Applications of the MLPG method in engineering & sciences: A review

CMES - Computer Modeling in Engineering and Sciences

Volumn 92, Issue 5, 2013, Pages 423-475

  Sladek, J ^a   Stanak, P ^a   Han, Z D ^b   Sladek, V ^a   Atluri, S N ^b  

^a INSTITUTE OF CHEMISTRY   (Slovakia)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Local weak forms; Meshless local approximation schemes for trial and test functions; Meshless local Petrov Galerkin (MLPG) method; Numerical applications

Indexed keywords

AXISYMMETRIC PROBLEMS; FINITE ELEMENT MESHES; HEAT TRANSFER AND FLUID FLOW; LOCAL APPROXIMATION; LOCAL WEAK FORM; MESHLESS LOCAL PETROV-GALERKIN METHOD; NUMERICAL APPLICATIONS; SCIENTIFIC DISCIPLINE;

ELASTICITY; PARTIAL DIFFERENTIAL EQUATIONS; RESEARCH; TEST FACILITIES;

NUMERICAL METHODS;

EID: 84883025155     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (260)

1. Abbasbandy, S.; Shirzadi, A. (2011): MLPG method for two-dimensional diffusion equation with Neumann's and non-classical boundary conditions. Applied Numerical Mathematics, vol. 61, No. 2, pp. 170-180.
2. Abbasbandy, S.; Sladek, V.; Shirzadi, A.; Sladek, J. (2011): Numerical simulations for coupled pair of diffusion equations by MLPG method. CMES: Computer Modeling in Engineering & Sciences, vol. 71, No. 1, pp. 15-37.
3. Akbari, A.; Bagri, A.; Bordas, S. P. A.; Rabczuk, T. (2010): Analysis of Thermoelastic Waves in a Two-Dimensional Functionally Graded Materials Domain by the Meshless Local Petrov-Galerkin (MLPG) Method. CMES: Computer Modeling in Engineering & Sciences, vol. 65, No. 1, pp. 27-74.
4. Aluru, N. R.; Li, G. (2001): Finite cloud method: A true meshless technique based on reproducing kernel approximation. Int. J. Numer. Methods Eng., vol. 50, pp. 2373-2410.
5. Anderson T. L. (2005): Fracture Mechanics -Fundamentals and Applications, 3rd ed.,CRC Press, Boca Raton.
6. Andreaus, U.; Batra, R. C.; Porfiri, M. (2005): Vibrations of Cracked Euler-Bernoulli Beams using Meshless Local Petrov-Galerkin (MLPG) Method. CMES: Computer Modeling in Engineering & Sciences, vol. 9, No. 2, pp. 111-131.
7. Arefmanesh, A.; Najafi, M.; Abdi, H. (2005): A meshless local Petrov-Galerkin method for fluid dynamics and heat transfer applications. Journal of Fluids Engineering, vol. 127, pp. 647-655.
8. Arefmanesh, A.; Najafi, M.; Abdi, H. (2008): Meshless local Petrov-Galerkin method with unity test function for non-isothermal fluid flow. CMES: Computer Modeling in Engineering & Sciences, vol. 25, No. 1, pp. 9-22.
9. Arefmanesh, A.; Najafi, M.; Nikfar, M. (2010): MLPG Application of Nanofluid Flow Mixed Convection Heat Transfer in a Wavy Wall Cavity. CMES: Computer Modeling in Engineering & Sciences, vol. 69, No. 2, pp. 91-118.
10. Atluri, S. N. (2004): The Meshless Method (MLPG) for Domain and BIE Discretizations, Tech Science Press, Forsyth.
11. Atluri, S. N.; Cho, J. Y.; Kim, H. G. (1999): Analysis of the beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations, Comput. Mech., vol. 24, pp. 334-347.
12. Atluri, S. N.; Han, Z. D.; Shen, S. (2003): Meshless Local Patrov-Galerkin (MLPG) approaches for weakly-singular traction & displacement boundary integral equations, CMES: Computer Modeling in Engineering & Sciences, vol. 4, no. 5, pp. 507-517.
13. Atluri, S. N.; Han, Z. D.; Rajendran, A. M. (2004): A New Implementation of the Meshless Volume Method, Through the MLPG "Mixed" Approach. CMES: Computer Modeling in Engineering & Sciences, vol. 6, No. 6, pp. 491-513.
14. Atluri, S. N.; Kim, H. G.; Cho, J. Y. (1999): A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods. Comput. Mech., vol. 24, pp. 348-372.
15. Atluri, S. N.; Liu, H. T.; Han, Z. D. (2006a): Meshless local Petrov-Galerkin (MLPG) mixed collocation method for elasticity problems, CMES: Computer Modeling in Engineering & Sciences, vol. 14, no. 3, pp. 141-152.
16. Atluri, S. N.; Liu, H. T.; Han, Z. D. (2006b): Meshless Local Petrov-Galerkin (MLPG) Mixed Finite Difference Method for Solid Mechanics. CMES: Computer Modeling in Engineering & Sciences, vol. 15, No. 1, pp. 1-16.
17. Atluri, S. N.; Shen, S. (2002a): The Meshless Local Petrov-Galerkin (MLPG) Method, Tech Science Press, Forsyth, GA.
18. Atluri, S. N.; Shen, S. (2002b): The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple & Less-costly Alternative to the Finite Element and Boundary Element Methods. CMES: Computer Modeling in Engineering & Sciences, vol. 3, No. 1, pp. 11-51.
19. Atluri, S. N.; Shen, S. (2005): Simulation of a 4th Order ODE: Illustrations of Various Primal & Mixed MLPG Methods. CMES: Computer Modeling in Engineering & Sciences, vol. 7, No. 3, pp. 241-268.
20. Atluri, S. N.; Sladek, J. (Eds.) (2009): Advances in the MLPG Meshless Methods. Tech. Sci. Press, Duluth.
21. Atluri, S. N.; Sladek, J.; Sladek, V.; Zhu, T. (2000): The local boundary integral equation (LBIE) and its meshless implementation for linear elasticity. Comput. Mech., vol. 25, pp. 180-198.
22. Atluri, S. N.; Zhu, T. (1998a): "A New Meshless Local Petrov-Galerkin (MLPG) Approach in Computational Mechanics", Computational Mechanics, vol. 22, pp. 117-127.
23. Atluri, S. N.; Zhu, T. (1998b): A new meshless local Petrov-Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation. Comput. Model. Simul. Eng., vol. 3, pp. 187-196.
24. Atluri, S. N.; Zhu, T. (2000): The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Computational Mechanics, vol. 25, pp. 169-179.
25. Augarde, C. E.; Deeks, A. J. (2005): On the effects of nodal distributions for imposition of essential boundary conditions in the MLPG meshfree method. Communications in Numerical Methods in Engineering, vol. 21, pp. 389-395.
26. Avila, R.; Atluri, S. N. (2009): Numerical Solution of Non-steady Flows, Around Surfaces in Spatially and Temporally Arbitrary Motions, by using the MLPG method. CMES: Computer Modeling in Engineering & Sciences, vol. 54, No. 1, pp. 15-64.
27. Avila, R.; Han, Z.; Atluri, S. N. (2011): A novel MLPG-Finite-Volume Mixed Method for Analyzing Stokesian Flows & Study of a New Vortex Mixing Flow. CMES: Computer Modeling in Engineering & Sciences, vol. 71, No. 4, pp. 363-396.
28. Babuska, I.; Melenk, J. M. (1997): The partition of unity method. Int. J. Num. Meth. Engrg, vol. 40, pp. 727-758.
29. Balas, J.; Sladek, J.; Sladek, V. (1989): Stress analysis by boundary element method. Elsevier, Amsterdam.
30. Baltacioglu, A. K.; Civalek, O. (2010): Geometrically Nonlinear Analysis of Anisotropic Composite Plate Resting on Nonlinear Elastic Foundations. CMES: Computer Modeling in Engineering & Sciences, vol. 68, No. 1, pp. 1-23.
31. Banerjee, P. K. (1994): The Boundary Element Methods in Engineering. Mc Graw-Hill, London.
32. Baradaran, G. H.; Mahmoodarabadi, M. J. (2010): Parametric study of the MLPG method for the analysis of three-dimensional steady state heat conduction problems. Journal of Mechanical Engineering, vol. 61, pp. 31-61.
33. Batra, R, C.; Ching, H. K. (2002): Analysis of Elastodynamic Deformations near a Crack/Notch Tip by the Meshless Local Petrov-Galerkin (MLPG) Method. CMES: Computer Modeling in Engineering & Sciences, vol. 3, No. 6, pp. 717-730.
34. Batra, R. C.; Porfiri, M.; Spinello, D. (2004): Treatment of material discontinuity in two mehless local Petrov-Galerkin (MLPG) formulations of axisymmetric transient heat conduction. Int J Numer Methods Eng, vol. 61, pp. 2461-2479.
35. Belytschko, T.; Krogauz, Y.; Organ, D.; Fleming, M.; Krysl, P. (1996): Meshless methods; an overview and recent developments. Comp. Meth. Appl. Mech. Engn., vol. 139, pp. 3-47.
36. Belytschko, T.; Lu, Y. Y.; Gu, L. (1994): Element-free Galerkin methods. Int. J. Numer. Methods. Eng., vol. 37, pp. 229-256.
37. Benjeddou, A. (2000): Advances in piezoelectric finite element modeling of adaptive structural elements: A survey. Computers and Structures, vol. 76, pp. 347-363.
38. Bergamaschi, L.; Martinez, A.; Pini, G. (2009): An Efficient Parallel MLPG Method for Poroelastic Models. CMES: Computer Modeling in Engineering & Sciences, vol. 49, No. 3, pp. 191-215.
39. Bishay P. L.; Atluri, S. N. (2012): High-Performance 3D Hybrid/Mixed, and Simple 3D Voronoi Cell Finite Elements, for Macro-& Micro-mechanical Modeling of Solids,Without Using Multi-field Variational Principles, CMES: Computer Modeling in Engineering and Sciences, Volume: 84, Issue: 1, pp. 41-97.
40. Bishay P. L.; Atluri, S. N. (2013): 2D and 3D Multiphysics Voronoi Cells, Based on Radial Basis Functions, for Direct Mesoscale Numerical Simulation (DMNS) of the Switching Phenomena in Ferroelectric Polycrystalline Materials, CMC: Computers Materials and Continua, Volume: 33, Issue: 1, pp. 19-62.
41. Bishay P. L.; Sladek, J.; Sladek, V.; Atluri, S. N. (2012): Analysis of Functionally Graded Magneto-Electro-Elastic Composites Using Hybrid/Mixed Finite Elements and Node-Wise Material Properties, CMC: Computers, Materials & Continua, Volume: 29, Issue: 3, pp. 213-262.
42. Brebbia, C. A.; Telles, J. C. F.; Wrobel, L. C. (1984): Boundary Element Techniques. Springer, Berlin.
43. Brooks, A. N.; Hughes, T. J. R. (1982): Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng., vol. 32, pp. 199-259.
44. Chen, L.; Liew, K. M. (2011): A local Petrov-Galerkin approach with moving Kriging interpolation for solving transient heat conduction problems. Computational Mechanics, vol. 47, No. 4, pp. 455-467.
45. Chen, W. (2000): New RBF collocation methods and kernel RBF with applications Meshfree methods for partial differential equations. Springer Verlag, pp. 75-86.
46. Cheng, R. J.; Liew, K. M. (2012): A meshless analysis of three-dimensional transient heat conduction problems. Eng. Anal. Bound. Elem., vol. 36, pp. 203-210.
47. Ching H. K.; Batra R. C. (2001): Determination of Crack Tip Fields in Linear Elastostatics by the Meshless Local Petrov-Galerkin (MLPG) Method. Computer Modeling in Engineering & Sciences, Vol. 2(2), pp. 273-289.
48. Ching, H. K.; Chen, J. K. (2006): Thermomechanical Analysis of Functionally Graded Composites under Laser Heating by the MLPG Method. CMES: Computer Modeling in Engineering & Sciences, vol. 13, No. 3, pp. 199-217.
49. Cleary, P. W.; Monaghan, J. J. (1999): Conduction modeling using smoothed particle hydrodynamics. J. Comput. Phys., vol. 148, pp. 227-264.
50. Dang, T. B.; Sankar, B. V. (2008): Meshless Local Petrov-Galerkin Micromechanical Analysis of Periodic Composites Including Shear Loading. CMES: Computer Modeling in Engineering & Sciences, vol. 26, No. 3, pp. 169-187.
51. Dehghan, M.; Mirzaei, D. (2008): The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional non-linear Schrodinger equation. Eng. Anal. Bound. Elem., vol. 32, pp. 747-756.
52. Dehghan, M.; Mirzaei, D. (2009): Meshless Local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity. Applied Numerical Mathematics, vol. 59, pp. 1043-1058.
53. Dominguez, J. (1993): Boundary Elements in Dynamics. CMP, Southampton, Elsevier Applied Science, London.
54. Dong, L.; Atluri, S. N. (2012a): T-Trefftz Voronoi Cell Finite Elements with eastic/rigid inclusions or voids for micromechanical analysis of composite and porous materials, CMES: Computer Modeling in Engineering and Sciences, Volume: 83, Issue: 2, pp. 183-220.
55. Dong, L.; Atluri, S. N. (2012b): A Simple Multi-Source-Point Trefftz Method for Solving Direct/Inverse SHM Problems of Plane Elasticity in Arbitrary Multiply-Connected Domains, CMES: Computer Modeling in Engineering and Sciences, Volume: 85, Issue: 1, pp. 1-43.
56. Dong, L.; Atluri, S. N. (2012c): SGBEM (Using Non-hyper-singular Traction BIE), and Super Elements, for Non-Collinear Fatigue-growth Analyses of Cracks in Stiffened Panels with Composite-Patch Repairs. CMES: Computer Modeling in Engineering & Sciences, vol.89, no. 5, pp. 417-458.
57. Dong, L.; Atluri, S. N. (2012d): Development of 3D T-Trefftz Voronoi Cell Finite Elements with/without Spherical Voids &/or Elastic/Rigid Inclusions for Micromechanical Modeling of Heterogeneous Materials, CMC: Computers Materials and Continua, Volume: 29, Issue: 2, pp. 169-211.
58. Dong, L.; Atluri, S. N. (2012e): Development of 3D Trefftz Voronoi Cells with Ellipsoidal Voids and/or Elastic/Rigid Inclusions for Micromechanical Modeling of Heterogeneous Materials, CMC: Computers Materials and Continua, Volume: 30, Issue: 1, pp. 39-81.
59. Dong, L.; Atluri, S. N. (2013a): SGBEM Voronoi Cells (SVCs), with Embedded Arbitrary-Shaped Inclusions, Voids, and/or Cracks, for Micromechanical Modeling of Heterogeneous Materials. CMC: Computers, Materials & Continua, Volume: 33, Issue: 2, pp. 111-154.
60. Dong, L.; Atluri, S. N. (2013b): Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 1: 2D Structures, CMES: Computer Modeling in Engineering & Sciences, Volume: 90, Issue: 2, pp. 91-146.
61. Dong, L.; Atluri, S. N. (2013c): Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 2: 3D Solids, CMES: Computer Modeling in Engineering & Sciences, Volume: 90, Issue: 5, pp. 379-413.
62. Feng, W. J.; Han, X.; Li, Y. S. (2009): Fracture Analysis for Two-dimensional Plane Problems of Nonhomogeneous Magneto-electro-Thermo-elastic Plates Subjected to Thermal Shock by Using the Meshless Local Petrov-Galerkin Method. CMES: Computer Modeling in Engineering & Sciences, vol. 48, No. 1, pp. 1-26.
63. Ferreira, A. J. M.; Roque, C. M. C.; Jorge, R. M. N. (2006): Modelling crossply laminated elastic shells by a higher-order theory and multiquadrics. Computers and Structures, vol. 84, pp. 1288-1299.
64. Ferronato, M.; Mazzia, A.; Pini, G. (2010): A Finite Element enrichment technique by the Meshless Local Petrov-Galerkin method. CMES: Computer Modeling in Engineering & Sciences, vol. 62, No. 2, pp. 205-224.
65. Gao, L.; Liu, K.; Liu, Y. (2006): Applications of MLPG Method in Dynamic Fracture Problems. CMES: Computer Modeling in Engineering & Sciences, vol. 12, No. 3, pp. 181-195.
66. Garcia-Sanchez, F.; Rojas-Diaz, R.; Saez, A.; Zhang, Ch. (2007): Fracture of magnetoelectroelastic composite materials using boundary element method (BEM). Theoretical and Applied Fracture Mechanics, vol. 47, pp. 192-204.
67. Gingold, R. A.; Monaghan, J. J. (1977): Smoothed particle hydrodynamics: Theory and application to non-spherical stars. Mon. Not. Roy. Astron. Soc., vol. 181, pp. 375-389.
68. Gu Y. T.; Liu G. R. (2001a): A Meshless Local Petrov-Galerkin (MLPG) Method for Free and Forced Vibration Analyses for Solids. Computational Mechanics, vol. 27, pp. 188-198.
69. Gu, Y. T.; Liu, G. R. (2001b): A meshless local Petrov-Galerkin (MLPG) formulation for static and free vibration analyses of thin plates. Computer Model. Engng. Sci., vol. 2, pp. 463-476.
70. Gunther, F.; Liu,W. K.; Diachin, D.; Christon, M. A. (2000): Multi-scale meshfree parallel computations for viscous, compressible flows. Comput. Methods Appl. Mech. Eng., vol. 190, No. (3-4), pp.279-303.
71. Hagihara, S.; Tsunori, M.; Ikeda, T.; Miyazaki, N. (2007): Application of Meshfree Method to Elastic-Plastic Fracture Mechanics Parameter Analysis. CMES: Computer Modeling in Engineering & Sciences, vol. 17, No. 2, pp. 63-72.
72. Han, Z. D.; Atluri, S. N. (2002): SGBEM (for Cracked Local Subdomain) -FEM (for uncracked global Structure) Alternating Method for Analyzing 3D Surface Cracks and Their Fatigue-Growth. CMES: Computer Modeling in Engineering & Sciences, vol.3, no.6, pp.699-716.
73. Han, Z. D.; Atluri, S. N. (2003a): On Simple Formulations of Weakly-Singular Traction & Displacement BIE, and Their Solutions through Petrov-Galerkin Approaches. CMES: Computer Modeling in Engineering & Sciences, vol. 4, no. 1, pp.5-20.
74. Han, Z. D.; Atluri, S. N. (2003b): Truly Meshless Local Petrov-Galerkin (MLPG) Solutions of Traction & Displacement BIEs. CMES: Computer Modeling in Engi neering & Sciences, vol. 4, No. 6, pp. 665-678.
75. Han, Z. D.; Atluri, S. N. (2004a): A Meshless Local Petrov-Galerkin (MLPG) approaches for solving 3-D Problems in elasto-statics. CMES: Computer Modeling in Engineering & Sciences, vol. 6, No. 2, pp. 169-188.
76. Han, Z. D.; Atluri, S. N. (2004b): A Meshless Local Petrov-Galerkin (MLPG) Approach for 3-Dimensional Elasto-dynamics. CMC: Computers, Materials & Continua, vol. 1, No. 2, pp. 129-140.
77. Han, Z. D.; Atluri, S. N. (2007): A Systematic Approach for the Development ofWeakly-Singular BIEs. CMES: Computer Modeling in Engineering & Sciences, vol. 21, No. 1, pp. 41-52.
78. Han Z. D.; Liu H. T.; Rajendran, A. M; Atluri, S. N. (2006): The Applications of Meshless Local Petrov Galerkin (MLPG) Approaches in High-Speed Impact, Penetration and Perforation Problems, CMES: Computer Modeling in Engineering & Sciences, vol. 14, no. 2, pp. 119-128.
79. Han, Z. D.; Rajendran, A. M.; Atluri, S. N. (2005): Meshless Local Petrov-Galerkin (MLPG) Approaches for Solving Nonlinear Problems with Large Deformations and Rotations. CMES: Computer Modeling in Engineering & Sciences, vol. 10, No. 1, pp. 1-12.
80. Heaney, C.; Augarde, Ch.; Deeks, A. (2010): Modelling Elasto-Plasticity Using the Hybrid MLPG Method. CMES: Computer Modeling in Engineering & Sciences, vol. 56, No. 2, pp. 153-177.
81. Hosseini, S. M.; Shahabian, F.; Sladek, J.; Sladek, V. (2011): Stochastic Meshless Local Petrov-Galerkin (MLPG) Method for Thermo-ElasticWave Propagation Analysis in Functionally Graded Thick Hollow Cylinders. CMES: Computer Modeling in Engineering & Sciences, vol. 71, No. 1, pp. 39-66.
82. Hosseini, S. M.; Sladek, J.; Sladek, V. (2011): Meshless local Petrov-Galerkin method for coupled thermoelasticity analysis of a functionally graded thick hollow cylinder. Eng. Anal. Bound. Elem., vol. 35, pp. 827-835.
83. Jarak, T.; Soric, J. (2008): Analysis of rectangular squatre plates by the mixed Meshless Local Petrov-Galerkin (MLPG) approach. CMES: Computer Modeling in Engineering & Sciences, vol. 38, No. 3, pp. 231-261.
84. Jarak, T.; Soric, J.; Hoster, J. (2007): Analysis of Shell Deformation Responses by the Meshless Local Petrov-Galerkin (MLPG) Approach. CMES: Computer Modeling in Engineering & Sciences, vol. 18, No. 3, pp. 235-246.
85. Johnson, J. N.; Owen, J. M. (2007): A Meshless Local Petrov-Galerkin Method for Magnetic Diffusion in Non-magnetic Conductors. CMES: Computer Modeling in Engineering & Sciences, vol. 22, No. 3, pp. 165-188.
86. Kansa, E. J. (1990): Multiquadrics-A scattered data approximation scheme with applications to computational fluid dynamics-II. Solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers and Mathematics with Applications, vol. 19, pp. 147-161.
87. Kim, H. G.; Atluri, S. N. (2000): Arbitrary placement of secondary nodes, and error control, in the meshless local Petrov-Galerkin (MLPG) method. CMES: Computer Modeling in Engineering & Sciences, vol.1, No. 3, pp. 11-32.
88. Lancaster, P.; Salkauskas, K. (1981): Surfaces generated by moving least square method. Mathematics of Computations, vol. 37, pp. 141-158.
89. Lam, K. Y.; Wang, Q. X.; Hua, L. (2004): A novel meshless approach -local Kriging (LoKriging) method with two-dimensional structural analysis. Comput. Mech., vol. 33, No. 3, pp. 235-244.
90. Li, Q.; Shen, S.; Han, Z. D.; Atluri, S. N. (2003): Application of Meshless Local Petrov-Galerkin (MLPG) to Problems with Singularities, and Material Discontinuities, in 3-D Elasticity. CMES: Computer Modeling in Engineering & Sciences, vol. 4, No. 5, pp. 571-585.
91. Li, Q. H.; Chen, S. S.; Kou, G. X. (2011): Transient heat conduction analysis using the MLPG method and modified precise time step integration method. Journal of Computational Physics, vol. 230, No. 7, pp. 2736-2750.
92. Li, Q.; Soric, J.; Jarak, T.; Atluri, S. N. (2005): A locking-free meshless local Petrov-Galerkin formulation for thick and thin plates. Journal of Computational Physics, vol. 208, No. 1, pp. 116-133.
93. Li, S.; Atluri, S. N. (2008a): Topology-optimization of Structures Based on the MLPG Mixed Collocation Method. CMES: Computer Modeling in Engineering & Sciences, vol. 26, No. 1, pp. 61-74.
94. Li, S.; Atluri, S. N. (2008b): The MLPG mixed collocation method for material orientation and topology optimization of anisotropic solids and structures. CMES: Computer Modeling in Engineering & Sciences, vol. 30, No. 1, pp. 37-56.
95. Li, S.; Liu, W. K. (2002): Meshfree and particle methods and their application. Applied Mechanics Reviews, vol. 55, pp. 1-34.
96. Li, S.; Liu,W. K. (2004): Meshfree Particle Methods. Springer-Verlag, Berlin.
97. Li, Y. S.; Feng, W. J.; Xu, Z. H. (2009): Fracture analysis of cracked 2D planar and axisymmetric problems of magneto-electro-elastic materials by the MLPG coupled with FEM. Computer Methods in Applied Mechanics and Engineering. vol. 198, No. 30-32, pp. 2347-2359.
98. Liew, K. M.; Zhao, X.; Ferreira, A. J. M. (2011): A review of meshless methods for laminated and functionally graded plates and shells. Composite Structures, vol. 93, pp. 2031-2041.
99. Lin, H.; Atluri, S. N. (2000): Meshless Local Petrov-Galerkin (MLPG) Method for Convection-Diffusion Problems. CMES: Computer Modeling in Engineering & Sciences, vol. 1, No. 2, pp. 45-60.
100. Lin, H.; Atluri, S. N. (2001): The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equation. CMES: Computer Modeling in Engineering & Sciences, vol. 2, pp. 117-142.
101. Ling, X.; Atluri, S. N. (2006): Stability analysis of inverse heat conduction problems. CMES: Computer Modeling in Engineering & Sciences, vol. 13, No. 3, pp. 219-228.
102. Liu, C. S. (2008a): A Highly Accurate MCMT for Direct and Inverse Problems of Biharmonic Equation in Arbitrary Plane Domain. CMES: Computer Modeling in Engineering & Sciences, vol. 30, No. 2, pp. 65-75.
103. Liu, C. S. (2008b): A Highly Accurate MCMT for Inverse Cauchy Problems of Laplace Equation in Arbitrary Plane Domain. CMES: Computer Modeling in Engineering & Sciences, vol. 35, No. 2, pp. 91-111.
104. Liu, C. S.; Atluri, S. N. (2008): A Novel Time Integration Method for Solving a Large System of Non-Linear Algebraic Equations. CMES: Computer Modeling in Engineering & Sciences, vol. 20, No. 3, pp. 147-156.
105. Liu, C. S.; Atluri S. N. (2009): A Highly Accurate Technique for Interpolations Using Very High-Order Polynomials, and Its Applications to Some Ill-Posed Linear Problems, CMES: Computer Modeling in Engineering & Sciences, vol. 43, No. 3, pp. 253-276.
106. Liu, C. S.; Yeih,W.; Atluri, S. N. (2009): On Solving the Ill-Conditioned System Ax=b: General-Purpose Conditioners Obtained From the Boundary-Collocation Solution of the Laplace Equation, Using Trefftz Expansions With Multiple Length Scales. CMES: Computer Modeling in Engineering & Sciences, vol. 44, No. 3, pp. 281-311.
107. Liu, G. R.; Gu, Y. T. (2001): A point interpolation method for two-dimensional solids. Int. J. Numer. Methods Eng., vol. 50, pp. 937-951.
108. Liu, G. R.; Wu, Y. L.; Ding, H. (2004): Meshfree weak-strong (MWS) form method and its application to incompressible flow problems. Int. J. Numer. Meth. Fluids, vol. 46, pp. 1025-1047.
109. Liu, H. T.; Han, Z. D.; Rajendran, A. M.; Atluri, S. N. (2006): Computational Modeling of Impact Response with the RG Damage Model and the Meshless Local Petrov-Galerkin (MLPG) Approaches. CMC: Computers, Materials & Continua, vol. 4, No. 1, pp. 43-53.
110. Liu, L. H. (2006): Meshless local Petrov-Galerkin method for solving radiative transfer equation. Journal of Thermophysics and Heat Transfer., vol. 20, pp. 150-154.
111. Liu, L. H.; Tan, J. Y.; Li, B. X. (2006): Meshless approach for coupled radiative and conductive heat transfer in one-dimensional graded index medium. Journal of Quantitative Spectroscopy & Radiative Transfer, vol. 101, pp. 237-248.
112. Liu, L. H.; Tan, J. Y. (2007): Meshless local Petrov-Galerkin approach for coupled radiative and conductive heat transfer. Int. J. Therm. Sci., vol. 46, pp. 672-681.
113. Liu, K.; Long, S.; Li, G. (2006): A simple and less-costly meshless local Petrov-Galerkin (MLPG) method for the dynamic fracture problem. Eng. Anal. Bound. Elem., vol. 30, pp. 72-76.
114. Liu, K. Y.; Long, S. Y.; Li, G. Y. (2008): A Meshless Local Petrov-Galerkin Method for the Analysis of Crack in the Isotropic Functionally Graded Material. CMC: Computers, Materials & Continua, vol. 7, No. 1, pp. 43-57.
115. Liu,W. K.; Chen, Y.; Jun, S.; Chen, J. S.; Belytschko, T.; Pan, C.; et al. (1996): Overview and applications of reproducing kernel particle methods. Arch. Comput. Methods Eng., vol. 3, pp. 3-80.
116. Liu, W. K.; Jun, S.; Zhang, Y. F. (1995): Reproducing kernel particle methods. Int. J. Numer. Meth. Fluids. vol. 20, pp. 1081-1106.
117. Lo, E. Y. M.; Shao, S. (2002): Simulation of near-shore solitary wave mechanics by an incompressible SPH method, Appl. Ocean Res., vol. 24, No. 5, pp. 275-286.
118. Long, S.; Atluri, S. N. (2002): A Meshless Local Petrov-Galerkin Method for Solving the Bending Problem of a Thin Plate. CMES: Computer Modeling in Engineering & Sciences, vol. 3, No. 1, pp. 53-63.
119. Long, S. Y.; Liu, K. Y.; Li, G. I. (2008): An Analysis for the Elasto-Plastic Fracture Problem by the Meshless Local Petrov-Galerkin Method. CMES: Computer Modeling in Engineering & Sciences, vol. 28, No. 3, pp. 203-216.
120. Loukopoulos, V. C.; Bourantas, G. C. (2012): MLPG6 for the Solution of Incompressible Flow Equations. CMES: Computer Modeling in Engineering & Sciences, vol. 88, No. 6, pp. 531-558.
121. Ma, Q. W. (2005): Meshless local Petrov-Galerkin method for two-dimensional nonlinear water wave problems. J. Comput. Phys., vol. 205, pp. 611-625.
122. Ma, Q. W.; Zhou, J. T. (2009): MLPG-R Method for Numerical Simulation of 2D Breaking Waves. CMES: Computer Modeling in Engineering & Sciences, vol. 43, No. 3, pp. 277-303.
123. Manolis, G. D.; Beskos, D. E. (1988): Boundary Element Methods in Elastody namics. Unwin-Hyman, London.
124. Marin, L. (2008): Stable MFS Solution to Singular Direct and Inverse Problems Associated with the Laplace Equation Subjected to Noisy Data. CMES: Computer Modeling in Engineering & Sciences, vol. 37, No. 3, pp. 203-242.
125. Masuda, S.; Noguchi, H. (2006): Analysis of Structure with Material Interface by Meshfree Method. CMES: Computer Modeling in Engineering & Sciences, vol. 11, No. 3, pp. 131-143.
126. Mazzia, A.; Pini, G.; Sartoretto, F. (2012): Numerical Investigation on Direct MLPG for 2D and 3D Potential Problems. CMES: Computer Modeling in Engineering & Sciences, vol. 88, No. 3, pp. 183-210.
127. Mindlin, R. D. (1951): Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. Journal of Applied Mechanics ASME, vol. 18, pp. 31-38.
128. Mirzaei, D.; Dehghan, M. (2011): MLPG Method for Transient Heat Conduction Problem with MLS as Trial Approximation in Both Time and Space Domains. CMES: Computer Modeling in Engineering & Sciences, vol. 72, No. 3, pp. 185-210.
129. Mohammadi, M. H. (2008): Stabilized meshless local Petrov-Galerkin (MLPG) method for incompressible viscous fluid flows. CMES: Computer Modeling in Engineering & Sciences, vol. 29, No. 2, pp. 75-94.
130. Monaghan, J. J. (1988): An introduction to SPH. Comput. Phys. Commun., vol. 48, pp. 89-96.
131. Najafi, M.; Arefmanesh, A.; Enjilela, V. (2012): Meshless local Petrov-Galerkin method -higher Reynolds numbers fluid flow applications. Eng. Anal. Bound. Elem., vol. 36, pp. 1671-1685.
132. Nayroles, B.; Touzot, G.; Villon, P. (1992): Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech., vol. 10, pp. 307-318.
133. Nguyen, V. P.; Rabczuk, T.; Bordas, S.; Duflot, M. (2008): Meshless methods: A review and computer implementation aspects. Mathematics and Computers in Simulation. vol. 79, pp. 763-813.
134. Nie, Y. F.; Atluri, S. N.; Zuo, C.W. (2006): The Optimal Radius of the Support of Radial Weights Used in Moving Least Squares Approximation. CMES: Computer Modeling in Engineering & Sciences, vol. 12, No. 2, pp. 137-142.
135. Nikfar, M.; Mahmoodi, M. (2012): Meshless local Petrov-Galerkin analysis of free convection of nanofluid in a cavity with a wavy side walls. Eng. Anal. Bound. Elem., vol. 36, No. 3, pp. 433-445.
136. Nikishkov, G. P.; Park, J. H.; Atluri, S. N. (2001): SGBEM-FEM alternating method for analyzing 3D non-planar cracks and their growth in structural compo nents. CMES: Computer Modeling in Engineering & Sciences, vol.2, no.3, pp.401-422.
137. Ohs, R. R.; Aluru, N. R. (2001): Meshless analysis of piezoelectric devices. Computational Mechanics, vol. 27, pp. 23-36.
138. Okada, H.; Rajiyah, H.; Atluri, S. N. (1988): A Novel Displacement Gradient Boundary Element Method for Elastic Stress Analysis with High Accuracy, Journal of Applied Mechanics, vol. 55, pp. 786-794.
139. Okada, H.; Rajiyah, H.; Atluri, S. N. (1989): Non-hyper-singular integral representations for velocity (displacement) gradients in elastic/plastic solids (small or finite deformations), Computational Mechanics., vol. 4, no. 3, pp. 165-175.
140. Onate, E.; Idelsohn, S.; Zienkiewicz, O. C.; Taylor, R. L. (1996): A finite point method in computational mechanics: Applications to convective transport and fluid flow. Int. J. Numer. Methods Eng., vol. 39, pp. 3839-3866.
141. Pini, G.; Mazzia, A.; Sartoretto, F. (2008): Accurate MLPG Solution of 3D Potential Problems. CMES: Computer Modeling in Engineering & Sciences, vol. 36, No. 1, pp. 43-64.
142. Pecher, R.; Elston, S.; Raynes, P. (2006): Meshfree Solution of Q-tensor Equations of Nematostatics Using the MLPG Method. CMES: Computer Modeling in Engineering & Sciences, vol. 13, No. 2, pp. 91-102.
143. Qian, L. F.; Batra, R.C. (2004): Transient thermoelastic deformations of thick functionally graded plate. Jour. Thermal Stresses, vol. 27, pp. 705-740
144. Qian, L. F.; Batra, R. C.; Chen, L. M. (2004a): Analysis of cylindrical bending thermoelastic deformation of functionally graded plates by a meshless local Petrov-Galerkin method. Computational Mechanics, vol. 33, pp. 263-273.
145. Qian, L. F.; Batra, R. C.; Chen, L. M. (2004b): 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. Composites, Part B Engineering. vol. 35, No. 6-8, pp. 685-697.
146. Raju, I. S.; Phillips, D. R. (2003): Further developments in the MLPG method for beam problems. CMES: Computer Modeling in Engineering & Sciences, vol. 4, No. 1, pp. 141-160.
147. Reddy, J. N. (1997): Mechanics of Laminated Composite Plates: Theory and Analysis. CRC Press, Boca Raton.
148. Rezaei Mojdehi, A.; Darvizeh, A.; Basti, A. (2012): Nonlinear Dynamic Analysis of Three-Dimensional Elasto-Plastic Solids by the Meshless Local Petrov-Galerkin (MLPG) Method. CMC: Computers, Materials & Continua, vol. 29, No. 1, pp. 15-39.
149. Sellountos, E. J.; Polyzos, D. (2003): A MLPG (LBIE) method for solving frequency domain elastic problems. CMES: Computer Modeling in Engineering & Sciences, vol. 4, No. 6, pp. 619-636.
150. Sellountos, E. J.; Polyzos, D.; Atluri, S. N. (2012): A New and Simple Meshless LBIE-RBF Numerical Scheme in Linear Elasticity. CMES: Computer Modeling in Engineering & Sciences, vol. 89, No. 6, pp. 513-551.
151. Sellountos, E. J.; Sequeira, A.; Polyzos, D. (2009): Elastic transient analysis with MLPG(LBIE) method and local RBFs. CMES: Computer Modeling in Engineering & Sciences, vol. 41, No. 3, pp. 215-241.
152. Sellountos, E. J.; Vavourakis, V.; Polyzos, D. (2005): A new singular/hypersingular MLPG (LBIE) method for 2D elastostatics. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 35-48.
153. Shen, S.; Atluri, S. N. (2004a): Multiscale Simulation Based on The Meshless Local Petrov-Galerkin (MLPG) Method. CMES: Computer Modeling in Engineering & Sciences, vol. 5, No. 3, pp. 235-256.
154. Shen, S.; Atluri, S. N. (2004b): Computational nanomechanics and multiscale simulation. CMC: Computers, Materials,& Continuua, vol. 1, No. 1, pp. 59-90.
155. Shen, S. P.; Atluri, S. N. (2005): A tangent stiffness MLPG method for atom/continuum multiscale simulation. CMES: Computer Modeling in Engineering & Sciences, vol. 7, No. 1, pp. 49-67.
156. Shibahara, M.; Atluri, S. N. (2011): The meshless local Petrov-Galerkin method for the analysis of heat conduction due to a moving heat source, in welding. International Journal of Thermal Sciences, vol. 50, pp. 984-992.
157. Shirzadi, A.; Sladek, V.; Sladek, J. (2013): A local integral equation formulation to solve coupled nonlinear reaction-diffusion equations by using moving least square approximation. Eng. Anal. Bound. Elem., vol. 37, pp. 8-14.
158. Singh, I. V.; Sandeep, K.; Prakash, R. (2002): The element free Galerkin method in three-dimensional steady state heat conduction. Int. J. Comput. Eng. Sci., vol. 3, pp. 291-303.
159. Sladek, J.; Sladek, V. (2011): The MLPG analysis of crack problems in magnetoelectroelastic solids. Computer Methods in Material Science, vol. 11, pp. 81-87.
160. Sladek, J.; Sladek, V.; Atluri, S. N. (2000): Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties, Computational Mechanics, vol. 24, pp. 456-462.
161. Sladek, J.; Sladek, V.; Atluri, S. N. (2001): A pure contour formulation for the meshless local boundary integral equation method in thermoelasticity. CMES: Computer Modeling in Engineering & Sciences, vol. 2, No. 4, pp. 423-434.
162. Sladek, J.; Sladek, V.; Atluri, S. N. (2004a): Meshless Local Petrov-Galerkin Method in Anisotropic Elasticity. CMES: Computer Modeling in Engineering & Sciences, vol. 6, No. 5, pp. 477-489.
163. Sladek, J.; Sladek, V.; Atluri, S. N. (2004b): Meshless Local Petrov-Galerkin Method for Heat Conduction Problem in an Anisotropic Medium. CMES: Computer Modeling in Engineering & Sciences, vol. 6, No. 3, pp. 309-318.
164. Sladek, J.; Sladek, V.; Hellmich, Ch.; Eberhardsteiner, J. (2007a): Analysis of thick functionally graded plates by local integral equation method. Communications in Numerical Method in Engineering, vol. 23, pp. 733-754.
165. Sladek, J.; Sladek, V.; Hellmich, Ch.; Eberhardsteiner, J. (2007f): Heat conduction analysis of 3-D axisymmetric and anisotropic FGM bodies by meshless
166. Sladek, J.; Sladek, V.; Hon, Y. C. (2006): Inverse heat conduction problems by meshless local Petrov-Galerkin method. Eng. Anal. Bound. Elem., vol. 30, pp. 650-661.
167. Sladek, J.; Sladek, V.; Krahulec, S.; Pan, E. (2012c): Enhancement of the magnetoelectric coefficient in functionally graded multiferroic composites. Journal of Intelligent Material Systems and Structures, vol. 23, pp. 1649-1658.
168. Sladek, J.; Sladek, V.; Krahulec, S.;Wunsche, M.; Zhang, Ch. (2012b): MLPG Analysis of Layered Composites with Piezoelectric and Piezomagnetic Phases. CMC: Computers, Materials & Continua, vol. 29, No. 1, pp. 75-101.
169. Sladek, J.; Sladek, V.; Krivacek, J.; Aliabadi, M. H. (2007c): Local boundary integral equations for orthotropic shallow shells, Int. J. Solids and Structures, vol. 44, pp. 2285-2303.
170. Sladek, J.; Sladek, V.; Krivacek, J.; Wen, P. H.; Zhang, Ch. (2007b): Meshless Local Petrov-Galerkin (MLPG) method for Reissner-Mindlin plates under dynamic load. Comput. Meth. Appl. Mech. Engng., vol. 196, pp. 2681-2691.
171. Sladek, J.; Sladek, V.; Krivacek, J.; Zhang, Ch. (2003): Local BIEM for transient heat conduction analysis in 3-D axisymmetric functionally graded solids. Comput. Mech., vol. 32, pp. 169-176.
172. Sladek, J.; Sladek, V.; Krivacek, J.; Zhang, Ch. (2005a): Meshless Local Petrov-Galerkin Method for Stress and Crack Analysis in 3-D Axisymmetric FGM Bodies. CMES: Computer Modeling in Engineering & Sciences, vol. 8, No. 3, pp. 259-270.
173. Sladek, J.; Sladek, V.; Mang, H. A. (2002): Meshless formulations for simply supported and clamped plate problems. Int. J. Num. Meth. Engn., vol. 55, pp. 359-375.
174. Sladek, J.; Sladek, V.; Solek, P. (2009): Elastic analysis in 3D anisotropic functionally graded solids by the MLPG. CMES: Computer Modeling in Engineering & Sciences, vol. 43, No. 3, pp. 223-251.
175. Sladek, J.; Sladek, V.; Solek, P.; Atluri, S. N. (2008e): Modeling of Intelligent Material Systems by the MLPG. CMES: Computer Modeling in Engineering & Sciences, vol. 34, No. 4, pp. 273-300.
176. Sladek, J.; Sladek, V.; Solek, P.; Pan, E. (2008f): Fracture analysis of cracks in magneto-electro-elastic solids by the MLPG. Computational Mechanics, vol. 42, pp. 697-714.
177. Sladek, J.; Sladek, V.; Solek, P.; Saez, A. (2008d): Dynamic 3D axisymmetric problems in continuously non-homogeneous piezoelectric solids. Int. J. Sol. Struct., vol. 45, No. 16, pp. 4523-4542.
178. Sladek, J.; Sladek, V.; Solek, P.; Tan, C. L.; Zhang, Ch. (2009a): Two-and Three-Dimensional Transient Thermoelastic Analysis by the MLPG Method. CMES: Computer Modeling in Engineering & Sciences, vol. 47, No. 1, pp. 61-96.
179. Sladek, J.; Sladek, V.; Solek, P.; Wen, P. H. (2008a): Thermal Bending of Reissner-Mindlin Plates by the MLPG. CMES: Computer Modeling in Engineering & Sciences, vol. 28, No. 1, pp. 57-76.
180. Sladek, J.; Sladek, V.; Solek, P.; Wen, P. H.; Atluri, S. N. (2008c): Thermal Analysis of Reissner-Mindlin Shallow Shells with FGM Properties by the MLPG. CMES: Computer Modeling in Engineering & Sciences, vol. 30, No. 2, pp. 77-97.
181. Sladek, J.; Sladek, V.; Solek, P.; Zhang, Ch. (2010d): Fracture analysis in continuously nonhomogeneous magneto-electro-elastic solids under a thermal load by the MLPG. International Journal of Solids and Structures, vol. 47, No. 10, pp. 1381-1391.
182. Sladek, J.; Sladek, V.; Stanak, P.; Pan, E. (2010b): The MLPG for Bending of Electroelastic Plates. CMES: Computer Modeling in Engineering & Sciences, vol. 64, No. 3, pp. 267297
183. Sladek, J.; Sladek, V.; Stanak, P.; Wen, P. H.; Atluri, S. N. (2012a): Laminated Elastic Plates with Piezoelectric Sensors and Actuators. CMES: Computer Modeling in Engineering & Sciences, vol. 85, No. 6, pp. 543-572.
184. Sladek, J.; Sladek, V.; Stanak, P.; Zhang, Ch. (2010a): Meshless Local Petrov-Galerkin (MLPG) Method for Laminate Plates under Dynamic Loading. CMC: Computers, Materials & Continua, vol. 15, No. 1, pp. 1-25.
185. Sladek, J.; Sladek, V.; Stanak, P.; Zhang, Ch.; Wunsche, M. (2011): An Interaction Integral Method for Computing Fracture Parameters in Functionally Graded Magnetoelectroelastic Composites. CMC: Computers, Materials & Continua, vol. 32, No. 1, pp. 35-68.
186. Sladek, J.; Sladek, V.; Stanak, P.; Zhang, Ch.; Wunsche, M. (2013): Analysis of the bending of circular piezoelectric plates with functionally graded material properties by a MLPG method. Engineering Structures, vol. 47, pp. 81-89.
187. Sladek, J.; Sladek, V.; Tan, C. L.; Atluri, S. N. (2008g): Analysis of Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG. CMES: Computer Modeling in Engineering & Sciences, vol. 32, No. 3, pp. 161-174.
188. Sladek, J.; Sladek, V.; Van Keer, R. (2003): Meshless local boundary integral equation method for 2D elastodynamic problems. Int. J. Num. Meth. Engn., vol. 57, pp. 235-249.
189. Sladek, J.; Sladek, V.; Wen, P. H.; Aliabadi, M. H. (2006c): Meshless Local Petrov-Galerkin (MLPG) Method for Shear Deformable Shells Analysis. CMES: Computer Modeling in Engineering & Sciences, vol. 13, No. 2, pp. 103-117.
190. Sladek, J.; Sladek, V.; Wen, P.; Hon, B. (2012e): Inverse heat conduction problems in three-dimensional anisotropic functionally graded solids. Journal of Engineering Mathematics, vol. 75, No. 1, pp. 157-171.
191. Sladek, J.; Sladek, V.;Wen, P. H.; Hon, Y. C. (2009c): Inverse fracture problems in piezoelectric solids by local integral equation method. Eng. Anal. Bound. Elem., vol. 33, pp. 1089-1099.
192. Sladek, J.; Sladek, V.; Wen, P. H.; Hon, Y. C. (2009d): The Inverse Problem of Determining Heat Transfer Coefficients by the Meshless Local Petrov-Galerkin Method. CMES: Computer Modeling in Engineering & Sciences, vol. 48, pp. 191-218.
193. Sladek, J.; Sladek, V.; Wunsche, M.; Zhang, Ch. (2009b): Interface crack problems in anisotropic solids analyzed by the MLPG. CMES: Computer Modeling in Engineering & Sciences, vol. 54, No. 2, pp. 223-253.
194. Sladek, J.; Sladek, V.; Wunsche, M.; Zhang, Ch. (2012d): Analysis of an interface crack between two dissimilar piezoelectric solids. Engineering Fracture Mechanics, vol. 89, pp. 114-127.
195. Sladek, J.; Sladek, V.; Zhang, Ch. (2003a): Application of Meshless Local Petrov-Galerkin (MLPG) Method to Elastodynamic Problems in Continuously Nonhomogeneous Solids. CMES: Computer Modeling in Engineering & Sciences, vol. 4, No. 6, pp. 637-647.
196. Sladek, J.; Sladek, V.; Zhang, Ch. (2003b): Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method. Comput. Material Science, vol. 28, pp. 494-504.
197. Sladek, J.; Sladek, V.; Zhang, Ch. (2008b): Local integral equation method for viscoelastic Reissner-Mindlin plates. Comput. Mech., vol. 41, pp 759-768.
198. Sladek, J.; Sladek, V.; Zhang, Ch. (2008c): Evaluation of the stress intensity factors for cracks in continuously nonhomogeneous solids, part II: Meshless method. Mechanics of Advanced Materials and Structures, vol. 15, No. 6-7, pp. 444-452.
199. Sladek, J.; Sladek, V.; Zhang, Ch.; Garcia-Sanchez, F.; Wunsche, M. (2006d): Meshless Local Petrov-Galerkin Method for Plane Piezoelectricity. CMC: Computers, Materials & Continua, vol. 4, No. 2, pp. 109-117.
200. Sladek, J.; Sladek, V.; Zhang, Ch.; Schanz, M. (2006a): Meshless local Petrov-Galerkin method for continuously nonhomogeneous linear viscoelastic solids. Comput. Mech., vol. 37, pp. 279-289.
201. Sladek, J.; Sladek, V.; Zhang, Ch.; Solek, P. (2007d): Application of the MLPG to Thermo-Piezoelectricity. CMES: Computer Modeling in Engineering & Sciences, vol. 22, No. 3, pp. 217-233.
202. Sladek, J.; Sladek, V.; Zhang, Ch.; Solek, P. (2008b): Static and dynamic analysis of shallow shells with functionally graded and orthotropic material properties. Mechanics of Advanced Materials and Structures, vol. 15, No. 2, pp. 142-156.
203. Sladek, J.; Sladek, V.; Zhang, Ch.; Solek, P.; Pan, E. (2007e): Evaluation of fracture parameters in continuously nonhomogeneous piezoelectric solids. International Journal of Fracture, vol. 145, pp. 313-326.
204. Sladek, J.; Sladek, V.; Zhang, Ch.; Tan, C. L. (2006b): Meshless Local Petrov-Galerkin Method for Linear Coupled Thermoelastic Analysis. CMES: Computer Modeling in Engineering & Sciences, vol. 16, No. 1, pp. 57-68.
205. Sladek, J.; Sladek, V.; Zhang, Ch.; Wunsche, M. (2010c): Crack analysis in piezoelectric solids with energetically consistent boundary conditions by the MLPG. CMES: Computer Modeling in Engineering & Sciences, vol. 68, No. 2, pp. 185-219.
206. Sladek, J.; Sladek, V.; Zhang, Ch.;Wunsche, M. (2012d): Semi-permeable crack analysis in magnetoelectroelastic solids. Smart Materials & Structures, vol. 21, No. 025003.
207. Sladek, V.; Sladek, J. (2010): Local integral equations implemented by MLSapproximation and analytical integrations. Eng. Anal. Bound. Elem., vol. 34, No. 11, pp. 904-913.
208. Sladek, V.; Sladek, J.; Atluri, S. N.; Van Keer, R. (2000): Numerical integration of singularities in meshless implementation of local boundary integral equations. Comput. Mech., vol. 25, No. 4, pp. 394-403.
209. Sladek, V.; Sladek, J.; Sator, L. (2013): Physical decomposition of thin plate bending problems and their solution by mesh-free methods. Eng. Anal. Bound. Elem., vol. 37, pp. 348-365.
210. Sladek, V.; Sladek, J.; Tanaka, M. (2005): Local Integral Equations and two Meshless Polynomial Interpolations with Application to Potential Problems in Nonhomogeneous Media. CMES: Computer Modeling in Engineering & Sciences, vol. 7, No. 1, pp. 69-83.
211. Sladek, V.; Sladek, J.; Tanaka, M.; Zhang, Ch. (2005b): Transient heat conduction in anisotropic and functionally graded media by local integral equations. Eng. Anal. Bound. Elem., vol. 29, pp. 1047-1065.
212. Sladek, V.; Sladek, J.; Zhang, C. (2006): A Comparative Study of Meshless Approximations in Local Integral Equation Method. CMC: Computers, Materials & Continua, vol. 4, No. 3, pp. 177-188.
213. Sladek, V.; Sladek, J.; Zhang, Ch. (2008d): Computation of stresses in nonhomogeneous elastic solids by local integral equation method: A comparative study. Computational Mechanics, vol. 41, pp. 827-845.
214. Sladek, V.; Sladek, J.; Zhang, Ch. (2008a): Local integral equation formulation for axially symmetric problems involving elastic FGM. Eng. Anal. Bound. Elem., vol. 32, pp. 1012-1024.
215. Sladek, V.; Sladek, J.; Zhang, Ch. (201): On Increasing Computational Efficiency of Local Integral Equation Method Combined with Meshless Implementations. CMES: Computer Modeling in Engineering & Sciences, vol. 63, No. 3, pp. 243-263.
216. Sladek, V.; Sladek, J.; Zhang, Ch. (2011): Mesh-free methods and time integrations for transient heat conduction. Computed Assisted Mechanics and Engineering Sciences, vol. 18, pp. 115-128.
217. Soares, D. Jr. (2009a): Numerical Modeling of ElectromagneticWave Propagation by Meshless Local Petrov-Galerkin Formulations. CMES: Computer Modeling in Engineering & Sciences, vol. 50, No. 2, pp. 97-114.
218. Soares, D. Jr. (2009b): An Iterative Time-Domain Algorithm for Acoustic-Elastodynamic Coupled Analysis Considering Meshless Local Petrov-Galerkin Formulations. CMES: Computer Modeling in Engineering & Sciences, vol. 54, No. 2, pp. 201-222.
219. Soares, D. Jr. (2010): A time-domain meshless local Petrov-Galerkin formulation for the dynamic analysis of nonlinear porous media. CMES: Computer Modeling in Engineering & Sciences, vol. 66, No. x, pp. 227-248.
220. Soares, D. Jr. (2011): Iterative analysis of pore-dynamic models discretized by meshless local Petrov-Galerkin formulations. CMES: Computer Modeling in Engineering & Sciences, vol. 76, No. 1, pp. 61-82.
221. Soares, D. Jr.; Sladek, J.; Sladek, V. (2009): Dynamic analysis by meshless local Petrov-Galerkin formulations considering a time-marching scheme based on implicit Green's functions. CMES: Computer Modeling in Engineering & Sciences, vol. 50, No. 2, pp. 115-140.
222. Soares, D. Jr.; Sladek, J.; Sladek, V. (2010): Non-linear dynamic analyses by meshless local Petrov-Galerkin formulations. Int. J. Num. Meth. Eng., vol. 81, No. 13, pp. 1687-1699.
223. Soares, D. Jr.; Sladek, V.; Sladek, J. (2012): Modified meshless local Petrov-Galerkin formulations for elastodynamics. International Journal for Numerical Methods in Engineering, vol. 90, No. 12, pp. 1508-1528.
224. Soares, D. Jr.; Sladek, V.; Sladek, J.; Zmindak, M.; Medvecky, S. (2012): Porous media analysis by modified MLPG formulations. CMC: Computers, Materials & Continua, vol. 27, No. 2, pp. 101-127.
225. Soric, J.; Jarak, T. (2010): Mixed meshless formulation for analysis of shell-like structures. Comput. Methods Appl. Mech. Engrg., vol. 199, pp. 1153-1164.
226. Soric, J.; Li, Q.; Jarak, T.; Atluri, S. N. (2004): Meshless Local Petrov-Galerkin (MLPG) Formulation for Analysis of Thick Plates. CMES: Computer Modeling in Engineering & Sciences, vol. 6, No. 4, pp. 349-357.
227. Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. W. (1984): Metallic Phase with Long-Range Orientational Order and No Translational Symmetry. Phys. Rev. Lett., vol. 53, pp. 1951-1953.
228. Sterk, M.; Trobec, R. (2008): Meshless solution of diffusion equation with parameter optimization and error analysis. Eng. Anal. Bound. Elem., vol. 32, pp. 567-577.
229. Suresh, S.; Mortensen A. (1998): Fundamentals of Functionally Graded Materials. Institute of Materials, London.
230. Tang, Z.; Shen, S.; Atluri, S. N. (2003a): Analysis of materials with straingradient effects: A meshless local Petrov-Galerkin (MLPG) approach, with nodal displacements only. CMES: Computer Modeling in Engineering & Sciences, vol. 4, No. 1, pp. 177-196.
231. Tang, Z.; Shen, S.; Atluri, S. N. (2003b): Analysis of Materials with Strain-Gradient Effects: A Meshless Local Petrov-Galerkin (MLPG) Approach, with Nodal Displacements only. CMES: Computer Modeling in Engineering & Sciences, vol. 4, No. 1, pp. 177-196.
232. Trobec, R.; Sterk, M.; Robic, B. (2009): Computational complexity and parallelization of the meshless local Petrov-Galerkin method. Compututers and Structures, vol. 87, pp. 81-90.
233. Tsai, C. C. (2011): A Meshless Numerical Method for Kirchhoff Plates under Arbitrary Loadings. CMC: Computers, Materials & Continua, vol. 22, No. 3, pp. 197-218.
234. Vavourakis, V.; Polyzos, D. (2007): A MLPG4 (LBIE) Formulation in Elastostatics. CMC: Computers, Materials & Continua, vol. 5, No. 3, pp. 185-196.
235. Vavourakis, V.; Polyzos, D. (2008): A MLPG (LBIE) numerical methos for solving 2D incompressible and nearly incompressible elastostatic problems. Commun. Numer. Meth. Engrg., vol. 24, pp. 281-296.
236. Vavourakis, V.; Sellountos, E. J.; Polyzos, D. (2006): A comparison study on different MLPG (LBIE) formulations. CMES: Computer Modeling in Engineering & Sciences, vol. 13, No. 3, pp. 171-183.
237. Wang, D.; Sun, Y.; Li, L. (2009): A Discontinuous Galerkin Meshfree Modeling of Material Interface. CMES: Computer Modeling in Engineering & Sciences, vol. 45, No. 1, pp. 57-82.
238. Wang, H.; Qin, Q.H.; Kang, Y.L. (2006): A meshless model for transient heat conduction in functionally graded materials. Computational Mechanics, vol. 38, pp. 51-60.
239. Wang, K.; Zhou, S.; Nie, Z.; Kong, S. (2008): Natural neighbour Petrov-Galerkin Method for Shape Design Sensitivity Analysis. CMES: Computer Modeling in Engineering & Sciences, vol. 26, No. 2, pp. 107-121.
240. Wang, L.; Brust, F. W.; Atluri, S. N. (1997a): The Elastic-Plastic Finite Element Alternating Method (EPFEAM) and the Prediction of Fracture Under WFD Conditions in Aircraft Structures Part I: EPFEAM Theory, Computational Mechanics, Volume: 19, Issue: 5, pp. 356-369.
241. Wang, L.; Brust, F. W.; Atluri, S. N. (1997b): The Elastic-Plastic Finite Element Alternating Method (EPFEAM) and the Prediction of Fracture Under WFD Conditions in Aircraft Structures, Part II: Fracture and the T. Parameter, Computational Mechanics, Volume: 19, Issue: 5, Pages: 370-379.
242. Wang, L.; Brust, F. W.; Atluri, S. N. (1997c):The Elastic-Plastic Finite Element Alternating Method (EPFEAM) and the Prediction of Fracture Under WFD Conditions in Aircraft Structures, Part III: Computational Predictions of the NIST Multiple Site Damage Experimental Results, Computational Mechanics, Volume: 20, Issue: 3, Pages: 199-212.
243. Wedland, H. (1999): Meshless Galerkin methods using radial basis function. Math. Comput., vol. 68, pp. 1521-1531.
244. Wen, P. H.; Aliabadi, M. H. (2010): Elastic Moduli of Woven Fabric Composite by Meshless Local Petrov-Galerkin (MLPG) Method. CMES: Computer Modeling in Engineering & Sciences, vol. 61, No. 2, pp. 133-154.
245. Wen, P. H.; Aliabadi, M. H. (2012): Analysis of functionally graded plates by meshless method: A purely analytical formulation. Eng. Anal. Bound. Elem., vol. 36, pp. 639-650.
246. Wen, P. H.; Aliabadi, M. H. (2013): Analytical formulation of meshless local integral equation method. Applied Mathematical Modelling, vol. 37, pp. 2115-2126.
247. Wrobel, L. C.; Aliabadi, M. H. (2002): The Boundary Element Method. New Jersey: Wiley.
248. Wu, C. P.; Chiu, K. H.;Wang, Y. M. (2008a): A Differential Reproducing Kernel Particle Method for the Analysis of Multilayered Elastic and Piezoelectric Plates. CMES: Computer Modeling in Engineering & Sciences, vol. 27, No. 3, pp. 163-186.
249. Wu, C. P.; Chiu, K. H.;Wang, Y. M. (2008b): A Review on the Three-Dimensional Analytical Approaches of Multilayered and Functionally Graded Piezoelectric Plates and Shells. CMC: Computers, Materials & Continua, vol. 8, No. 2, pp. 93-132.
250. Wu, X. H.; Chang, Z. J.; Lu, Y. L.; Tao,W. Q.; Shen, S. P. (2012): An analysis of the convection-diffusion problems using meshless and meshbased methods. Eng. Anal. Bound. Elem., vol. 36, pp. 1040-1048.
251. Wu, X. H.; Shen, S. P.; Tao,W. Q. (2007): Meshless Local Petrov-Galerkin Collocation Method for Two-dimensional Heat Conduction Problems. CMES: Computer Modeling in Engineering & Sciences, vol. 22, No. 1, pp. 65-76.
252. Wu, X. H.; Tao, W. Q. (2008): Meshless method based on the local weak-forms for steady state heat conduction problems, Int. J. Heat Mass Tran., vol. 51, pp. 3103-3112.
253. Wu, X. H.; Tao, W. Q.; Shen, S. P.; Zhu, X. W. (2010): A stabilized MLPG method for steady state incompressible fluid flow simulation. Journal of Computational Physics, vol. 229, No. 22, pp. 8564-8577.
254. Wu, Y. L.; Liu, G. R.; Gu, Y. T. (2005): Application of meshless local Petrov-Galerkin (MLPG) approach to simulation of incompressible flow. Numer. Heat Tran. B, vol.48, pp. 459-475.
255. Yazid, A.; Abdelkader, N.; Abdelmadjid, H. (2009): A state-of-The-art review of the X-FEM for computational fracture mechanics. Appl. Math. Model., vol. 33, pp. 4269-4282.
256. Yuan, W.; Chen, P.; Liu, K. (2007) A New Quasi-Unsymmetric Sparse Linear System Solver for Meshless Local Petrov-Galerkin Method (MLPG). CMES: Computer Modeling in Engineering & Sciences, vol. 17, No. 2, pp. 115-134.
257. Yuan, W. R.; Chen, Y. J.; Gagalowicz, A.; Liu, K. X. (2008): Application of Meshless Local Petrov-Galerkin (MLPG) Method in Cloth Simulation. CMES: Computer Modeling in Engineering & Sciences, vol. 35, No. 2, pp. 133-155.
258. Zhou, J. T.; Ma, Q.W. (2010): MLPG Method Based on Rankine Source Solution for Modelling 3D Breaking Waves. CMES: Computer Modeling in Engineering & Sciences, vol. 56, No. 2, pp. 179-210.
259. Zhu, T.; Zhang, J. D.; Atluri, S. N. (1998): A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach. Comput. Mech. vol. 21, pp. 223-235.
260. Zhu, T.; Zhang, J.; Atluri, S. N. (1999): A Meshless Numerical Method Based on The Local Boundary Integral Equation (LBIE) to Solve Linear and Nonlinear Boundary Value Problems. Eng. Anal. Bound. Elem., vol. 23, pp. 375-389.