The boundary value contact problem of electroelasticity for piecewise-homogeneous piezo-electric plate with elastic inclusion and cut

TL;DR

This paper addresses a complex electroelastic contact problem involving piezo-electric plates with inclusions and cuts, reducing it to a solvable system of singular integro-differential equations using advanced mathematical methods.

Contribution

It introduces a novel analytical approach to solve boundary value problems in electroelasticity for heterogeneous piezo-electric plates with inclusions and cuts.

Findings

Explicit solutions to the formulated problem.

Reduction to a Riemann boundary value problem.

Application of analytic function methods to complex geometries.

Abstract

A contact problem of the theory of electroelasticity for piecewise-homogeneous plate of piezo-electric material with infinite cut and elastic finite inclusion of variable bending rigidity is considered. By using methods of the theory of analytic function, the problem is reduced to a system of singular integro-differential equation with fixed singularity. Using an integral transformation a Riemann problem is obtained, the solution of which is presented in explicit form.