Thermoelastic contact problem of a rigid punch sliding on a functionally graded piezoelectric layered half plane with heat generation

In this study, the plane steady state thermoelastic frictional contact problem between a rigid cylindrical punch and a functionally graded piezoelectric material (FGPM) layer bonded to the homogeneous half plane is considered. The rigid punch is assumed to be a perfect electric conductor and thermal insulator and slides over the FGPM layer with a small constant speed and heat flux is generated due to the friction. Applying the Fourier integral transform technique and thermoelasticity, general stress, displacement, and electrical expressions for the thermoelastic piezoelectric contact problem are derived. Using the boundary conditions, the contact problem is reduced to Cauchy-type singular integral equations of the second kind in which the contact stress, the electrical displacement and the contact widths are unknown. The system of singular integral equation is solved numerically using Gauss-Jacobi and Gauss-Chebyshev integration formula. The effect of material inhomogeneity parameter, moving velocity, friction coefficient, external load, electric charge, punch radius on the contact stress, in-plane stress, electric displacement, and generated temperature are discussed in detail.