A three-dimensional laminated medium is studied by an approach which replaces the heterogeneous medium by an equivalent homogeneous material. A set of macroscopic elastic constants is developed in terms of the properties of the constituent layers by considering a representative small element of the laminated medium and imposing the condition of continuity of stress and displacement at the layer interfaces. An example boundary value problem is also considered. Based on the solution of the boundary value problem for the homogeneous material, stress and strain fields corresponding to each layer are then calculated. This individual layer solution contains certain dis continuous stresses and strains as does the exact solution for the layered material.

This paper presents a method of solution for an infinite wedge containing a symmetrically located circular hole. The solution is formulated separately according to the given in-plane edge tractions being even or odd with respect to the axis of the wedge. In either case, the stress function is constructed as the sum of four parts of biharmonic functions, two in the form of integrals and the other two in the form of series, in addition to a basic stress function for an otherwise unperforated wedge. The four parts as a whole give no traction along the edges and no stress at infinity of the wedge. Together with the basic stress function, the boundary conditions of no traction at the rim of hole are adjusted. Complex expressions are used in adjusting the boundary conditions. Finally, numerical examples are given for illustration.