Monogenic series expansions and an application to linear elasticity
Bauhaus-Universitaet Weimar, Germany
In the talk we shall give a brief overview of some interesting characteristics of recently studied orthogonal Appell bases [1,2] of solid spherical monogenics in IR3. In this context, a compact closed form representation of the Appell basis elements in terms of classical spherical harmonics is shown. Based on a recently developed spatial generalization of the Kolosov-Muskhelishvili formulae in terms of a monogenic and an anti-monogenic function , the Appell basis is used to construct a polynomial basis of solutions to the Lamé-Navier equation from linear elasticity. Finally, a hypercomplex version of the classical Kelvin solution which describes the elastic displacements of a concentrated force acting at the origin of an infinite body is discussed.
ISSN 1611 - 4086 | © IKM 2015