A meshfree poly-cell Galerkin (MPG) approach for problems of elasticity and fracture
C. Zheng; S. C. Wu; X. H. Tang; and J. H. Zhang

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 38, No. 2, pp. 149-178, 2008
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Keywords Meshfree; Poly-cell local support; Improved MLS; Superconvergence; Fracture.
Abstract A novel meshfree poly-cell Galerkin method is developed for problems of elasticity and fracture. To improve accuracy, a poly-cell support is proposed to ensure the alignment of shape function support and the integration domain. By orthonormalizing basis functions, the improved moving least-square is formulated soundly, in which frequent matrix inversions are avoided. The Nitsche's method is introduced to treat the essential boundary conditions. It is found that computed solutions are more accurate than those obtained using the circle support used in standard MLS. Furthermore, numerical results present the superconvergent property, compared with the theoretical values in both displacement and energy norms. In fracture analyses, the stress intensity factors can be evaluated independent of$J$-integral path with better accuracy, and rather smooth stress field can be achieved, even near to region of the crack tip. It is also found the present MPG works well even for extremely distorted meshes.
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