Effect of higher order taylor series expansion terms of the ni-prim on the solution accuary of 2 nd lastic prblems.

Abstract

In this study, effects of higher order Taylor series expansion terms in the nodal integration scheme of radial point interpolation method (NI-RPIM) are investigated on the solution accuracy of 2D elastic problems. The nodal integration scheme is proposed by Liu et al. [1] and based on the Taylor series expansion. It is used with increasing the order of terms up to 4th order in this study. 3 different case studies are applied and the results are compared with analytical, FEM and RPIM with Gaussian integration solutions. Also the effect of number of nodes is investigated. It can be accepted that the usage of Taylor series expansion and Gaussian method in integration of RPIM give similar solution times. However NI-RPIM with higher order Taylor series expansion terms has better solution speed than using Gaussian integration, especially in the solutions of model which has higher number of nodes. It is detected that 2nd order terms of nodal integration give sufficient results. If stress values are investigated, 4th order terms of nodal integration can be used for accuracy of the solution.