A three-dimensional stress field solution for pointed and sharply radiused V-notches in plates of finite thickness

By making use of the generalized plane strain hypothesis, an approximate stress field theory has been developed according to which the three-dimensional governing equations lead to a system where a bi-harmonic equation and a harmonic equation should be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, and the latter provides the solution of the corresponding out-of-plane shear notch problem. The system can be applied not only to pointed three-dimensional V-notches but also to sharply radiused V-notches characterized by a notch tip radius small enough. Limits and degree of accuracy of the analytical frame are discussed comparing theoretical results and numerical data from FE models.