FRICTIONLESS CONTACT IN A LAYERED PIEZOELECTRIC MEDIUM COMPOSED OF MATERIALS WITH HEXAGONAL SYMMETRY
FRICTIONLESS CONTACT IN A LAYERED PIEZOELECTRIC MEDIUM COMPOSED OF MATERIALS WITH HEXAGONAL SYMMETRY
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A matrix formulation is presented for the solution of frictionless contact problems on arbitrarily multilayeredpiezoelectric half-planes. Different arrangements of elastic and transversely orthotropic piezoelectric materials within themultilayered 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 isthen reformulated using the local/global stiffness method, in which a local stiffness matrix relating the stresses and electricdisplacement 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 mixedboundary conditions reduces the problem to an integral equation. This integral equation is numerically solved for theunknown contact pressure using a technique based on the Chebyshev polynomials.
Resumen: Se presenta una formulación matricial para la solución de problemas de contacto sin fricción en semiplanos piezoeléctricos elásticos de múltiples capas. Se consideran diferentes disposiciones de materiales piezoeléctricos elásticos y transversalmente ortotrópicos dentro del medio de múltiples capas. Se usa una deformación de plano generalizada para obtener las ecuaciones gobernantes de equilibrio para cada capa individual, que se resuelven con la técnica de transformada de Fourier infinita. Entonces el problema se reformula con el método de rigidez local/global, en el cual se formula para cada capa una matriz de rigidez local que relaciona los esfuerzos y el desplazamiento eléctrico con los desplazamientos mecánicos y el potencial eléctrico en el dominio transformado. En seguida se ensambla en una matriz de rigidez global para todo el semiplano imponiendo la continuidad interfacial de tracciones y desplazamientos. Este enfoque por rigidez local/global no sólo elimina la necesidad de hallar explícitamente los coeficientes de Fourier desconocidos, sino que también permite el uso de algoritmos numéricos eficientes, muchos de los cuales se desarrollaron para análisis por elementos finitos. A diferencia de los métodos de elementos finitos, este enfoque requiere una entrada miníma. El uso de condiciones de borde mezcladas reduce el problema a una ecuación integral, que se resuelve para la presión de contacto desconocida con una técnica basada en los polinomios de Chebyshev.
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