Perforated finite structures are prevalent in engineering and their mechanical integrity is often controlled by the stresses near geometric discontinuities. Theoretical stress analyses are virtually impossible and numerical analyses can be challenging for finite structures containing discontinuities. Theoretical and numerical analyses both necessitate knowing the loading, but such information is typically unavailable in practice. This thesis therefore presents an effective experimental-analytical-numerical hybrid-method to determine the stresses/strains/displacements reliably at and near geometric discontinuities in loaded, finite orthotropic or isotropic members. The technique processes measured information with a combination of Airy stress functions, conformal mapping, analytic continuation and least squares. Knowing the external loading is unnecessary. Since one often does not know a priori where the most serious stresses will occur in such structures, full-field analyses are required. Measured information at or near discontinuities is also typically unreliable. In addition to overcoming the latter difficulty, hybridizing experimentally measured data with the indicated analytical and numerical tools satisfies equilibrium, compatibility and local traction-free boundary conditions. The approach is applied to round and elliptical holes and cracks in finite orthotropic composite plates as well as to perforated or notched isotropic members. In the latter cases, the structurally critical locations are far from any reliable measured input data.

The technique provides reliable stresses and/or displacements throughout the structure, including along the edge of geometric discontinuities, from only a single component of measured information. Measured thermal or displacement data are employed. Stress intensity factors are available by post-processing the hybrid-determined stresses or displacements with fracture mechanics concepts. An advantage of the displacement-based approach is that it does not involve physically differentiating the measured data to obtain strains/stresses. Rather the method is established on strong mechanics-based algorithms. Results by the hybrid-method are validated using FEA, force equilibrium, strain-gages and other published information.

The present hybrid-method can analyze extremely finite plates of any material properties containing virtually any types/sizes of holes or cracks. Ability to obtain reliable results at important locations but which are located very far from reliable measured input is a desirable feature of the current hybrid technique. The displacement-based approach is particularly well-suited to nonlaboratory-type environments.