Orthogonal polynomial solutions for a flat elliptic indenter on a multilayered elastic half-space (Q1287049)

We discuss a general mathematical formulation of a contact problem involving a flat elliptic indenter resting on a multilayered elastic medium. A standard matrix formulation results in a dual integral equation for the unknown stress under the indenter, in which kernel function is given in terms of product of suitable matrices. The dual integral equation is solved specifically for a two-layered medium. To this end, the dual integral equation is first transformed into an infinite system of equations involving the Abelian transform of unknown stresses. Then the unknown quantities are expanded in orthogonal Jacobi polynomials.