Frictionless contact in a layered piezoelectric medium composed of materials with hexagonal symmetry (2004)
A matrix formulation is presented for the solution of frictionless contact problems on arbitrarily multilayered piezoelectric half-planes. Different arrangements of elastic and transversely orthotropic piezoelectric materials within the multilayered medium are considered. A generalized plane deformation is used to obtain the governing equilibrium equations for each individual layer. These equations are solved using the infinite Fourier transform technique. The problem is then reformulated using the local/global stiffness method, in which a local stiffness matrix relating the stresses and electric displacement to the mechanical displacements and electric potential in the transformed domain is formulated for each layer. Then it is assembled into a global stiffness matrix for the entire half-plane by enforcing interfacial continuity of tractions and displacements. This local/global stiffness approach not only eliminates the necessity of explicitly finding the unknown Fourier coefficients, but also allows the use of efficient numerical algorithms, many of which have been developed for finite element analysis. Unlike finite element methods, the present approach requires minimal input. Application of the mixed boundary conditions reduces the problem to an integral equation. This integral equation is numerically solved for the unknown contact pressure using a technique based on the Chebyshev polynomials.