An adaptive edge-based smoothed point interpolation method for mechanics problems.

Bibliographic Details
Title: An adaptive edge-based smoothed point interpolation method for mechanics problems.
Authors: Chen, L.1 (AUTHOR), Zhang, G.Y.1,2 (AUTHOR), Zhang, J.3 (AUTHOR), Nguyen-Thoi, T.1 (AUTHOR), Tang, Q.4 (AUTHOR)
Source: International Journal of Computer Mathematics. Jul2011, Vol. 88 Issue 11, p2379-2402. 24p.
Subject Terms: Interpolation, Smoothing (Numerical analysis), Mathematical physics, Mechanics (Physics), Meshfree methods, Error analysis in mathematics, Stochastic convergence, Stress concentration
Abstract: This paper develops a smoothing domain-based energy (SDE) error indicator and an efficient adaptive procedure using edge-based smoothed point interpolation methods (ES-PIM), in which the strain field is constructed via the generalized smoothing operation over smoothing domains associated with edges of three-node triangular background cells. Because the ES-PIM can produce a close-to-exact stiffness and achieve 'super-convergence' and 'ultra-accurate' solutions, it is an ideal candidate for adaptive analysis. A SDE error indicator is first devised to make use of the features of the ES-PIM. A local refinement technique based on the Delaunay algorithm is then implemented to achieve high efficiency. The refinement of nodal neighbourhood is accomplished simply by adjusting a scaling factor assigned to control local nodal density. Intensive numerical studies, including the problems with stress concentration and solution singularity, demonstrate that the proposed adaptive procedure is effective and efficient in producing solutions with desired accuracy. [ABSTRACT FROM AUTHOR]
Database: Library, Information Science & Technology Abstracts
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