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 develop structural analysis algorithm using two scales. The shape function of RKPM is decomposed into two scales, high and low. The two scale decomposition is incorporated into linear elastic formulation to obtain high and low scale components of von Mises stresses. The advantage of using this algorithm is that the high scale component of von Mises stress indicates the high stress gradient regions without posteriori estimation. This algorithm is applied to the analysis of 2- and 3-dimensional stress concentration problems. It is important to note that the two scale analysis method has been applied to 3-dimensional stress concentration problem for the very first time. Also, the possibility of applying this algorithm to adaptive refinement technique is studied. The proposed method is verified by analyzing typical 2- and 3-dimensional linear elastic stress concentration problems. The results show that the algorithm can effectively locate the high stress concentration regions and can be utilized as an efficient indicator for the adaptive refinement technique.