The stress and strain concentrations of out-of-plane bending plate containing a circular hole

The elastic stress and strain fields of a finite thickness plate containing a circular hole subjected to out-of-plane bending are systematically investigated using the finite element method. It is found that the stress and strain concentration factors of the finite thickness plate are different except at the notch root of the free surface even if the plate is in elasticity state. The through-thickness distributions of strain components are not linear with the distance from the mid-plane in the stress concentration region. The nonlinearity of these distributions is very severe near the free surface especially in thick plate. The Euler–Bernoulli hypothesis and Kane–Mindlin's plate theory may not be reasonable to be used in the stress concentration region especially near the free surface. The maximum stress and strain do not always occur on the free surface and their locations depend on the moment ratio and the plate thickness. The maximum stress and strain concentration factors occur on the free surface only in thin plates of small moment ratio. The differences between the maximum value and surface value of stress concentration factor increase with the plate thickness and the moment ratio. This relation of strain concentration factor is similar to the one of stress concentration factor. But the difference magnitude of stress concentration factor is larger than that of strain concentration factor in same plate.