Estimation with a Few Strain Gages of Stress Fields near a Notch Root of Actual Structures Under In-Plane Loading

Abstract

Abstract In this paper, a simple method is proposed for estimating with a few strain gages stress fields near a notch root in plates under in-plane loading. In the present method, the stress fields are estimated by solving the boundary value problems. Concretely, we use the Airy's stress function for an arbitrary plate with a free circular hole, considering an edge near a notch root as a part of a free circular hole. The unknown coefficients of the Airy's stress function are determined from stress values with strain gages along a certain closed curve so that the Airy's stress function satisfies the boundary conditions at the curve. The strain values are measured only at four points on a circular arc whose radius is 1.5 times as large as the notch root radius. The method of least squares is used for determining the unknown coefficients. We demonstrate the present method using eight types of notched plates. We obtained accurate estimation results except for a few cases.