Thesis (PhD) - Cyprus International University. Institute of Graduate Studies and Research Civil Engineering

In many applications, such as structure, soil mechanics, soil-foundation interaction,
composite materials behavior, or welded materials, when the free surface is close by,
the problem of two joined quarter spaces under a body force is useful to explain the
behavior of the two media under load. Due to the domain's complexity, up to date, no
analytical solution for determining elastic fields inside the two regions has been
offered. The problem of a point load acting at the interior of one of the two joined
isotropic quarter spaces is addressed in this study. In terms of Papkovich-Neuber
functions, the elastic fields for the two regions are presented. Both traction-free
boundary conditions and complete interface bonding were used for the solution. To
overcome the complexity of the partial differential equations of boundary conditions,
Green's analysis and a proposed potential Green's function of two joined quarter spaces
were integrated with the integral image method. For various material combinations,
stress distributions across the two regions and displacement on the free surfaces of the
two-quarter spaces are shown. The continuity of stresses and displacements at the
interface was preserved, but some stress disruption on the free surface was seen. The
proposed harmonic functions and/or the domain's complexity may be responsible for
the stress disturbance. Despite the disturbance of the stress on the free boundary, the
solution leads back to all the previously well-known problems, such as Rongved,
Mindlin, Boussinesq, Cerutti, and Kelven’s problem.