Based on ANSYS finite element software, the deformation regularity of inner hole for prestressed two-layer flat container was analyzed, and polynomial interpolating functions were obtained in a sectional way.

Integration of fractal interpolation functions on various scales;

Establishment of multi-fields in MSC Patran by interpolation functions of Matlab;

Some properties of a fractal interpolation function;

The research of the application of the function interpolation in making up the Flash animation;

Error estimate about the third class of half - logarithm spline interpolating function;

The asymptotic expansion term of remainder term for error of inequality distance first kind cubic spline interpolating function is advanced using interpolation method for basic spline.

A method to form the interpolating function by using the moved least square method is introduced.

The interpolation functions of the RFE is polynomials of degree 4, which is the solution of elastic theory basic equation, the superiority and high efficiency of the plane 8-node RFE as compaired with the plane 4-node with several examples.