用边界元法求具有应力集中的轴对称零件最优过渡形状

A Solution to the Optimum Trasition Shape of Axisymmetric Parts with Stress Concentration by BEM

用轴对称边界元法和DFP优化算法确定了受拉或受扭阶梯圆轴的最佳过渡形状。优化目标在于使过渡曲线处的表面应力均布,而过渡曲线是用拉格朗日插值多项式描述的。在优化过程中采用了逐步升维法以避免过渡曲线发生畸变。将优化结果与文献中用液体动力学方法求得的过渡轮廓曲线进行了对照,对照结果表明,本文所得结果更为合理。

An optimum transition shape of a stepped shaft in tension or in torsion is detenrmined by using the axisymmetric BEM and the DFP optimization algorithm. The objective is used to make the surface stress of the transition curve be uniformly distributed, and this curve is discribed in Lagrangian interpolation poly nomials. During optimization process, a progressively ascending dimention procedurs is proposed to avoid the distortion of the transition curve. The optimized results are compared with the transition boundary curve derived from hydrodynamics in literature and the calculated surface stress distributions show that the results obtained in this paper is more reasonable.