R. Gachechiladze, J. Gwinner, D. Natroshvili
abstract:
We study unilateral frictionless contact problems with hemitropic materials in
the theory of linear elasticity. We model these problems as unilateral (Signorini
type) boundary value problems, give their variational formulation as spatial
variational inequalities, and transform them to boundary variational
inequalities with the help of the potential method for hemitropic materials.
Using the self-adjointness of the Steklov-Poincaré
operator, we obtain the equivalence of the boundary variational inequality
formulation and the corresponding minimization problem. Based on our variational
inequality approach we derive existence and uniqueness theorems. Our
investigation includes the special particular case of only traction-contact
boundary conditions without prescribing the displacement and microrotation
vectors along some part of the boundary of the hemitropic elastic body.
Mathematics Subject Classification: 35J85, 74A35, 49J40
Key words and phrases: Elasticity theory, hemitropic material, boundary variational inequalities, potential method, unilateral problems.