Frictionless contact in a layered piezoelectric medium characterized by complexeigenvalues

Abstract

A local/global stiffness matrix formulation is presented to study the response of anarbitrarily multilayered piezoelectric half-plane indented by a rigid frictionlessparabolic punch. The methodology is extended to accommodate the presenceof piezoelectric layers that are characterized by complex eigenvalues. Differentarrangements of elastic and transversely orthotropic piezoelectric materials within themultilayered medium are considered. A generalized plane deformation is usedto obtain the governing equilibrium equations for each individual layer. Theseequations are solved using the infinite Fourier transform technique. The problemis then reformulated using the local/global stiffness method, in which a localstiffness matrix relating the stresses and electric displacement to the mechanicaldisplacements and electric potential in the transformed domain is formulatedfor each layer. Then it is assembled into a global stiffness matrix for the entirehalf-plane by enforcing continuity conditions along the interface. Application ofthe mixed boundary conditions reduces the problem to an integral equation forthe unknown pressure in the contact area. This integral has a divergent kernelthat is decomposed into a Cauchy-type and regular parts using the asymptoticproperties of the local stiffness matrix. The resulting equation is numerically solvedfor the unknown contact pressure using a technique based on the Chebyshevpolynomials.