Research On Calculation Accuracy Of Rpim And Its Application

Radial Point Interpolation Meshless Method (RPIM) is a new numerical method developed in recent years. It is advantageous over the original PIM with polynomial basis in avoiding singularity when shape functions are construct ed. In addition, it overcomes the difficulty in implementation of esstionial bou ndary condition by previous meshless methods, because interpolation has the charater of Kronecher Delta function. For only the node data needs to be prepared and element division is not required, this mothod simplifies the data proce ssing and thus improves the calculation speed. In this paper, we do some resea rch on factors existed in RPIM which influence the calculation accuracy, and apply this method to different computing areas.First of all, the paper briefly introduces the development of RPIM and the difference between Meshless Method and Finite Element Method. Secondly, the construction and the property of point interpolation shape functions are describ ed. At last, the basic principle of radial point interpolation meshless method with polynomial basis is mainly studied, and then gives the calculation process of RPIM.Next the paper discusses the factors that influnce the computation accura- cy of RPIM, which include the shape parameter and radius of influence domain in radial basis function. And finally this paper gives some valuable conclusions.Lastly, RPIM is applied to slove the thick plate bending problems and te- mperature field problems, then the corresponding programs are given accord- ing to each example. The results show that RPIM is applicable in the thick pla- te bending problems and temperature field, and have a good application prospect.