A local point interpolation method (LPIM) for static and dynamic analysis of thin beams

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A meshfree method: meshfree weak–strong (MWS) form method, for 2-D solids (2003, methodology): “... the local Petrov-Galerkin weak forms (or short as meshfree local weak-form methods) are proposed and developed, such as the meshless local Petrov-Galerkin (MLPG) method (Atluri and Zhu, 1998, 2002; Atluri et al. 1999; Gu and Liu 2001a,c), the method of finite spheres (De and Bathe 2000), the loc”
Coupling of the meshfree and finite element methods for determination of the crack tip fields (2008, unknown): “…progress, such as the smooth particle hydrodynamics (SPH) [1], the element-free Galerkin (EFG) method [2], the reproducing kernel particle method (RKPM) [3][4], the meshfree local Petrov-Galerkin (MLPG) method [5][6][7], and the local radial point interpolation method (LRPIM) [8][9][10][11].”
A LOCAL RADIAL POINT INTERPOLATION METHOD (LRPIM) FOR FREE VIBRATION ANALYSES OF 2-D SOLIDS (2001, unknown): “The LPIM has been used for 2-D elasto-statics [13] and 1-D fourth order thin beam analyses [14].”
A meshfree radial point interpolation method (RPIM) for three-dimensional solids (2005, methodology): “The RPIM has been successfully applied to 1D and 2D solid mechanics (Gu and Liu, 2001; Liu and Gu, 2001b; Liu and Yan, et al. 2002), plate and shell structures (Liu and Chen, 2001; Liu and Liu, et al.”