Fatigue, the birth and growth of cracks in metal parts subjected to repeated loading, has been a problem plaguing engineers since the Industrial Revolution and the advent of rotating or reciprocating machinery. Designing against metal fatigue was studied briefly in several aspects. Examples of fatigue failures were shown. Fatigue was classified by loading: uniaxial Fatigue, multiaxial fatigue, cumulative fatigue da¬mage. Fatigue design criteria were discussed: Infinite-Life Design, Safe-Life Design, Fail-Safe Design, and Damage Tolerant Design. Mitigation of notch effects by design, improvement of fatigue strength of metal parts by residual stress and surface finishing were discussed. Relative fatigue beha¬vior was studied under various environmantal conditions. Especially the effects of corrosion, temperature, fretting, and irradiation were covered.

In this paper, it is demonstrated that, with the distribution of lowestorder concentrated (discrete) singularities of delta function nature, the solution to the linear free surface problem can be obtaianed with a remarkable degree of accuracy. The linearized bounday valve problem is formulated subject to boundary conditions for the determination of strengths of singularities; the simple sources above (not on) the free surface and the vortices on the body surface. Three sample calculations were performed; the flow about a submerged vortex of known strength, the flow past a submerged circular cylinder, and the flow around a hydrofoil section. The convergence of the numerical procedure is achieved with a relatively small number of elements, The final results are compared with those of the publi¬shed works, and are considered very satisfactory.