Radial basis functions with applications to solid mechanics

Univ.-Prof. Dr. Sergej Rjasanow

Dec. 18, 2012, 3:30 p.m. S2 059

Radial basis functions (RBFs) have become increasingly popular for the
construction of smooth interpolant s : R^n --> 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.