THE ERROR ANALYSIS OF ELEMENT-FREE METHOD BASED ON RADIAL BASIS FUNCTION USED IN MECHANICAL PROBLEMS

Although the choice of shape parameters in the radial PIM (point interpolation method) is a hot issue in the numerical computation based on the element-free method and some empirical formulas of the shape parameters are proposed, but how the influence domain affects these shape parameters remains to be studied. In this paper, the effect of the MQ (multi-quadrics) radial basis function's shape parameters on the errors of the element-free method is studied. The variations of the shape function's derivative with the shape parameters and the symmetrical and unsymmetrical node distributions around the evaluation point are analyzed together with the effect of the size of the influence domain on the error, and based on the analysis, the relationship between the errors and the shape parameters and the range of the suitable influence domain are obtained.