Double scaling and master curve to predict K_ts for elliptically notched orthotropic plates from K_ts in circularly notched isotropic plates

摘要

The key role played by the so-called stress concentration factors (symbolically usually referred to as K(t)s) while performing either analysis or design in both mechanical engineering and structural engineering is a well-proven fact; hence, the corresponding accuracy and ease of determination in their estimation have critical implications related to engineering matters. In a previous work, we showed that starting with the K(t)s for rectangular isotropic plates with circular holes the K(t)s for rectangular orthotropic plates with elliptic holes can be easily and accurately predicted, using a double scaling procedure (a geometric scaling and a material scaling) together with a basic K-t curve employed as a master curve. In the present work we investigate, in an engineering heuristic manner, whether the stated double scaling procedure exhibits a more general structure so that it can accurately be applied to different plate stress raiser geometries. Specifically, we examine if starting with the known K(t)s for rectangular isotropic plates with circular notches, used as a master curve, the K(t)s for orthotropic plates with elliptic notches can be easily and accurately predicted as well. Using a simple hand calculator, we show that the resulting proposed set of predicting mathematical expressions makes virtually unnecessary the use of complex numerical programs (FEM based for example) to determine the corresponding K(t)s, producing at the same time accurate results with a maximum average recorded error of 2.59%. Additionally, given that a K-t predictive procedure for holed plates was presented in our previous work, and for notched plates in this work, we found necessary first to examine the hypothesis that suggests using K(t)s from holed plates as good approximations for K(t)s for notched ones and vice versa. We found this hypothesis not to be valid for either isotropic or orthotropic plates. In the course of this work it was found, rather significantly, that the well-known double square root material contribution to Kts is valid for both holed plates as well as notched ones.