Recent developments in multi-parametric three-dimensional stress field representation in plates weakened by cracks and notches

P. Lazzarin, M. Zappalorto, F. Berto


The paper deals with the three-dimensional nature and the multi-parametric representation of the
stress field ahead of cracks and notches of different shape. Finite thickness plates are considered, under
different loading conditions. Under certain hypotheses, the three-dimensional governing equations of elasticity
can be reduced to a system where a bi-harmonic equation and a harmonic equation have to be simultaneously
satisfied. The former provides the solution of the corresponding plane notch problem, the latter provides the
solution of the corresponding out-of-plane shear notch problem. The analytical frame is applied to some
notched and cracked geometries and its degree of accuracy is discussed comparing theoretical results and
numerical data from 3D FE models.

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