W2 Formulations
Node-based methods (NS-PIM, NS-RPIM, NS-FEM)
[JA233]G. R. Liu, G. Y. Zhang, K. Y. Dai, Y. Y. Wang, Z. H. Zhong, G. Y. Li and X. Han, A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems, International Journal of Computational Methods, 2(4): 645-665, 2005.
[JA_2006_07] G. R. Liu, Y. Li, K. Y. Dai, M. T. Luan, W. Xue, A Linearly conforming radial point interpolation method for solid mechanics problems, International Journal of Computational Methods, 3(4):401-428, 2006.
[JA_2007_01] Y. Li, G. R. Liu, M. T. Luan, K. Y. Dai, Z. H. Zhong, G. Y. Li and X. Han, Contact analysis for solids based on linearly conforming radial point interpolation method, Computational Mechanics, 39: 537-554, 2007.
[JA_2008_17] G.R. Liu, Z. Khin, Y.Y. Wang, B. Deng, A novel reduced-basis method with upper and lower bounds for real-time computation of linear elasticity problems, Comput. Methods Appl. Mech. Engrg., 198: 269-279, 2008.
[JA_2008_22] S.C. Wu, G. R. Liu, H.O. Zhang, G.Y. Zhang. A node-based smoothed point interpolation method (NS-PIM) for three-dimensional thermoelastic problems. Numerical Heat Transfer, Part A: Applications, 54: 1121-1147, 2008.
[JA_2009_01] G.R. Liu, T. Nguyen-Thoi, H. Nguyen-Xuan, K.Y. Lam. A node-based smoothed finite element method (NS-FEM) for upper bound solution to solid mechanics problems. Computers and Structures, 87: 14-26, 2009..
[JA_2007_09] G. Y. Zhang, G. R. Liu, T. T. Nguyen, C. X. Song, X. Han, Z. H. Zhong and G. Y. Li. The upper bound property for solid mechanics of the linearly conforming radial point interpolation method (LC-RPIM). International Journal of Computational Methods, 4(3): 521-541, 2007.
[JA_2007_11] G. Y. Zhang, G. R. Liu, Y. Y. Wang H. T. Huang, Z. H. Zhong, G. Y. Li and X. Han. A linearly conforming point interpolation method (LC-PIM) for three-dimensional elasticity problems. International Journal for Numerical Methods in Engineering, 72: 1524-1543, 2007.
[JA_2008_02] G. R. Liu and G. Y. Zhang. Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM). International Journal for Numerical Methods in Engineering, 74: 1128-1161, 2008.
[JA_2008_12] G. R. Liu, X. Zhao, K. Y. Dai, Z. H. Zhong, G. Y. Li and X. Han. Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method. Composites Science and Technology, 68(2): 354-366, 2008.
[JA_2009_09] X. Zhao, G.R. Liu, K.Y. Dai, Z.H. Zhong, G.Y. Li, X. Han, A linearly conforming radial point interpolation method (LC-RPIM) for shells. Computational Mechanics, 43: 403-413, 2009.
[JA_2009_11] S.C. Wu, G.R. Liu, H.O. Zhang, G.Y. Zhang, A node-based smoothed point interpolation method (NS-PIM) for thermoelastic problems with solution bounds. International Journal of Heat and Mass Transfer, 52: 1464-1471, 2009.
Edge-based methods (ES-PIM, ES-RPIM, ES-FEM)
[JA_2008_16] G.R. Liu, G.R. Zhang. Edge-based Smoothed Point Interpolation Methods. International Journal of Computational Methods, 5(4): 621-646, 2008.
[JA_2009_02] G.R. Liu, T. Nguyen-Thoi, K.Y. Lam. An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses in solids. Journal of Sound and Vibration, 320: 1100-1130, 2009.
Cell-based methods (CS-PIM, CS-RPIM, CS-FEM/SFEM)
[JA_2009_05] G.R. Liu, G.R. Zhang. A normed G space and weakened weak (W2) formulation of a cell-based Smoothed Point Interpolation Method. International Journal of Computational Methods, 6(1): 147-179, 2009.
[JA_2007_02] G. R. Liu, K. Y. Dai, T. T. Nguyen, A smoothed finite element method for mechanics problems, Computational Mechanics, 39: 859-877, 2007.
[JA_2007_04] G. R. Liu, T. T. Nguyen, K. Y. Dai and K. Y. Lam, Theoretical aspects of the smoothed finite element method (SFEM), International Journal for Numerical Methods in Engineering, 71: 902-930, 2007.
[JA_2007_10] T. T. Nguyen, G. R. Liu, K. Y. Dai and K. Y. Lam. Selective smoothed finite element method. Tsinghua Science and Technology, 12(5): 497-508, 2007.
[JA_2008_05] X. Y. Cui, G. R. Liu G. Y. Li, X. Zhao, T. T. Nguyen and G. Y. Sun. A smoothed finite element method (SFEM) for linear and geometrically nonlinear analysis of plates and shells. CMES-Computer Modeling in Engineering & Sciences, 28(2): 109-125, 2008.
Other methods (Strain Constructed methods, SC-PIMs)
[JA_2009_06] G.R. Liu, G.R. Zhang. A novel scheme of strain-constructed point interpolation method for static and dynamic mechanics problems. International Journal of Applied Mechanics, 1(1): 233-258, 2009.
[JA_2009_07] G.R. Liu, X. Xu, G.Y. Zhang, T. Nguyen-Thoi, A superconvergent point interpolation method (SC-PIM) with piecewise linear strain field using triangular mesh. International Journal for Numerical Methods in Engineering, 77: 1439-1467, 2009.
[JA_2009_08] G.R. Liu, X. Xu, G.Y. Zhang, Y. T. Gu, An extended Galerkin weak form and a point interpolation method with continuous strain field and superconvergence using triangular mesh. Computational Mechanics, 43: 651-673, 2009.
