# Radial basis functions with applications to solid mechanics

## Univ.-Prof. Dr. Sergej Rjasanow

**Dec. 18, 2012, 2:30 p.m. S2 059**

Radial basis functions (RBFs) have become increasingly popular for the construction of smooth interpolant $s: R^n \rightarrow R$ through a set of $N$ scattered, pairwise distinct data points.

In the first part of the talk we introduce the RBF's and discuss their properties.

The second part of the talk is devoted to the reconstruction of the threedimensional metal sheet surfaces obtained via incremental forming techniques. In this application, the data comes from optical measurements of sheet metal parts. The top and the bottom surfaces of the part are measured in a fixed frame of reference, and a distribution of thickness along the part is sought.

In the third part of the talk, a boundary integral formulation for a mixed boundary value problem in linear elastostatics with a conservative right hand side is considered. A meshless interpolant for the scalar potential of the volume force density is constructed by means of radial basis functions. An exact

particular solution to the Lame system with the gradient of this interpolant as the right hand side is found. Thus, the need of approximating the Newton potential is eliminated. The procedure is illustrated on numerical examples.