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

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.

Keywords:

• numerical method
• meshfree method
• adaptive analysis
• error indicator
• local refinement
• edge-based smoothed point interpolation methods
• strain smoothing

2010 AMS Subject Classifications :

• 35Q74
• 37N15
• 65D05
• 65D10
• 65N50