Frictional Contact Problem of One Dimensional Hexagonal Piezoelectric Quasicrystals Layer

Based on three-dimensional (3D) general solutions for one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs), this paper studied the frictional contact problem of 1D-hexagonal PEQCs layer. The frequency response functions (FRFs) for 1D-hexagonal PEQCs layer are analytically derived by applying double Fourier integral transforms to the general solutions and boundary conditions, which are consequently converted to the corresponding influence coefficients (ICs). The conjugate gradient method (CGM) is used to obtain the unknown pressure distribution, while the discrete convolution-fast Fourier transform technique (DC-FFT) is applied to calculate the displacements and stresses of phonon and phason, electric potentials and electric displacements. Numerical results are given to reveal the influences of material parameters and loading conditions on the contact behavior. The obtained 3D contact solutions are not only helpful further analysis and understanding of the coupling characteristics of phonon, phason and electric field, but also provide a reference basis for experimental analysis and material development.

OPTIMIZATION PROBLEMS FOR A THERMOELASTIC FRICTIONAL CONTACT PROBLEM

In the present paper, we analyze and study the control of a static thermoelastic contact problem. We consider a model which describes a frictional contact problem between a thermoelastic body and a deformable heat conductor obstacle. We derive a variational formulation of the model which is in the form of a coupled system of the quasi-variational inequality of elliptic type for the displacement and the nonlinear variational equation for the temperature. Then, under a smallness assumption, we prove the existence of a unique weak solution to the problem. Moreover, we establish the dependence of the solution with respect to the data and prove a convergence result. Finally, we introduce an optimization problem related to the contact model for which we prove the existence of a minimizer and provide a convergence result.