A Second-Order Perturbation Method for the Stress Analysis of Solids with Slightly Wavy or Irregular Surfaces

Abstract

Actual shapes of welded plate structures slightly deviate from the designed geometry due to imperfections mainly caused by welding. In order to investigate the stress concentration due to weld geometry, a second-order perturbation method is applied to the two-dimensional elastic problem of a semi-infinite plane, whose surface slightly deviates from a straight line. The accuracy of the method is confirmed by solving the problem of a semi-elliptical notch under combined tensile and in-plane bending conditions. The method is applied to the problem of a slightly wavy surface, which is sometimes observed in actual weld beads. Since it is well known that the fatigue strength of weldment cannot be predicted simply by using the peak stress of highly stress-concentrated regions, the stress gradient and the stress distribution in the neighborhood of the peak point are also presented. The present method is found to be effective for the analyses of geometrical imperfections with arbitrary surface shapes, which may be difficult to analyze by conventional numerical analysis procedures.