CONTINUOUS MESHLESS APPROXIMATIONS FOR NONCONVEX BODIES BY DIFFRACTION AND TRANSPARENCY

Continuous meshless approximations are developed for domains with non- convex boundaries, with emphasis on cracks. Two techniques are develop ed in the context of the element-free Galerkin method: a transparency method wherein smooth approximations are generated by making boundarie s partially transparent, and a diffraction method, where the domain of influence wraps around a concave boundary. They are compared to the o riginal method based on the visibility criterion in which the approxim ations 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. The continuous ap proximations show only moderate imporvement in accuracy over the disco ntinous approximations, but yield significant improvements for enhance d bases, such as crack-tip singular functions.