Stress Concentration Problems

Abstract

Stress concentration in an elastic body may be caused mainly by the two-mechanisms i.e., concentrated forces acting to a body and geometrical discontinuities of a body such as holes or abrupt change of its surface geometry. The local stress increase induced by stress concentration sometimes causes the initiation of a fatigue crack in a structure, which must be carefully examined for engineering design. We shall first discuss the stress concentration by a concentrated applied force. Then, stress concentrations due to a circular hole and an elliptic hole are calculated by using the Airy’s stress function. The general solution in a polar coordinate system derived in the previous chapter and the complex potential method discussed in Appendix A will be utilized to obtain the solutions, where the latter is essential for the analysis of elliptic hole problem, which is closely related to a crack problem to be explained in the next chapter.