An optimization transition shape of a stepped shaft in tension or in torsion is determined by using the BEM and the DFP optimization algorithm. The objective is to have the distributive tangential stress on the transition curve of the stepped shaft be uniformed and the stress concentration factor be minimized. The transition curve is discribed in Lagrangian interpolation polynomial. During optimization process, a progressively - ascending - dimension procedure is proposed to avoid the distortion of the transition curve. The optimized results are compared with the transition curve derived from hydrodynamics in literature and the calculated surface stress distributions show that the results obtained in this paper is more reasonable.
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