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Continuous meshless approximations for nonconvex bodies by diffraction and transparency. (English) Zbl 0864.73076
Summary: Continuous meshless approximations are developed for domains with non-convex boundaries, with emphasis on cracks. Two techniques are developed in the context of the element-free Galerkin method: a transparency method wherein smooth approximations are generated by making boundaries partially transparent, and a diffraction method, where the domain of influence wraps around a concave boundary. They are compared to the original method based on the visibility criterion in which the approximations are discontinuous in the vicinity of nonconvex boundaries. The performance of the methods is compared using two elastostatic examples: an infinite plate with a hole and a crack problem.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74R99 Fracture and damage
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