Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.cma.2008.12.011
Title: A point interpolation method with least square strain field (PIM-LSS) for solution bounds and ultra-accurate solutions using triangular mesh
Authors: Xu, X.
Liu, G.R. 
Zhang, G.Y.
Keywords: Finite element method
Least square method
Meshfree method
Numerical methods
Point interpolation method
Solution bound
Strain constructed Galerkin weak form
Issue Date: 15-Apr-2009
Source: Xu, X., Liu, G.R., Zhang, G.Y. (2009-04-15). A point interpolation method with least square strain field (PIM-LSS) for solution bounds and ultra-accurate solutions using triangular mesh. Computer Methods in Applied Mechanics and Engineering 198 (17-20) : 1486-1499. ScholarBank@NUS Repository. https://doi.org/10.1016/j.cma.2008.12.011
Abstract: A point interpolation method with least square strain field (PIM-LSS) is developed for solid mechanics problems using triangular background mesh. In the PIM-LSS, PIM shape functions are used for displacement field construction that may or may not be compatible, and a least square fitting technique is adopted to construct the strain field. A strain constructed Galerkin (SC-Galerkin) weak formulation is then proposed for establishing discretized PIM-LSS models that have a number of special properties. We proved theoretically (1) the PIM-LSS provides a "softening" effect to the FEM model, and a "stiffing" effect to the node-based smoothed point interpolation method (NS-PIM) model; (2) the exact solution is bounded from both by PIM-LSS solutions with strain field of zero-order fitting and that with higher order fitting; (3) There exists a preferred order of fitting for the strain field such that ultra-accurate (one order higher accuracy) solution can be obtained using the PIM-LSS. These theorems and properties have been confirmed in numerical examples. © 2009 Elsevier B.V. All rights reserved.
Source Title: Computer Methods in Applied Mechanics and Engineering
URI: http://scholarbank.nus.edu.sg/handle/10635/54718
ISSN: 00457825
DOI: 10.1016/j.cma.2008.12.011
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