Composite laminates are increasingly being used as primary load bearing members in
structures.  However, because of the directional dependence of the properties of
composite materials, additional failure modes appear that are absent in
homogeneous, isotropic materials.  Therefore, a stress analysis of a composite
laminate is not complete without an accurate representation of the transverse
(out-of-plane) stresses.

Stress recovery is a common method to estimate the transverse stresses from a
plate or shell analysis.  This dissertation extends stress recovery to problems
in which geometric nonlinearities, in the sense of von K\'{a}rm\'{a}n,  are
important.  The current work presents a less complex formulation for the stress
recovery procedure for plate geometries, compared with other implementations,
and results in a post-processing procedure which can be applied to data from
any plate analyses; analytical or numerical methods, resulting in continuous or
discretized data.

Recovered transverse stress results are presented for a variety of
geometrically nonlinear example problems: a semi-infinite plate subjected to
quasi-static transverse and shear loading, and a finite plate subjected to both
quasi-static and dynamic transverse loading.  For all cases, the corresponding
results from a fully three-dimensional stress analysis are shown alongside the
distributions from the stress recovery procedure.  Good agreement is observed
between the stresses obtained from each method for the cases considered.
Discussion is included regarding the applicability and accuracy of the
technique to varying plate geometries and varying degrees of nonlinearity, as
well as the viability of the procedure in replacing a three-dimensional
analysis in regard to the time required to obtain a solution.

The proposed geometrically nonlinear stress recovery procedure results in
estimations for transverse stresses which show good correlation to the
three-dimensional finite element solutions.  The procedure is accurate for
quasi-static and dynamic loading cases and proves to be a viable replacement
for more computationally expensive analyses.