Rigid‐ and elastic‐ plastic solids obeying quite a general yield criterion represented by linear functions of the principal stresses are considered. A general axisymmetric state of stress satisfying the hypothesis of Haar and von Karman is analyzed in quasi‐static flow. The circumferential velocity vanishes. A superimposed restriction on the yield criterion is that the system of stress equations is hyperbolic. The primary objective of this study is to select optimal coordinates and unknowns for deriving the integrable differential relations in their most convenient form for numerical treatments. It is shown that there exists a simple relation between the scale factors of the principal lines coordinate system (the coordinate curves of this coordinate system coincide with the trajectories of the principal stresses). Another simple relation exists between the scale factors and the principal stresses. The mapping between the principal lines and cylindrical coordinates is determined by a system of hyperbolic differential equations.

中文翻译：

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轴向对称下分段线性屈服准则的主应力轨迹几何

刚体和弹塑性固体服从相当普遍的屈服准则，由主应力的线性函数表示。在准静态流中分析了满足Haar和von Karman假设的一般轴对称应力状态。圆周速度消失。屈服准则的叠加限制是应力方程组是双曲线的。这项研究的主要目的是选择最佳坐标和未知数，以最方便的形式导出可积分微分关系，以进行数值处理。结果表明，主线坐标系的比例因子之间存在简单的关系（该坐标系的坐标曲线与主应力的轨迹重合）。比例因子和主应力之间存在另一个简单关系。主线和圆柱坐标之间的映射由双曲型微分方程组确定。