:421-49.
215. Zhao X, Lee YY, Liew KM. Mechanical and thermal buckling analysis of functionally graded plates. Compos Struct 2009;90:161-71.
216. Liu GR, Chen XL. A mesh-free method for static and free vibration analysis of thin plates of complicated shape. J Sound Vib 2001;241:839-55.
217. Chen XL, Liu GR, Lim SP. An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape. Compos Struct 2003;59:279-89.
218. Liu L, Liu GR, Tan VBC. Element free method for static and free vibration analysis of spatial thin shell structures. Comput Meth Appl Mech Eng 2002;191:5923-42.
219. Zhao X, Liew KM, Ng TY. Vibration analysis of laminated composite cylindrical panels via a mesh-free approach. Int J Solids Struct 2003;40:161-80.
220. Zhao X, Ng TY, Liew KM. Free vibration of laminated two-side simply-supported cylindrical panels via the kp-Ritz method. Int J Mech Sci 2004;46:123-42.
221. Liew KM, Ng TY, Zhao X, Reddy JN. Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells. Comput Methods Appl Mech Eng 2002;191:37-8.
222. Liew KM, Ng TY, Zhao X. Free vibration analysis of conical shells via the element-free kp-Ritz method. J Sound Vib 2005;281:627-45.
223. Zhao X, Liew KM, Ng TY. The element-free kp-Ritz method for free vibration analysis of conical shell panels. J Sound Vib 2006;295:906-22.
224. Zhao X, Lee YY, Liew KM. Free vibration analysis of functionally graded plates using element free kp-Ritz method. J Sound Vib 2009;319:918-39.
225. Liew KM, Hu YG, Zhao X, Ng TY. Dynamic stability analysis of composite laminated cylindrical shells via the mesh-free kp-Ritz method. Comput Methods Appl Mech Eng 2006;196:147-60.
226. Liew KM, Ng TY, Zhao X. Dynamic stability of rotating cylindrical shells subjected to periodic axial loads. Int J Solids Struct 2006;43:7553-70.
227. Peng LX, Kitipornchai S, Liew KM. Free vibration analysis of folded plate structures by the FSDT mesh-free method. Comput Mech 2007;39:799-814.
228. Amirani MC, Khalili SMR, Nemati N. Free vibration analysis of sandwich beam with FG core using the element free Galerkin method. Compos Struct 2009;90:373-9.
229. Liu WK, Hao W, Chen Y, Jun S, Gosz J. Multiplesolution reproducing kernel particle methods. Comput Mech 1997;20:295-309.
230. Liu WK, Chen Y. Wavelet and multiple scale reproducing kernel particle methods. Int J Numer Methods Fluids 1995;21:901-31.
231. Liu WK, Chen Y, Chang CT, Belytschko T. Advances in multiple scale kernel particle methods. Comput Mech 1996;18:73-111.
232. Liu WK, Hao S, Belytschko T, Li S, Chang CT. Multi-scale methods. Int J Numer Methods Eng 2000;47:1343-61.
233. Liu WK, Jun S. Multiple-scale reproducing kernel particle methods for large deformation problems. Int J Numer Methods Eng 1998;41:1339-62.
234. Liu WK, Hao S, Belytschko T, Li S, Chang CT. Multiple scale meshfree methods for damage fracture and localization. Comput Mater Sci 1999;16:197-205.
235. Li S, Dong Q, Liu WK, Belytschko T. A meshfree contact-detection algorithm. Comput Methods Appl Mech Eng 2001;190:3271-92.
236. Park HS, Liu WK. An introduction and tutorial on multiple-scale analysis in solids. Comput Methods Appl Mech Eng 2004;193:1733-72.
237. Lee SH, Kim HJ, Jun S. Two scale meshfree method for the adaptivity of 3-D stress concentration problems. Comput Mech 2000;26:376-87.
238. Xiong S, Liu WK, Cao J, Li CS, Rodrigue JMC, Martin PAF. Simulation of bulk metal forming processes using the reproducing kernel particle method. Comput Struct 2005;83:574-87.
239. Yoon S, Chen JS. Accelerated meshfree method for metal forming simulation. Finite Elem Anal Des 2002;38:937-48.
240. Shangwu X, Liu WK, Cao J, Rodrigues JMC, Martin PF. On the the utilization of reproducing kernel particle method for the numerical simulation of plane strain rolling. Int J Mach Tools Manuf 2003;43:89-102.
241. Liew KM, Ng TY, Wu YC. Meshfee method for large deformation analysis-a reproducing kernel particle approach. Eng Struct 2002;24:543-51.
242. Liew KM, Ren J, Reddy JN. Numerical simulation of thermomechanical behaviours of shape memory alloys via a non-linear mesh-free Galerkin formulation. Int J Numer Methods Eng 2005;63:1014-40.
243. Liew KM, Wang J, Tan MJ, Rajendran S. Nonlinear analysis of laminated plates using the mesh-free kp-Ritz method based on FSDT. Comput Methods Appl Mech Eng 2004;193:4763-79.
244. Liew KM, Wang J, Tan MJ, Rajendran S. Postbuckling analysis of laminated composite plates using the mesh-free kp-Ritz method. Comput Methods Appl Mech Eng 2006;195:551-70.
245. Zhao X, Hu YG, Liew KM. Geometrically nonlinear analysis of cylindrical shells using the element-free kp-Ritz method. Eng Anal Boundary Elem 2007;31:783-92.
246. Zhao X, Liew KM. Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method. Comput Methods Appl Mech Eng 2009;198:2796-811.
247. Zhao X, Liew KM. Geometrically nonlinear analysis of functionally graded shells. Int J Mech Sci 2009;51:131-44.
248. Belinha J, Dinis LMJS. Nonlinear analysis of plates and laminates using the element free Galerkin method. Compos Struct 2007;78:337-50.
249. Ren J, Liew WK, Merguid SA. Modelling and simulation of the superelastic behaviour of shape memeory alloys using the element-free Galerkin method. Int J Mech Sci 2002;44:2393-413.
250. Liew KM, Peng LX, Kitipornchai S. Geometric non-linear analysis of folded plate structures by the spline strip kernel particle method. Int J Numer Methods Eng 2007;71:1102-33.
251. Chen SS, Liu YH, Cen ZZ. Lower bound shakedown analysis by using the element free Galerkin method and non-linear programming. Comput Methods Appl Mech Eng 2008;197:3911-21.
252. Barbieri E, Meo M, Polimeno U. Nonlinear wave propagation in damaged hysteretic materials using a frequency domain-based PM space formulation. Int J Solids Struct 2009;46:165-80.
253. Areias RabczukT, PMA BelyyschkoT. A meshfree thin shell method for nonlinear dynamic fracture. Int J Numer Methods Eng 2007;72:524-48.
254. Li S, Liu WK. Reproducing kernel hierarchical partition of unity, part I-formulation and theory. Int J Numer Methods Eng 1999;45:251-88.
255. Li S, Liu WK. Reproducing kernel hierarchical partition of unity. Part II - applications. Int J Numer Methods Eng 1999;45:289-317.
256. Rahman S, Rao BN. An element-free Galerkin method for probalistic mechanics and reliability. Int J Solids Struct 2001;38:9313-30.
257. Liew KM, Cheng YM, Kitipornchai S. Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems. Int J Numer Methods Eng 2006;65:1310-32.
258. Liew KM, Cheng YM, Kitipornchai S. Boundary element-free (BEFM) for twodimensional elastodynamic analysis using Laplace transform. Int J Numer Methods Eng 2005;64:1610-27.
259. Kitipornchai S, Liew KM, Cheng YM. A boundary element-free method (BEFM) for three-dimensional elasticity problems. Comput Mech 2005;36:13-20.
260. Karim MR, Nogami T, Wang JG. Analysis of transient response of saturated porus elstic soil under cyclic loading using element-free Galerkin method. Int J Solids Struct 2002;39:6011-33.
261. Shishvan SS, Noorzad A, Ansari A. A time integration algorithm for linear transient analysis based on the reproducing kernel method. Comput Methods Appl Mech Eng 2009;198:3361-77.
262. Danielson KT, Hao S, Liu WK, Uras RA, Li S. Parallel computing of meshless methods for explicit dynamic analysis. Int J Numer Methods Eng 2000;47:1323-41.
263. Rabczuk T, Belytschko T. Adaptivity of structured meshfree particle methods in 2D and 3D. Int J Numer Methods Eng 2005;63:1559-82.
264. Qian LF, Batra RC, Chen LM. 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 2004;35:685-97.
265. Qian LF, Batra RC, Chen LM. Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov-Galerkin method. Comput Mech 2004;33:263-73.
266. Qian LF, Batra RC. Design of bidirectional functionally graded plate for pptimal natural frequencies. J Sound Vib 2005;280:415-24.
267. Qian LF, Batra RC. Transient thermoelastic deformations of a thick functionally graded plate. J Therm Stresses 2004;27:705-40.
268. Ferreira AJM, Batra RC, Roque CMC, Qian LF, Martins PALS. Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos Struct 2005;69:449-57.
269. Qian LF, Batra RC. 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 2005;35:214-26.
270. Ferreira AJM, Batra RC, Roque CMC, Qian LF, Jorge RMN. Natural frequencies of functionally graded plates by a meshless method. Compos Struct 2006;75:593-600.
271. Gilhooley DF, Batra RC, Xiao JR, McCarthy MA, Gillespie JW. 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 2007;80:539-52.
272. Ferreira AJM, Fasshauer GE, Batra RC, Rodrigues JD. Static deformations and vibration analysis of composite and sandwich plates using a Layerwise theory and RBF-PS discretizations with optimal shape parameter. Compos Struct 2008;86:328-43.
273. Ferreira AJM, Fasshauer GE, Batra RC. Natural frequencies of thick plates made of orthotropic, monoclinic, and hexagonal materials by a meshless method. J Sound Vib 2009;319:984-92.