Assessment of smoothed point interpolation methods for elastic mechanics

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Abstract
A generalized gradient smoothing technique and a smoothed bilinear form of Galerkin weak form have been recently proposed by Liu et al. to create a wide class of efficient smoothed point interpolation methods (PIMs) using the background mesh of triangular cells. In these methods, displacement fields are constructed by polynomial or radial basis shape functions and strains are smoothed over the smoothed domain associated with the nodes or the edges of the triangular cells. This paper summarizes and assesses bound property, convergence rate and computational efficiency for these methods. It is found that: (1) the incorporation of the PIMs with the node‐based strain smoothing operation allows us to obtain an upper bound to the exact solution in the strain energy; (2) the incorporation of the PIMs with the edge‐based strain smoothing operation using triangular background mesh can produce a solution of ‘ultra‐accuracy’ and ‘super‐convergence’; (3) the edge‐based strain smoothing operation together with the linear interpolation can provide better computational efficiency compared with other smoothed PIMs and the finite element method when the same triangular mesh is used. These conclusions have been examined and confirmed by intensive examples. Copyright © 2009 John Wiley & Sons, Ltd.

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