Green’s Functions for the Biharmonic Equation: Bonded Elastic Media

Abstract

A comprehensive formulation of Green’s functions for biharmonic equations with respect to perfectly bonded, bimaterial, linear, isotropic, elastic media is presented. This is accomplished by extending Mindlin’s nuclei of strain method, which employs the method of images. The analysis involves properly scaling the nuclei, grouping the nuclei into different classes and introducing a matrix structure for each class. The strength vectors of the nuclei, required at the object and image points to represent the solution, are obtained by matrix-vector multiplications involving two invariant matrices, the “reflection matrix” and the “transmission matrix.” Algebraic expressions for the elements of the reflection and transmission matrices, which depend on the elastic properties of the materials, are presented.