L. Giorgashvili and D. Natroshvili
abstract:
We consider the differential equations of statics of the theory of elasticity of
hemitropic materials. We derive general representation formulas for solutions,
i.e., for the displacement and microrotation vectors by means of three harmonic
and three metaharmonic functions. These formulas are very convenient and useful
in many particular problems for domains with concrete geometry. Here we
demonstrate an application of these formulas to the Neumann type boundary value
problem for a ball. We construct explicit solutions in the form of absolutely
and uniformly convergent series.
Mathematics Subject Classification: 74H20, 74H45
Key words and phrases: Elasticity theory, hemitropic materials, boundary value problems, general representation of solutions, transmission problems.