Formulization of Three-Dimensional Stress and Strain Fields at Elliptical Holes in Finite Thickness Plates

Stress raisers such as holes are inevitable in structures at which stress concentration occurs and the static as well as fatigue strength of the structures can be significantly weakened. Therefore, to accurately evaluate the stress concentration factor and stress fields at holes is of essential importance for structure design and service life prediction. Although stress and strain concentration and fields at holes in finite thickness plates strongly change with and along the thickness, manuals of stress concentration for engineering design are mainly based on two-dimensional theory and no explicit formula is available even for circular holes in finite thickness plates. Here we obtain for the first time a complete set of explicit formulae for stress and strain concentration factors and the out-of-plane constraint factor at circular as well as elliptical holes in finite thickness plates by integrating comprehensive three-dimensional finite element analyses and available theoretical solutions. The three-dimensional stress distributions ahead of holes can also be predicted by the obtained formulae. With their accuracy and the corresponding applicable range being analyzed and outlined in detail, the formulae can serve as an important fundamental solution for three-dimensional engineering structure design and guideline for developing three-dimensional analytical methods.