Two scale meshfree method for the adaptivity of 3-D stress concentration problems

In this study, a meshfree method called Reproducing Kernel Particle Method (RKPM) with an inherent characteristic of multi-resolution is modified to d evelop structural analysis algorithm using two scales. The shape function o f RKPM is decomposed into two scales, high and low. The two scale decomposi tion is incorporated into linear elastic formulation to obtain high and low scale components of von Mises stresses. The advantage of using this algori thm is that the high scale component of von Mises stress indicates the high stress gradient regions without posteriori estimation. This algorithm is a pplied to the analysis of 2- and 3-dimensional stress concentration problem s. It is important to note that the two scale analysis method has been appl ied to S-dimensional stress concentration problem for the very first time. Also, the possibility of applying this algorithm to adaptive refinement tec hnique is studied. The proposed method is verified by analyzing typical 2- and S-dimensional Linear elastic stress concentration problems. The results show that the algorithm can effectively locate the high stress concentrati on regions and can be utilized as an efficient indicator for the adaptive r efinement technique.