A linearly conforming point interpolation method (LC‐PIM) for three‐dimensional elasticity problems

By Guiyong Zhang, Guirong Liu, Y. Y. Wang, H. Huang, Z. Zhong, Guangyao Li, Xiao Han. 2007

135 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f6033008e1563148f9e6edcd6d4ec11bf979b2b3

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC‐PIM) (2008, methodology): “have developed the linearly conforming radial point interpolation method (LC-RPIM) [13] and the LC-PIM [14, 15].”
A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems (2010, methodology): “Typical W2 models are the NS-PIM [2, 3], NS-RPIM [9], ES-PIM [19], ES-RPIM [19], ES-PIM [20], and CS-PIM [20].”
An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for 3D static and dynamic problems (2013, methodology): “Using the node-based strain smoothing operation, a node-based smoothed point interpolation method (NS-PIM or LC-PIM [31,32]) and a node-based smoothed finite element method (NS-FEM) [33] have been formulated in the frame of meshfree and FEM, respectively.”
An edge‐based smoothed finite element method for primal–dual shakedown analysis of structures (2010, methodology): “has generalized the gradient (strain) smoothing technique [10] and applied it in the meshfree context to formulate the node-based smoothed point interpolation method (NS-PIM or LC-PIM) [15, 16] and the node-based smoothed radial point interpolation method (NS-RPIM or LC-RPIM) [17].”
An n‐sided polygonal edge‐based smoothed finite element method (nES‐FEM) for solid mechanics (2010, methodology): “When only linear triangular or tetrahedral elements are used, the NS-FEM produces the same results as the method proposed by Dohrmann et al. [25] or to the LC-PIM [6] using linear interpolation.”
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”
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 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)].”
Assessment of smoothed point interpolation methods for elastic mechanics (2010, methodology): “Using the polynomial basis shape functions and performing the strain smoothing operation in smoothing domains associated with the field nodes, a node-based smoothed point interpolation method (NS-PIM or LC-PIM) has been developed [42, 43].”
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems (2009, methodology): “[19] or to the LC-PIM using linear interpolation [20].”