Fundamental solutions for small deformations superposed on finite biaxial extension of an elastic body

Infinite and semi-infinite isotropic elastic bodies in finite biaxial extension are in addition subjected to infinitesimal concentrated forces parallel and perpendicular to the extension plane respectively. In the semi-infinite case the forces are on the plane boundary. The problems are analogous to those for transversely isotropic bodies subjected to the infinitesimal concentrated forces only. Solutions to both categories of problems are given with the aid of potential functions. To facilitate the evaluation, expressions for the resultant force on a surface are given in terms of line integrals around the bounding curve. The solutions to the semi-infinite body problems are derived from those to the infinite body problems by adding appropriate potential functions so as to meet the boundary conditions on the plane surface. Computations for the semiinfinite cases of the superposition problems are given.