A LINEARLY CONFORMING POINT INTERPOLATION METHOD (LC-PIM) FOR 2D SOLID MECHANICS PROBLEMS

By Guirong Liu, Guiyong Zhang, K. Y. Dai, Y. Y. Wang, Z. Zhong, Guangyao Li, Xu Han. 2005

233 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/35f674b98a8af6a5eaa28da0f2c0a716f428f438

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids (2009, methodology): “Liu et al. [10,11] have provided an intuitive explanation and showed numerically that the NS-PIM can produce an upper bound to the exact solution in the strain energy, when a reasonably fine mesh is used.”
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems (2009, methodology): “The model that gives an upper bound can be one of the following models: the stress equilibrium FEM model [1], the recovery of a statically admissible stress field from displacement FEM model [2–4], the hybrid equilibrium FEM model [5,6], the element-based smoothed finite element method (SFEM) model ”
Adaptive analysis using the node‐based smoothed finite element method (NS‐FEM) (2011, methodology): “have applied this technique to formulate the linear conforming point interpolation method (LC-PIM) [20] and the linearly conforming radial point interpolation method [21].”
A singular edge-based smoothed finite element method (ES-FEM) for crack analyses in anisotropic media (2011, unknown): “When triangular elements are used, the NS-FEM gives the same results as the node-based uniform strain elements [48] or as the LC-PIM (known also as NS-PIM) [49] when the linear shape functions are used for interpolation.”
A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS (2008, methodology): “In the other front of development related to meshfree methods, the node-based smoothed point interpolation method (NS-PIM)a has been developed recently [Liu et al. (2005); Zhang et al. (2007)] using the node-based smoothing operations [Chen et al. (2001)].”
A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements (2009, methodology): “The generalized gradient smoothing technique offers a theoretical foundation to the socalled weakened weak formulation [9] for a wide class of compatible and incompatible methods, including the linear conforming point interpolation method (LC-PIM) [10, 11] and the linearly conforming radial point in”
On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM) (2009, methodology): “The generalized smoothing technique forms the theoretical foundation for NS-PIM [19], NS-RPIM [18–21], ES-PIM and ES-RPIM [22] where incompatible PIM shape functions were used to establish conforming models.”
Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method (2008, methodology): “The radial point interpolation meshless method (RPIM) [12,31] has been demonstrated to be an efficient meshless method and successfully applied in many engineering problems [32–36].”
An edge-based smoothed finite element method for visco-elastoplastic analyses of 2D solids using triangular mesh (2009, methodology): “has generalized the gradient (strain) smoothing technique [9] and applied it in the meshfree context to formulate the node-based smoothed point interpolation method (NS-PIM or LC-PIM) [17,18] and the linearly conforming radial point interpolation method (NS-RPIM or LC-RPIM) [11].”
A novel alpha finite element method (αFEM) for exact solution to mechanics problems using triangular and tetrahedral elements (2008, methodology): “When only the linear shape function for interpolation is used, the LC-PIM is identical to the NI-FEM or N-SFEM using triangular and tetrahedral elements [14].”